diff --git a/include/bee2/core/util.h b/include/bee2/core/util.h index 5697304a..f5eecc46 100644 --- a/include/bee2/core/util.h +++ b/include/bee2/core/util.h @@ -62,8 +62,8 @@ extern "C" { #ifdef NDEBUG #define ASSERT(e) ((void)0) #else - extern void utilAssert(int e, const char* file, int line); - #define ASSERT(e) utilAssert(!!(e), __FILE__, __LINE__) + extern void utilAssert(int e, const char* file, int line, char const *msg); +#define ASSERT(e) utilAssert(!!(e), __FILE__, __LINE__, #e) #endif /*! \brief Проверяется выполнение условия diff --git a/include/bee2/crypto/bign.h b/include/bee2/crypto/bign.h index 4183e024..48eabe8a 100644 --- a/include/bee2/crypto/bign.h +++ b/include/bee2/crypto/bign.h @@ -62,6 +62,13 @@ extern "C" { ******************************************************************************* */ +/*! \brief Предвычисления bign */ +typedef struct +{ + size_t w; /*!< размер окна w */ + octet const *Gs; /*!< малые нечетные кратные {(1-2^w)G, ..., -3G, -1G, 1G, 3G, .., (2^w-1)G, 2G} базовой точки G в аффинных координатах */ +} bign_precomp; + /*! \brief Долговременные параметры bign */ typedef struct { @@ -71,7 +78,8 @@ typedef struct octet b[64]; /*!< коэффициент b */ octet q[64]; /*!< порядок q */ octet yG[64]; /*!< y-координата точки G */ - octet seed[8]; /*!< параметр seed */ + octet seed[8]; /*!< параметр seed */ + bign_precomp precomp; /*!< предвычисления опционально */ } bign_params; /*! \brief Загрузка стандартных долговременных параметров diff --git a/include/bee2/math/ec.h b/include/bee2/math/ec.h index 5aa6d433..4d1db8eb 100644 --- a/include/bee2/math/ec.h +++ b/include/bee2/math/ec.h @@ -6,7 +6,7 @@ \author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}] \created 2012.04.19 \version 2019.06.13 -\license This program is released under the GNU General Public License +\license This program is released under the GNU General Public License version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ @@ -32,114 +32,114 @@ extern "C" { ******************************************************************************* \file ec.h -Определяются вычисления на эллиптических кривых над конечными полями. -Поле представляется как кольцо вычетов с помощью структуры -типа qr_o (см. заголовочный файл qr.h). Описание кривой соответствует +Определяются вычисления на эллиптических кривых над конечными полями. +Поле представляется как кольцо вычетов с помощью структуры +типа qr_o (см. заголовочный файл qr.h). Описание кривой соответствует соглашениям ANSI X 9.62 (ECDSA) и последующих стандартов. Эллиптическая кривая описывается структурой типа ec_o. Пусть ec -- указатель на такую структуру. Тогда ec->f указывает на описание базового поля, -ec->A и ec->B --- коэффициенты из базового поля, которые определяют +ec->A и ec->B --- коэффициенты из базового поля, которые определяют уравнение эллиптической кривой. В описание ec->f базового поля включается функции арифметики в этом поле. -Описание должно быть настроено вызывающей программой -(см. описание qrCreate() в qr.h). +Описание должно быть настроено вызывающей программой +(см. описание qrCreate() в qr.h). Используется внутреннее (для ec->f) представление элементов базового поля. -Импорт элементов базового поля из строк октетов выполняется +Импорт элементов базового поля из строк октетов выполняется с помощью функции ec->f->from(), экспорт -- с помощью функции ec->f->to(). Можно также использовать макросы qrFrom, qrTo (см. заголовочный файл qr.h). -Точка эллиптической кривой задается ec->d координатами из базового поля. -Каждая координата представляется ec->f->n машинными словами. Координаты -записываются друг за другом и в целом образуют массив pt из ec->d * ec->f->n -машинных слов. Первые три координаты именованные: X, Y, Z. Макросы +Точка эллиптической кривой задается ec->d координатами из базового поля. +Каждая координата представляется ec->f->n машинными словами. Координаты +записываются друг за другом и в целом образуют массив pt из ec->d * ec->f->n +машинных слов. Первые три координаты именованные: X, Y, Z. Макросы ecX, ecY, ecZ поддерживают извлечение именованных координат из буфера pt. -Точки с двумя координатами называются аффинными, а точки +Точки с двумя координатами называются аффинными, а точки pt = (X : Y : Z :...) с тремя и более координатами -- проективными. Бесконечно удаленную точку O нельзя представить аффинной, но можно проективной: точке O соответствует точка pt, у которой Z == 0. Макросы ecSetO, ecIsO выполняют присваивание pt = O и проверку pt == O. -Для организации вычислений требуется, чтобы среди точек эллиптической -кривой имелась бесконечно удаленная. Поэтому должны обязательно использоваться +Для организации вычислений требуется, чтобы среди точек эллиптической +кривой имелась бесконечно удаленная. Поэтому должны обязательно использоваться проективные координаты (проективные точки). Размерность ec->d >= 3. -Проективную точку можно построить по аффинной точке (x, y) с помощью функции +Проективную точку можно построить по аффинной точке (x, y) с помощью функции интерфейса ec_froma_i. Как правило, построение состоит в присваиваниях \code - X <- x, Y <- y, Z <- ec->f->unity,.... -\endcode -Обратно, проективную точку можно преобразовать в аффинную с помощью -функции интерфейса ec_toa_i (при преобразовании бесконечно удаленной точки + X <- x, Y <- y, Z <- ec->f->unity,.... +\endcode +Обратно, проективную точку можно преобразовать в аффинную с помощью +функции интерфейса ec_toa_i (при преобразовании бесконечно удаленной точки функция возвращает соответствующий признак). -Описание ec может быть использовано для организации вычислений в аффинных +Описание ec может быть использовано для организации вычислений в аффинных координатах, несмотря на заданные этим описанием проективные. -\remark Если используется ec->d == 3, то Z-координата точки pt всегда -равняется единице для pt != O и нулю для pt == O, то вычисления на кривой +\remark Если используется ec->d == 3, то Z-координата точки pt всегда +равняется единице для pt != O и нулю для pt == O, то вычисления на кривой фактически ведутся в аффинных координатах. -В структуре типа ec_o предусмотрены поля для описания циклической группы -точек эллиптической кривой. Эта группа задается образующим ec->base. -Образующий представляется аффинной точкой, т.е. задается -2 * ec->f->n машинными словами. Порядок циклической группы -ec->order задается 2 * ec->f->n + 1 машинным словом. Кофактор -- +В структуре типа ec_o предусмотрены поля для описания циклической группы +точек эллиптической кривой. Эта группа задается образующим ec->base. +Образующий представляется аффинной точкой, т.е. задается +2 * ec->f->n машинными словами. Порядок циклической группы +ec->order задается 2 * ec->f->n + 1 машинным словом. Кофактор -- отношение числа всех ec->f-рациональных точек к ec->order -- задается одним машинным словом ec->cofactor. -Если работа с группой точек не предусматривается, то поля base, order +Если работа с группой точек не предусматривается, то поля base, order и cofactor могут не задаваться. -По адресу ec->params могут размещаться дополнительные данные, например, -определенные кратные базовой точки, с помощью которых можно ускорить -криптографические вычисления на эллиптической кривой. +По адресу ec->params могут размещаться дополнительные данные, например, +определенные кратные базовой точки, с помощью которых можно ускорить +криптографические вычисления на эллиптической кривой. -Описание ec эллиптической кривой включает указатели на функции арифметики +Описание ec эллиптической кривой включает указатели на функции арифметики в группе точек этой кривой. Функцию интерфейса ec_tpl_i -можно не поддерживать. Указатель на неподдерживаемую функцию +можно не поддерживать. Указатель на неподдерживаемую функцию должен быть нулевым. -Описание кольца организовано как объект, и можно применять функции, +Описание кольца организовано как объект, и можно применять функции, описанные в заголовочном файле obj.h. -Эллиптическая кривая должна создаваться специальной функцией ecCreate(), -которая является аналогом конструктора. В эту функцию должен передаваться -указатель ec на структуру типа ec_o. По этому указателю будет размещаться -описание (состояние) кривой. По адресу ec может быть зарезервировано больше -памяти, чем sizeof(ec_o). Дело в том, что коэффициенты A, B, порядок order, -базовая точка base могут размещаться в поле descr открытого размера. -Функция ecCreate() должна сопровождаться функцией ecCreate_keep(), +Эллиптическая кривая должна создаваться специальной функцией ecCreate(), +которая является аналогом конструктора. В эту функцию должен передаваться +указатель ec на структуру типа ec_o. По этому указателю будет размещаться +описание (состояние) кривой. По адресу ec может быть зарезервировано больше +памяти, чем sizeof(ec_o). Дело в том, что коэффициенты A, B, порядок order, +базовая точка base могут размещаться в поле descr открытого размера. +Функция ecCreate() должна сопровождаться функцией ecCreate_keep(), которая поддерживает расчет длины состояния (в октетах). -Функция ecCreate_keep() должна оценивать длину состояния сверху. -Оценка может быть неточной. Точная длина состояния фиксируется при +Функция ecCreate_keep() должна оценивать длину состояния сверху. +Оценка может быть неточной. Точная длина состояния фиксируется при непосредственном выполнении ecCreate() и сохраняется в поле keep описания кривой. -В функцию ecCreate() должен передаваться указатель на память для стека. -Функция ecCreate() должна сопровождаться функцией ecCreate_deep(), которая -выполняет расчет глубины стека. При расчете глубины следует предполагать, -что в ecCreate() явно или неявно вызываются все функции интерфейсов кривой. -Получив результат работы ecCreate_deep(), внешние программы могут определить, -сколько вспомогательной памяти потребуется при всевозможных способах +В функцию ecCreate() должен передаваться указатель на память для стека. +Функция ecCreate() должна сопровождаться функцией ecCreate_deep(), которая +выполняет расчет глубины стека. При расчете глубины следует предполагать, +что в ecCreate() явно или неявно вызываются все функции интерфейсов кривой. +Получив результат работы ecCreate_deep(), внешние программы могут определить, +сколько вспомогательной памяти потребуется при всевозможных способах работы с функциями арифметики на кривой. -Оценка глубины стека, определяемая функцией ecCreate_deep(), может быть +Оценка глубины стека, определяемая функцией ecCreate_deep(), может быть неточной. Точная глубина фиксируется при непосредственном выполнении ecCreate() и сохраняется в поле deep описания кривой. -В функцию ecCreate() могут не передаваться параметры base, order и cofactor, -определяющие строение группы точек, хотя буферы для base и order могут -подготавливаться в ecCreate(). Параметры могут устанавливаться позднее -с помощью функции ecCreateGroup(). +В функцию ecCreate() могут не передаваться параметры base, order и cofactor, +определяющие строение группы точек, хотя буферы для base и order могут +подготавливаться в ecCreate(). Параметры могут устанавливаться позднее +с помощью функции ecCreateGroup(). -\pre Все указатели действительны. +\pre Все указатели действительны. -\pre Буферы точек кривой не пересекаются с буферами, поддерживающими описание +\pre Буферы точек кривой не пересекаются с буферами, поддерживающими описание эллиптической кривой. ******************************************************************************* */ @@ -148,14 +148,14 @@ struct ec_o; /*! \brief Импорт из аффинной точки - По аффинной точке [2 * ec->f->n]a эллиптической кривой ec строится + По аффинной точке [2 * ec->f->n]a эллиптической кривой ec строится точка [ec->d * ec->f->n]b. \pre Описание ec работоспособно. \pre Буферы a и b либо не пересекаются, либо указатели a и b совпадают. \pre Координаты a лежат в базовом поле. \expect Описание ec корректно. \expect Точка a лежит на кривой. - \return TRUE, если преобразование успешно выполнено, и FALSE в противном + \return TRUE, если преобразование успешно выполнено, и FALSE в противном случае. */ typedef bool_t (*ec_froma_i)( @@ -167,14 +167,14 @@ typedef bool_t (*ec_froma_i)( /*! \brief Экспорт в аффинную точку - По точке [ec->d * ec->f->n]a эллиптической кривой ec строится + По точке [ec->d * ec->f->n]a эллиптической кривой ec строится аффинная точка [2 * ec->f->n]b. \pre Описание ec работоспособно. \pre Буферы a и b либо не пересекаются, либо указатели a и b совпадают. \pre Координаты a лежат в базовом поле. \expect Описание ec корректно. \expect Точка a лежит на кривой. - \return TRUE, если аффинная точка построена, и FALSE, если точке a + \return TRUE, если аффинная точка построена, и FALSE, если точке a соответствует бесконечно удаленная точка. */ typedef bool_t (*ec_toa_i)( @@ -204,15 +204,34 @@ typedef void (*ec_neg_i)( void* stack /*!< [in] вспомогательная память */ ); +/*! \brief Обратная аффинная точка + + На эллиптической кривой ec определяется точка [2 * ec->f->n]b, + обратная к точке [2 * ec->f->n]a: + \code + b <- -a. + \endcode + \pre Описание ec работоспособно. + \pre Буфер b либо не пересекается, либо совпадает с буфером a. + \pre Координаты a лежат в базовом поле. + \expect Описание ec корректно. + \expect Точка a лежит на кривой. +*/ +typedef void (*ec_nega_i)( + word b[], /*!< [out] обратная аффинная точка */ + const word a[], /*!< [in] обращаемая аффинная точка */ + const struct ec_o* ec /*!< [in] описание эллиптической кривой */ +); + /*! \brief Сложение точек - На эллиптической кривой ec определяется сумма [ec->d * ec->f->n]c точек + На эллиптической кривой ec определяется сумма [ec->d * ec->f->n]c точек [ec->d * ec->f->n]a и [ec->d * ec->f->n]b: \code c <- a + b. \endcode \pre Описание ec работоспособно. - \pre Буфер с либо не пересекается с каждым из буферов a и b, либо + \pre Буфер с либо не пересекается с каждым из буферов a и b, либо совпадает с некоторым из них. \pre Координаты a и b лежат в базовом поле. \expect Описание ec корректно. @@ -228,13 +247,13 @@ typedef void (*ec_add_i)( /*! \brief Сложение с аффинной точкой - На эллиптической кривой ec определяется сумма [ec->d * ec->f->n]c + На эллиптической кривой ec определяется сумма [ec->d * ec->f->n]c проективной точки [ec->d * ec->f->n]a и аффинной точки [2 * ec->f->n]b: \code c <- a + b. \endcode \pre Описание ec работоспособно. - \pre Буфер с либо не пересекается с каждым из буферов a и b, либо + \pre Буфер с либо не пересекается с каждым из буферов a и b, либо указатель c совпадает с некоторым из указателей a или b. \pre Координаты a и b лежат в базовом поле. \expect Описание ec корректно. @@ -250,13 +269,13 @@ typedef void (*ec_adda_i)( /*! \brief Вычитание точек - На эллиптической кривой ec определяется разность [ec->d * ec->f->n]c точек + На эллиптической кривой ec определяется разность [ec->d * ec->f->n]c точек [ec->d * ec->f->n]a и [ec->d * ec->f->n]b: \code c <- a - b. \endcode \pre Описание ec работоспособно. - \pre Буфер с либо не пересекается с каждым из буферов a и b, либо + \pre Буфер с либо не пересекается с каждым из буферов a и b, либо совпадает с некоторым из них. \pre Координаты a и b лежат в базовом поле. \expect Описание ec корректно. @@ -270,15 +289,15 @@ typedef void (*ec_sub_i)( void* stack /*!< [in] вспомогательная память */ ); -/*! \brief Вычитание аффинной точки точек +/*! \brief Вычитание аффинной точки из проективной точки - На эллиптической кривой ec определяется разность [ec->d * ec->f->n]c + На эллиптической кривой ec определяется разность [ec->d * ec->f->n]c проективной точки [ec->d * ec->f->n]a и аффинной точки [2 * ec->f->n]b: \code c <- a - b. \endcode \pre Описание ec работоспособно. - \pre Буфер с либо не пересекается с каждым из буферов a и b, либо + \pre Буфер с либо не пересекается с каждым из буферов a и b, либо указатель c совпадает с некоторым из указателей a или b. \pre Координаты a и b лежат в базовом поле. \expect Описание ec корректно. @@ -294,7 +313,7 @@ typedef void (*ec_suba_i)( /*! \brief Удвоение точки - На эллиптической кривой ec определяется точка [ec->d * ec->f->n]b, + На эллиптической кривой ec определяется точка [ec->d * ec->f->n]b, полученная удвоением точки [ec->d * ec->f->n]a: \code b <- 2 a. @@ -314,8 +333,8 @@ typedef void (*ec_dbl_i)( /*! \brief Удвоение аффинной точки - На эллиптической кривой ec определяется проективная - точка [ec->d * ec->f->n]b, полученная удвоением аффинной + На эллиптической кривой ec определяется проективная + точка [ec->d * ec->f->n]b, полученная удвоением аффинной точки [2 * ec->f->n]a: \code b <- 2 a. @@ -335,7 +354,7 @@ typedef void (*ec_dbla_i)( /*! \brief Утроение точки - На эллиптической кривой ec определяется точка [ec->d * ec->f->n]b, + На эллиптической кривой ec определяется точка [ec->d * ec->f->n]b, полученная утроением точки [ec->d * ec->f->n]a: \code b <- 3 a. @@ -353,38 +372,108 @@ typedef void (*ec_tpl_i)( void* stack /*!< [in] вспомогательная память */ ); +/*! \brief Удвоение проективной и вычитание/сложение с аффинной точкой + + На эллиптической кривой ec определяется точка [ec->d * ec->f->n]с, + полученная удвоением точки [3 * ec->f->n]a и сложением с точкой ((-1) ^ (1 + neg_b)) * [2 * ec->f->n]b: + \code + c <- 2 a + ((-1) ^ (1 + neg_b)) b. + \endcode + \pre Описание ec работоспособно. + \pre Буфер c либо не пересекается, либо совпадает с буфером a. + \pre Буферы a и b не пересекается. + \pre Буферы b и c не пересекается. + \pre Координаты a и b лежат в базовом поле. + \expect Описание ec корректно. + \expect Точки a и b лежат на кривой. + \expect Точки a и b не равны. +*/ +typedef void (*ec_dbl_adda_i)( + word с[], /*!< [out] результат удвоения и сложения */ + const word a[], /*!< [in] первоначальная точка 1 */ + const word b[], /*!< [in] первоначальная точка 2 */ + bool_t neg_b, /*!< [in] флаг вычитания/сложения с точкой b */ + const struct ec_o* ec, /*!< [in] описание эллиптической кривой */ + void* stack /*!< [in] вспомогательная память */ +); + + +/*! \brief Условное аддитивное обращение аффинной точки + + На эллиптической кривой ec определяется точка [2 * ec->f->n]b, + полученная умножением точки [2 * ec->f->n]a на выражение ((-1) ^ (1 + neg)) + \code + b <- ((-1) ^ (1 + neg_b)) a. + \endcode + \pre Описание ec работоспособно. + \pre Буфер b либо не пересекается, либо совпадает с буфером a. + \pre Координаты a и b лежат в базовом поле. + \expect Описание ec корректно. + \expect Точка a лежит на кривой. +*/ +typedef void (*ec_set_signa_i)( + word b[], /*!< [out] результат условного аддитивного обращения */ + const word a[], /*!< [in] первоначальная точка */ + bool_t neg, /*!< [in] флаг отрицательности */ + const struct ec_o* ec /*!< [in] описание эллиптической кривой */ +); + +typedef void (*ec_smulsa_i)( + word* c, /*!< [out] линейный массив нечетных малых кратных (2i-1)[2n]a для i=1,2^{w-1} в аффинных координатах */ + word d[], /*!< [out] опционально (если d != NULL) удвоенная точка (2)[2n]a в аффинных координатах */ + const word a[], /*!< [in] базовая точка в аффинных координатах */ + const size_t w, /*!< [in] размер окна, число точек в массиве есть 2^{w-1} */ + const struct ec_o* ec, /*!< [in] описание эллиптической кривой */ + void* stack /*!< [in] вспомогательная память */ +); + +typedef void (*ec_smulsj_i)( + word* c, /*!< [out] линейный массив нечетных малых кратных (2i-1)[2n]a для i=1,2^{w-1} в якобиевых координатах */ + word d[], /*!< [out] опционально (если d != NULL) удвоенная точка (2)[2n]a в якобиевых координатах */ + const word a[], /*!< [in] базовая точка в аффинных координатах */ + const size_t w, /*!< [in] размер окна, число точек в массиве есть 2^{w-1} */ + const struct ec_o* ec, /*!< [in] описание эллиптической кривой */ + void* stack /*!< [in] вспомогательная память */ +); /*! \brief Описание эллиптической кривой - Описывается эллиптическая кривая, правила представления ее элементов, + Описывается эллиптическая кривая, правила представления ее элементов, группа точек и функции, реализующие операции в группе. - \remark В таблицу указателей описания кривой как объекта входят поля + \remark В таблицу указателей описания кривой как объекта входят поля f, A, B, base, order, params. Поле f является указателем на объект. */ typedef struct ec_o { - obj_hdr_t hdr; /*!< заголовок */ + obj_hdr_t hdr; /*!< заголовок */ // ptr_table { - const qr_o* f; /*!< базовое поле */ - word* A; /*!< коэффициент A */ - word* B; /*!< коэффициент B */ - word* base; /*!< базовая точка */ - word* order; /*!< порядок группы точек */ - void* params; /*!< дополнительные параметры */ + const qr_o* f; /*!< базовое поле */ + word* A; /*!< коэффициент A */ + word* B; /*!< коэффициент B */ + word* base; /*!< базовая точка */ + word* order; /*!< порядок группы точек */ + void* params; /*!< дополнительные параметры */ // } - size_t d; /*!< размерность */ - word cofactor; /*!< кофактор группы точек */ - ec_froma_i froma; /*!< функция импорта из аффинной точки */ - ec_toa_i toa; /*!< функция экспорта в аффинную точку */ - ec_neg_i neg; /*!< функция обращения */ - ec_add_i add; /*!< функция сложения */ - ec_adda_i adda; /*!< функция сложения с аффинной точкой */ - ec_sub_i sub; /*!< функция вычитания */ - ec_suba_i suba; /*!< функция вычитания аффинной точки */ - ec_dbl_i dbl; /*!< функция удвоения */ - ec_dbla_i dbla; /*!< функция удвоения аффинной точки */ - ec_tpl_i tpl; /*!< функция утроения */ - size_t deep; /*!< максимальная глубина стека функций */ - octet descr[]; /*!< память для размещения данных */ + size_t d; /*!< размерность */ + word cofactor; /*!< кофактор группы точек */ + ec_froma_i froma; /*!< функция импорта из аффинной точки */ + ec_toa_i toa; /*!< функция экспорта в аффинную точку */ + ec_neg_i neg; /*!< функция обращения */ + ec_nega_i nega; /*!< функция обращения аффинной точки */ + ec_add_i add; /*!< функция сложения */ + ec_adda_i adda; /*!< функция сложения с аффинной точкой */ + ec_sub_i sub; /*!< функция вычитания */ + ec_suba_i suba; /*!< функция вычитания аффинной точки */ + ec_dbl_i dbl; /*!< функция удвоения */ + ec_dbla_i dbla; /*!< функция удвоения аффинной точки */ + ec_tpl_i tpl; /*!< функция утроения */ + ec_dbl_adda_i dbl_adda; /*!< функция удвоения якобиевой точки и вычитания/сложения с аффинной точкой */ + ec_set_signa_i set_signa; /*!< функция условного аддитивного обращения афинной точки */ + ec_smulsa_i smulsa; /*!< расчет малых кратных в аффинных координатах */ + ec_smulsj_i smulsj; /*!< расчет малых кратных в якобиевых координатах */ + size_t precomp_w; /*!< размер окна w */ + word const *precomp_Gs; /*!< малые нечетные кратные {(1-2^w)G, ..., -3G, -1G, 1G, 3G, .., (2^w-1)G, 2G} базовой точки G в аффинных координатах */ + size_t deep; /*!< максимальная глубина стека функций */ + octet descr[]; /*!< память для размещения данных */ } ec_o; /* @@ -422,6 +511,9 @@ typedef struct ec_o #define ecNeg(b, a, ec, stack)\ (ec)->neg(b, a, ec, stack) +#define ecNegA(b, a, ec)\ + (ec)->nega(b, a, ec) + #define ecAdd(c, a, b, ec, stack)\ (ec)->add(c, a, b, ec, stack) @@ -440,6 +532,7 @@ typedef struct ec_o #define ecDblA(b, a, ec, stack)\ (ec)->dbla(b, a, ec, stack) +//todo - also set some value to ecX and ecY because stack used for 'a' may contain values which will break ecpSeemsOnA? #define ecSetO(a, ec)\ wwSetZero(ecZ(a, (ec)->f->n), (ec)->f->n) @@ -454,7 +547,7 @@ typedef struct ec_o /*! \brief Описание эллиптической кривой работоспособно? - Проверяется работоспособность описания ec эллиптической кривой. + Проверяется работоспособность описания ec эллиптической кривой. Проверяются следующие условия: - объект ec работоспособен; - objKeep(ec) >= sizeof(ec_o); @@ -494,7 +587,7 @@ bool_t ecIsOperable2( /*! \brief Создание группы точек эллиптической кривой - В описание ec эллиптической кривой добавляется описание группы, + В описание ec эллиптической кривой добавляется описание группы, порожденной точкой ([ec->f->no]xbase, [ec->f->no]ybase). Группа имеет порядок [order_len]order и ее кофактор равняется cofactor. \pre Описание ec работоспособно. @@ -503,10 +596,10 @@ bool_t ecIsOperable2( машинных слов. \expect{FALSE} cofactor != 0 && cofactor укладывается в машинное слово. \expect Описание ec корректно. - \return TRUE, если описание группы успешно задано, и FALSE в + \return TRUE, если описание группы успешно задано, и FALSE в противном случае. - \remark Любой из указателей xbase, ybase может быть нулевым. При нулевом - указателе соответствующая координата базовой точки устанавливается равной + \remark Любой из указателей xbase, ybase может быть нулевым. При нулевом + указателе соответствующая координата базовой точки устанавливается равной нулю. \deep{stack} ecCreateGroup_deep(f_deep). */ @@ -517,6 +610,8 @@ bool_t ecCreateGroup( const octet order[], /*!< [in] порядок группы точек */ size_t order_len, /*!< [in] длина order */ u32 cofactor, /*!< [in] кофактор группы точек */ + size_t w, /*!< [in] размер окна */ + const octet Gs[], /*!< [in] малые нечетные кратные в аффинных координатах */ void* stack /*!< [in] вспомогательная память */ ); @@ -524,7 +619,7 @@ size_t ecCreateGroup_deep(size_t f_deep); /*! \brief Группа точек эллиптической кривой работоспособна? - Проверяется работоспособность описания группы точек эллиптической + Проверяется работоспособность описания группы точек эллиптической кривой ec. Проверяются следующие условия: - буферы [ec->n + 1]ec->order, [2 * ec->n]ec->base корректны; - ec->order != 0; @@ -545,7 +640,7 @@ bool_t ecIsOperableGroup( /*! \brief Кратная точка - Определяется аффинная точка [2 * ec->f->n]b эллиптической кривой ec, + Определяется аффинная точка [2 * ec->f->n]b эллиптической кривой ec, которая является [m]d-кратной аффинной точки [2 * ec->f->n]a: \code b <- d a. @@ -556,22 +651,61 @@ bool_t ecIsOperableGroup( \expect Точка a лежит на ec. \return TRUE, если кратная точка является аффинной, и FALSE в противном случае (b == O). + \safe Имеется ускоренная нерегулярная редакция. \deep{stack} ecpMulA_deep(ec->f->n, ec->d, ec->f->deep, m). */ -bool_t ecMulA( +bool_t SAFE(ecMulAOrig)( word b[], /*!< [out] кратная точка */ - const word a[], /*!<[in] базовая точка */ + const word a[], /*!< [in] базовая точка */ const ec_o* ec, /*!< [in] описание кривой */ const word d[], /*!< [in] кратность */ size_t m, /*!< [in] длина d в машинных словах */ void* stack /*!< [in] вспомогательная память */ ); -size_t ecMulA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t m); +size_t SAFE(ecMulAOrig_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t m); + +bool_t FAST(ecMulAOrig)(word b[], const word a[], const ec_o* ec, const word d[],size_t m, void* stack); + +size_t FAST(ecMulAOrig_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t m); + + +bool_t FAST(ecMulA)( + word b[], /*!< [out] кратная точка */ + const word a[], /*!< [in] базовая точка */ + const ec_o* ec, /*!< [in] описание кривой */ + const word d[], /*!< [in] кратность */ + size_t m, /*!< [in] длина d в машинных словах */ + void* stack /*!< [in] вспомогательная память */ +); + +size_t FAST(ecMulA_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t m); + +bool_t SAFE(ecMulA)( + word b[], /*!< [out] кратная точка */ + const word a[], /*!< [in] базовая точка */ + const ec_o* ec, /*!< [in] описание кривой */ + const word d[], /*!< [in] кратность */ + size_t m, /*!< [in] длина d в машинных словах */ + void* stack /*!< [in] вспомогательная память */ +); + +size_t SAFE(ecMulA_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t order_bit_len); + + +bool_t ecMulDivpJ(word b[], const word a[], const size_t w, const ec_o* ec, const word d[], + size_t m, void* stack); + +size_t ecMulDivpJ_deep(size_t n, size_t w, size_t ec_d, size_t ec_deep); + +bool_t ecMulDivpA(word b[], const word a[], const size_t w, const ec_o* ec, const word d[], + size_t m, void* stack); + +size_t ecMulDivpA_deep(size_t n, size_t w, size_t ec_d, size_t ec_deep); /*! \brief Имеет порядок? - Проверяется, что аффинная точка [2 * ec->f->n]a имеет порядок [m]q + Проверяется, что аффинная точка [2 * ec->f->n]a имеет порядок [m]q в группе точек кривой ec. \pre Описание ec работоспособно. \pre Координаты a лежат в базовом поле. @@ -611,7 +745,7 @@ size_t ecHasOrderA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t m); в противном случае (b == O). \deep{stack} ecAddMulA_deep(ec->f->n, ec->d, ec->deep, m[1], ..., m[k]). */ -bool_t ecAddMulA( +bool_t FAST(ecAddMulA)( word b[], /*!< [out] кратная точка */ const ec_o* ec, /*!< [in] описание кривой */ void* stack, /*!< [in] вспомогательная память */ @@ -619,7 +753,65 @@ bool_t ecAddMulA( ... /*!< [in] тройки (a[i], d[i], m[i]) */ ); -size_t ecAddMulA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t k,...); +size_t FAST(ecAddMulA_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t k,...); + +bool_t SAFE(ecAddMulA)( + word b[], /*!< [out] кратная точка */ + const ec_o* ec, /*!< [in] описание кривой */ + void* stack, /*!< [in] вспомогательная память */ + size_t k, /*!< [in] число троек (a[i], d[i], m[i]) */ + ... /*!< [in] тройки (a[i], d[i], m[i]) */ +); + +size_t SAFE(ecAddMulA_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t k,...); + +/*! \brief Удвоение якобиевой и вычитание/сложение с аффинной точкой + + На эллиптической кривой ec определяется точка [3 * ec->f->n]с, + полученная удвоением точки [3 * ec->f->n]a и сложением с точкой ((-1) ^ (1 + neg_b)) * [2 * ec->f->n]b: + \code + c <- 2 a + ((-1) ^ (1 + neg_b)) b. + \endcode + \pre Описание ec работоспособно. + \pre Буфер c либо не пересекается, либо совпадает с буфером a. + \pre Буферы a и b не пересекается. + \pre Буферы b и c не пересекается. + \pre Координаты a и b лежат в базовом поле. + \expect Описание ec корректно. + \expect Точки a и b лежат на кривой. +*/ +void ecDblAddA( + word с[], /*!< [out] результат удвоения и сложения*/ + const word a[], /*!< [in] первоначальная точка */ + const word b[], /*!< [in] первоначальная точка */ + bool_t neg_b, /*!< [in] флаг вычитания/сложения с точкой b*/ + const struct ec_o* ec, /*!< [in] описание эллиптической кривой */ + void* stack /*!< [in] вспомогательная память */ +); + +//size_t ecDblAddA_deep(); = max(ec->dbl_deep, ec->suba_deep, ec->adda_deep) - уже учитываются в функциях ecCreate + +void ecSmallMultAdd2J( + word c[], /*!< [out] кратные якобиевы точки */ + word d[], /*!< [out] удвоенная якобиева точка */ + const word a[], /*!< [in] аффинная точка */ + const size_t w, /*!< [in] ширина окна */ + const ec_o* ec, /*!< [in] описание кривой */ + void* stack /*!< [in] вспомогательная память */ +); + +size_t ecSmallMultAdd2J_deep(); + +void ecSmallMultAdd2A( + word c[], /*!< [out] кратные аффинные точки */ + word d[], /*!< [out] удвоенная аффинная точка */ + const word a[], /*!< [in] аффинная точка */ + const size_t w, /*!< [in] ширина окна */ + const ec_o* ec, /*!< [in] описание кривой */ + void* stack /*!< [in] вспомогательная память */ +); + +size_t ecSmallMultAdd2A_deep(size_t n, size_t ec_d); #ifdef __cplusplus } /* extern "C" */ diff --git a/include/bee2/math/ecp.h b/include/bee2/math/ecp.h index 316ad174..0ce494de 100644 --- a/include/bee2/math/ecp.h +++ b/include/bee2/math/ecp.h @@ -249,6 +249,60 @@ void ecpSWU( size_t ecpSWU_deep(size_t n, size_t f_deep); +/*! \brief Расчет малых нечетных кратных в якобиевых координатах + + Для i \in \{1,2,\ldots,2^{w-1}-1\} определяются кратности (2i+1) a + аффинной точки [2 * ec->f->n]a кривой ec: + \code + da <- 2 a + c[i] <- (2i+1) a. + \endcode + Кратности помещаются в буфер [(2^{w-1}-1) * 3 * ec->f->n]c. + \pre Описание ec работоспособно. + \pre Координата a лежит в базовом поле. + \expect Описание ec корректно. + \expect Точка a лежит на ec. + \deep{stack} ecpOddSmall_deep(w, ec->f->n, ec->f->deep). + \safe Алгоритм регулрен. +*/ +void ecpSmallMultDivpJ( + word c[], /*!< [out] кратные якобиевы точки */ + word da[], /*!< [out] удвоенная якобиева точка */ + const word a[], /*!< [in] аффинная точка */ + const size_t w, /*!< [in] ширина окна */ + const ec_o* ec, /*!< [in] описание кривой */ + void* stack /*!< [in] вспомогательная память */ +); + +size_t ecpSmallMultDivpJ_deep(bool_t da, const size_t w, size_t n, size_t f_deep); + +/*! \brief Расчет малых нечетных кратных в аффинных координатах + + Для i \in \{1,2,\ldots,2^{w-1}-1\} определяются кратности (2i+1) a + аффинной точки [2 * ec->f->n]a кривой ec: + \code + da <- 2 a + c[i] <- (2i+1) a. + \endcode + Кратности помещаются в буфер [(2^{w-1}-1) * 2 * ec->f->n]c. + \pre Описание ec работоспособно. + \pre Координата a лежит в базовом поле. + \expect Описание ec корректно. + \expect Точка a лежит на ec. + \deep{stack} ecpOddSmall_deep(w, ec->f->n, ec->f->deep). + \safe Алгоритм регулрен. +*/ +void ecpSmallMultDivpA( + word c[], /*!< [out] кратные аффинные точки */ + word da[], /*!< [out] удвоенная аффинная точка */ + const word a[], /*!< [in] аффинная точка */ + const size_t w, /*!< [in] ширина окна */ + const ec_o* ec, /*!< [in] описание кривой */ + void* stack /*!< [in] вспомогательная память */ +); + +size_t ecpSmallMultDivpA_deep(bool_t da, const size_t w, size_t n, size_t f_deep); + #ifdef __cplusplus } /* extern "C" */ #endif diff --git a/include/bee2/math/gfp.h b/include/bee2/math/gfp.h index c3d1665d..9577fe3c 100644 --- a/include/bee2/math/gfp.h +++ b/include/bee2/math/gfp.h @@ -112,6 +112,15 @@ size_t gfpIsValid_deep(size_t n); #define gfpHalf(b, a, f)\ zzHalfMod(b, a, (f)->mod, (f)->n) +#define gfpMul2(c, a, b, a2, b2, f, stack)\ + do {\ + qrAdd(c, a, b, f);\ + qrSqr(c, c, f, stack);\ + qrSub(c, c, a2, f);\ + qrSub(c, c, b2, f);\ + gfpHalf(c, c, f);\ + } while(0) + #ifdef __cplusplus } /* extern "C" */ #endif diff --git a/include/bee2/math/qr.h b/include/bee2/math/qr.h index 5822952b..0849b3d8 100644 --- a/include/bee2/math/qr.h +++ b/include/bee2/math/qr.h @@ -446,6 +446,29 @@ void qrPower( size_t qrPower_deep(size_t n, size_t m, size_t r_deep); +/*! \brief Вычисление обратных элеметнов в кольце вычетов для нескольких элементов сразу + + +//todo описаниие (ссылка на статью, больше деталей) + В кольце вычетов r вычисляются обратные елементы c помощью алгоритма Монтгомери + + \pre Описание кольца r работоспособно. + \pre буфферы c и u совпадают или не пересекаются + \expect Описание кольца r корректно. + \deep{stack} qrMontInv_deep(r->n, m, r->deep). + \safe алгоритм регулярен +*/ +void qrMontInv( + word c[], /*!< [out] обратные элементы */ + const word u[], /*!< [in] входные элементы */ + size_t m, /*!< [in] количиство входных элементов */ + const qr_o* r, /*!< [in] описание кольца */ + void* stack /*!< [in] вспомогательная память */ +); + +size_t qrMontInv_deep(size_t n, size_t m, size_t r_deep); + + #ifdef __cplusplus } /* extern "C" */ #endif diff --git a/include/bee2/math/ww.h b/include/bee2/math/ww.h index 41fd7dab..f582a8d6 100644 --- a/include/bee2/math/ww.h +++ b/include/bee2/math/ww.h @@ -6,7 +6,7 @@ \author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}] \created 2012.04.18 \version 2019.06.27 -\license This program is released under the GNU General Public License +\license This program is released under the GNU General Public License version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ @@ -275,7 +275,7 @@ bool_t FAST(wwIsZero)(const word a[], size_t n); /*! \brief Принимает значение -- машинное слово? - Проверяется, что слово [n]a принимает значение w, которое + Проверяется, что слово [n]a принимает значение w, которое является машинным словом: \code a[0] == w && a[1] == ... == a[n - 1] == 0? @@ -484,6 +484,97 @@ size_t wwNAF( size_t w /*!< [in] длина окна */ ); +/*! \brief Расчет OddRecording + + В [m]oddRecording помещается кодированное представление нечетного слова + [n]a (a_0, a_1,..., a_{k-1}) такое, что + - a_i \in {\pm 1, \pm 3, ..., \pm 2^w - 1}; + - a как число равняется \sum {i=0}^{k-1} a_i 2^{i*w}; + . + \remark Кодирование символов состоит в следующем + (\ -- двоичная запись числа b): + - положительные a_i представляются двоичными символами 0\ длины w+1; + - отрицательные a_i представляются двоичными символами 1\<|a_i|> длины w+1; + - кодированное представление - это конкатенация кода a_{k-1} + (первые символы), ...., кода a_1, кода a_0 (последние символы). + . + \remark Для [n]a длину представления k можно оценить следующим образом: + k >= (n * B_PER_W + w - 1) / w. + \remark Для данной реализации значение k всегда должно равняться (n * B_PER_W + w - 1) / w? + \remark Для хранения кодированного представления [n]a потребуется + m = W_OF_B(k * (w + 1)) слов. + \remark Для кодирования k последовательных элементов a_i потребуется + k * (w+1) бит. Поэтому для хранения всего кодового представления + потребуется не менее W_OF_B(k * (w + 1)) слов. + \pre 2 <= w < B_PER_W. + \pre Буфер recording не пересекается с буфером a. + \pre a -- нечетное + \pre k * w >= n * B_PER_W + \pre m >= W_OF_B(k * (w + 1)) + \safe Время работы функции зависит от n, k, w; +*/ +void wwOddRecording( + word oddRecording[], /*!< [out] кодированное представление */ + size_t m, /*!< [in] длина представления в машинных словах */ + const word a[], /*!< [in] слово */ + size_t n, /*!< [in] длина a в машинных словах */ + size_t k, /*!< [in] количество элементов представления */ + size_t w /*!< [in] длина окна */ +); + +/*! \brief Расчет OddRecording_size + Для n --- длины числа в машинных словах и ширины окна w вычисляет оптимальное + (наименьшее) количество элементов кодированного представления OddRecording + k = (n * B_PER_W + w - 1) / w. + \return (n * B_PER_W + w - 1) / w +*/ +size_t wwOddRecording_size(const size_t n, const size_t w); + +/*! \brief Расчет odd windowed form + + В [n]owf помещается кодированное представление нечетного слова + [n]a (a_0, a_1,..., a_{k-1}) такое, что + - k = n * B_PER_W / w + - a_i \in {\pm 1, \pm 3, ..., \pm 2^w - 1}; + - a как число равняется \sum {i=0}^{k-1} a_i 2^{i*w}; + . + \remark Кодирование символов состоит в следующем + (\ -- двоичная запись числа b): + - положительные a_i представляются двоичными символами 0\ длины w+1; + - отрицательные a_i представляются двоичными символами 1\<|a_i|> длины w+1; + - кодированное представление - это конкатенация кода a_{k-1} + (первые символы), ...., кода a_1, кода a_0 (последние символы). + . + \remark Для [n]a длину представления k можно оценить следующим образом: + k >= (n * B_PER_W + w - 1) / w. + \remark Для данной реализации значение k всегда должно равняться (n * B_PER_W + w - 1) / w? + \remark Для хранения кодированного представления [n]a потребуется + m = W_OF_B(k * (w + 1)) слов. + \remark Для кодирования k последовательных элементов a_i потребуется + k * (w+1) бит. Поэтому для хранения всего кодового представления + потребуется не менее W_OF_B(k * (w + 1)) слов. + \pre 2 <= w < B_PER_W. + \pre Буфер recording не пересекается с буфером a. + \pre a -- нечетное + \pre k * w >= n * B_PER_W + \pre m >= W_OF_B(k * (w + 1)) + \safe Время работы функции зависит от n, k, w; +*/ +void wwOWF( + word owf[], /*!< [out] кодированное представление */ + const word a[], /*!< [in] слово */ + size_t n, /*!< [in] длина a в машинных словах */ + size_t w /*!< [in] длина окна */ +); + +/*! \brief Расчет OddRecording_size + Для n --- длины числа в машинных словах и ширины окна w вычисляет оптимальное + (наименьшее) количество элементов кодированного представления OddRecording + k = (n * B_PER_W + w - 1) / w. + \return (n * B_PER_W + w - 1) / w +*/ +size_t wwOWF_size(const size_t n, const size_t w); + /* ******************************************************************************* Сдвиги и очистка diff --git a/include/bee2/math/zm.h b/include/bee2/math/zm.h index 09a8c3b7..657cee23 100644 --- a/include/bee2/math/zm.h +++ b/include/bee2/math/zm.h @@ -259,6 +259,9 @@ qr_sub_i, qr_neg_i идут прямые обращения к zzAddMod(), zzSub #define zmNeg(b, a, r)\ zzNegMod(b, a, (r)->mod, (r)->n) +#define zmSetSign(b, a, r, neg)\ + zzSetSignMod(b, a, (r)->mod, (r)->n, neg) + #ifdef __cplusplus } /* extern "C" */ #endif diff --git a/include/bee2/math/zz.h b/include/bee2/math/zz.h index c37657b3..d6ffc2d0 100644 --- a/include/bee2/math/zz.h +++ b/include/bee2/math/zz.h @@ -297,6 +297,27 @@ void zzNeg( size_t n /*!< [in] длина a в машинных словах */ ); +/*! \brief Утстановить знак + + Определяется число [n]b, отрицательное к [n]a по модулю B^n если neg = TRUE, и равное [n]a если neg = FALSE + \code + b <- neg ? B^n - a : a. + \endcode + \pre Буфер b либо не пересекается, либо совпадает с буфером a. + \pre neg = TRUE или neg = FALSE + \safe Имеется ускоренная нерегулярная редакция +*/ +void zzSetSign( + word b[], /*!< [out] отрицательное число */ + const word a[], /*!< [in] число */ + size_t n, /*!< [in] длина a в машинных словах */ + bool_t neg /*!< [in] флаг отрицательности */ +); + +void SAFE(zzSetSign)(word b[], const word a[], size_t n, bool_t neg); +void FAST(zzSetSign)(word b[], const word a[], size_t n, bool_t neg); + + /* ******************************************************************************* Мультипликативные операции @@ -770,6 +791,29 @@ void zzNegMod( void SAFE(zzNegMod)(word b[], const word a[], const word mod[], size_t n); void FAST(zzNegMod)(word b[], const word a[], const word mod[], size_t n); +/*! \brief Установить знак числа по модулю + + Определяется число [n]b равное (-1)^neg [n]a по модулю [n]mod: + \code + b <- (-1)^neg a \mod mod. + \endcode + \pre n > 0 && mod[n - 1] != 0. + \pre a < mod. + \pre Буфер b либо не пересекается, либо совпадает с буфером a. + \pre Буфер b не пересекается с буфером mod. + \safe Имеется ускоренная нерегулярная редакция. +*/ +void zzSetSignMod( + word b[], /*!< [in/out] результирующее число */ + const word a[], /*!< [in] число */ + const word mod[], /*!< [in] модуль */ + size_t n, /*!< [in] длина чисел в машинных словах */ + bool_t neg /*!< [in] флаг необходимости аддитивного обращения */ +); + +void SAFE(zzSetSignMod)(word b[], const word a[], const word mod[], size_t n, bool_t neg); +void FAST(zzSetSignMod)(word b[], const word a[], const word mod[], size_t n, bool_t neg); + /*! \brief Умножение чисел по модулю Определяется произведение [n]c чисел [n]a и [n]b по модулю [n]mod: diff --git a/src/core/util.c b/src/core/util.c index 95507405..15ae0de4 100644 --- a/src/core/util.c +++ b/src/core/util.c @@ -37,11 +37,11 @@ Assert ******************************************************************************* */ -void utilAssert(int b, const char* file, int line) +void utilAssert(int b, const char* file, int line, char const *msg) { if (!b) { - fprintf(stderr, "Assertion in %s::%d\n", file, line); + fprintf(stderr, "Assertion in %s::%d: %s\n", file, line, msg); abort(); } } diff --git a/src/crypto/bign.c b/src/crypto/bign.c index 20f0c836..9476551f 100644 --- a/src/crypto/bign.c +++ b/src/crypto/bign.c @@ -33,6 +33,150 @@ version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ +// bign-curve96v1 +static const char _curve96v1_name[] = "1.2.112.0.2.0.34.101.45.3.0"; + +static const octet _curve96v1_p[24] = { + 0x13, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, +}; + +static const octet _curve96v1_a[24] = { + 0x10, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, +}; + +static const octet _curve96v1_b[24] = { + 0x83, 0x4C, 0x34, 0x64, 0x4C, 0xE8, 0xDD, 0x6A, + 0x7A, 0x73, 0x01, 0x89, 0x88, 0x8E, 0x18, 0x87, + 0xA8, 0x98, 0x23, 0xFD, 0x25, 0xB9, 0x99, 0x31, +}; + +static const octet _curve96v1_seed[8] = { + 0xC6, 0x6C, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, +}; + +static const octet _curve96v1_q[24] = { + 0xAD, 0x11, 0x64, 0xFD, 0xBE, 0xEC, 0x0B, 0x91, + 0x37, 0xD3, 0x3A, 0x65, 0xFE, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, +}; + +static const octet _curve96v1_yG[24] = { + 0xEC, 0xCC, 0x48, 0xF6, 0xEB, 0x7F, 0x21, 0xE0, + 0x0C, 0x93, 0xDA, 0x03, 0xB2, 0x1B, 0xF9, 0xE6, + 0x17, 0xC3, 0x68, 0xC1, 0x4B, 0x96, 0x38, 0x81, +}; + +#define CURVE96V1_PRECOMP_W 6 +static const octet _curve96v1_precomp_Gs[48 * (2 + (1 << CURVE96V1_PRECOMP_W))] = { + 0x8e,0x54,0x48,0x9d,0x1a,0xf3,0xc3,0x00,0xf0,0x62,0x6d,0xd8,0xfa,0xe3,0xed,0x08,0x7f,0x29,0x7d,0xf9,0x8d,0x14,0xca,0xfa,0x36,0x32,0xcd,0xd7,0x46,0x67,0x1b,0x33, + 0xbe,0x96,0x34,0x18,0xa3,0xc7,0xcd,0x96,0xec,0x41,0xe1,0x10,0xbe,0x8b,0x29,0xb3,0x09,0x87,0x9d,0xa3,0xb7,0x4c,0x80,0x6d,0x57,0x5a,0x5d,0x2e,0xf9,0x30,0xa8,0xae, + 0x2f,0x82,0x88,0xe0,0xf0,0xfa,0x35,0x54,0xc2,0x31,0x8e,0x92,0x49,0xb3,0x09,0xd6,0x3e,0x92,0x61,0x11,0xdf,0x20,0x47,0x8a,0xfe,0xf4,0xd1,0xb5,0x88,0x96,0xb8,0x59, + 0x95,0x25,0xa8,0x2b,0x66,0x1a,0xd3,0x8a,0x52,0x8d,0xaf,0xe5,0xa5,0xa2,0xd5,0x6c,0x82,0x61,0xac,0xa8,0x2a,0x7d,0x77,0xe2,0xd9,0xee,0x02,0xc6,0xe7,0x9a,0xdd,0xde, + 0x2b,0x9d,0x64,0x0a,0xdf,0x58,0xbb,0xe9,0x25,0x09,0x06,0xe7,0x36,0x58,0x81,0xa0,0xfe,0x96,0x3f,0x47,0xfe,0x9d,0x08,0x74,0x7e,0x82,0x8f,0xe0,0x8c,0x55,0x24,0xda, + 0xad,0x7e,0xbc,0xfa,0x9d,0x9f,0xe5,0x0a,0x5a,0x70,0xe3,0x33,0x96,0xaa,0x80,0xe8,0x03,0x92,0xbb,0xfe,0x83,0xc5,0x6c,0x38,0xd7,0x10,0x2a,0x94,0x98,0x9a,0xd1,0x3b, + 0x2d,0x6b,0x57,0xe1,0x9f,0xcd,0x5c,0x46,0x81,0x6e,0xf3,0x5e,0x37,0x64,0xb8,0xae,0xdf,0xe9,0xbd,0x9e,0x28,0x92,0x54,0xb3,0xf8,0x1d,0x02,0xcd,0x30,0x83,0x72,0xab, + 0x59,0xe3,0x87,0x7e,0x00,0x86,0x5b,0x79,0x0f,0x9f,0x4a,0x9d,0xe6,0x33,0x63,0x42,0x0b,0xc1,0x69,0x67,0x6d,0x02,0xdb,0xa2,0x68,0xff,0xfa,0x8f,0x84,0xfa,0x8e,0x62, + 0x88,0xc9,0x59,0x7f,0x8c,0x26,0xd7,0x25,0xf8,0x19,0x2a,0x58,0xcb,0x77,0xd9,0xb5,0xe5,0x6e,0x2e,0x10,0xf0,0x08,0xaf,0x11,0xf3,0x0e,0x98,0x81,0x5f,0xff,0xba,0x36, + 0xe1,0x4b,0xfa,0x30,0x9d,0x98,0xf3,0x32,0x29,0x7b,0xe1,0x67,0x4d,0x27,0x76,0xf0,0xff,0xe2,0x31,0xfc,0x47,0x81,0x3d,0xfb,0x8f,0x8d,0xf0,0x0a,0xcd,0x41,0xfc,0xb8, + 0xaa,0x4b,0x03,0x43,0x63,0x02,0xc3,0xe7,0x79,0xe5,0xef,0x7a,0x16,0xdd,0x79,0x36,0xcb,0x7d,0x08,0x1a,0x5f,0x5a,0xe2,0x86,0x06,0xb4,0x1e,0x5f,0x77,0x8d,0xb6,0x7d, + 0x37,0x44,0x90,0x9d,0x9f,0xe5,0x5c,0x7c,0x1f,0x15,0xbe,0xf0,0xf4,0xca,0x93,0x6a,0xc7,0x57,0x6c,0x8b,0xb9,0x34,0xce,0x25,0xf6,0x60,0x23,0xf0,0x6d,0x35,0x50,0x0b, + 0x02,0xcf,0x17,0x34,0x47,0x4e,0x9d,0x30,0xa6,0xc2,0x9a,0x9d,0x22,0x0b,0x7f,0xba,0xa2,0xf6,0xc4,0x99,0xa8,0x83,0xc2,0x8c,0x32,0x94,0xde,0x12,0x87,0x59,0x07,0xcd, + 0x40,0x49,0x86,0x69,0x02,0xc5,0x6b,0x3f,0x38,0x2e,0xb8,0x0b,0x3e,0x3a,0xe4,0xdb,0x3f,0x16,0xbc,0x62,0xad,0xda,0xaa,0xb3,0x54,0x27,0x7b,0x44,0x3e,0x44,0x39,0x55, + 0x22,0xb3,0x0d,0xea,0x73,0x4c,0x78,0xfc,0xc3,0x1f,0xaf,0xbc,0xf8,0xde,0x34,0x5d,0xc9,0x7a,0x67,0xf6,0xdc,0xed,0x97,0x81,0x2d,0x26,0x1a,0xba,0x9a,0xcd,0xe8,0xcf, + 0xf8,0x0d,0xa1,0x11,0xd2,0xca,0xa8,0x2b,0x2f,0x45,0xc5,0xa4,0x57,0x38,0xc2,0x9b,0xed,0x2b,0xde,0x22,0x56,0x82,0x7d,0x8d,0x8a,0x68,0x42,0xa4,0xa2,0xc3,0x38,0x59, + 0xe1,0x75,0x5b,0x76,0xa5,0x42,0x1e,0x44,0x83,0x1f,0xed,0xb4,0x4b,0xb7,0x93,0xf5,0xea,0x5c,0xf6,0x3a,0x56,0x30,0xc4,0x56,0x7e,0xa5,0xf2,0x65,0xa2,0x44,0x53,0x61, + 0x05,0xc7,0xe4,0x4b,0x29,0x5f,0xb1,0x33,0x32,0xcc,0xd2,0x17,0xc2,0xb6,0xad,0x94,0x08,0x01,0x80,0xd2,0x40,0x34,0x66,0x75,0x75,0xb6,0x9f,0xdd,0x2d,0x9f,0x4f,0x9c, + 0xf1,0xc9,0xfa,0xba,0xcb,0x8c,0x06,0xbd,0xca,0x9d,0xdb,0x1e,0x51,0xfe,0x30,0x5b,0x49,0x0c,0xa0,0x85,0xf2,0x22,0x0c,0xd0,0xd8,0x80,0x4b,0x02,0xb4,0x00,0xe9,0x9e, + 0x78,0x77,0xb1,0xe6,0x78,0x7a,0xeb,0xc7,0x30,0x31,0xb9,0x76,0x99,0x9f,0x04,0x6e,0x3a,0x20,0x84,0x7f,0x85,0xcf,0x82,0x83,0x0a,0x62,0x7d,0x71,0x15,0x57,0xe2,0x82, + 0x6f,0x6c,0xe0,0x37,0xba,0xf6,0x04,0xb3,0xc9,0x1a,0x37,0x97,0x89,0x35,0x72,0x89,0xde,0x14,0x23,0xa5,0x16,0xd5,0x3b,0x29,0x44,0xd5,0x94,0x1a,0xf1,0xcf,0xb8,0x1c, + 0x7b,0x11,0x13,0x02,0x3f,0x21,0xec,0xfa,0xe7,0x08,0xf3,0xce,0xf4,0x8c,0xfb,0xc0,0xe0,0xb9,0x9f,0x7a,0x8b,0x77,0x8d,0x3c,0x33,0xc7,0x44,0x60,0xc7,0x2f,0xdd,0x01, + 0x72,0xa8,0xa5,0xf8,0xdb,0xac,0xe3,0xef,0xc2,0x31,0xc3,0x3a,0xdc,0x82,0x19,0x15,0x7e,0x97,0xd2,0x67,0x7c,0xd3,0x74,0x2e,0x6b,0xff,0x7a,0x4c,0x7d,0x3d,0x2e,0x9d, + 0xeb,0x8f,0xf6,0xb7,0xa6,0xac,0x6e,0x5d,0xa2,0x72,0xaf,0xbf,0x31,0x6a,0x2a,0x0b,0xd9,0x14,0xaa,0xda,0x92,0x3d,0xfd,0x8c,0x7d,0xc1,0xe7,0x2e,0xe9,0x1e,0xb1,0x98, + + 0xee,0x59,0x70,0x6c,0x43,0x22,0x01,0x5b,0xdd,0xeb,0x3b,0xc8,0xd4,0x56,0x4c,0x17,0x52,0x50,0x6e,0xb8,0xda,0xf3,0x4d,0xa4,0x29,0x0b,0xa8,0x4c,0xde,0xc3,0x6f,0x88, + 0xab,0xcc,0x9c,0x67,0xf6,0xe4,0x79,0x1a,0x4a,0xa9,0x0e,0x0f,0x5e,0x0b,0xc8,0x0e,0x54,0xdf,0xdb,0x84,0x78,0xa3,0x50,0xf6,0xec,0xcf,0x04,0x1e,0x2f,0xd9,0xed,0x37, + 0xb0,0x39,0x17,0x6a,0x20,0x14,0x97,0xb6,0xc8,0xd1,0x71,0x7e,0xad,0x9b,0xaa,0xa8,0xe9,0x1b,0xcf,0x35,0x10,0x7b,0xe4,0x55,0xff,0x0f,0x84,0xda,0x77,0xe8,0xa6,0xf3, + 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0x3f,0x16,0xbc,0x62,0xad,0xda,0xaa,0xb3,0x54,0x27,0x7b,0x44,0x3e,0x44,0x39,0x55,0x22,0xb3,0x0d,0xea,0x73,0x4c,0x78,0xfc,0x50,0xdf,0x50,0x43,0x07,0x21,0xcb,0xa2, + 0x36,0x85,0x98,0x09,0x23,0x12,0x68,0x7e,0xd2,0xd9,0xe5,0x45,0x65,0x32,0x17,0x30,0x02,0xcf,0x17,0x34,0x47,0x4e,0x9d,0x30,0xa6,0xc2,0x9a,0x9d,0x22,0x0b,0x7f,0xba, + 0xa2,0xf6,0xc4,0x99,0xa8,0x83,0xc2,0x8c,0xe1,0x6a,0x21,0xed,0x78,0xa6,0xf8,0x32,0xbf,0xb6,0x79,0x96,0xfd,0x3a,0x94,0xc0,0xc7,0xd1,0x47,0xf4,0xc1,0xc5,0x1b,0x24, + 0xcb,0x7d,0x08,0x1a,0x5f,0x5a,0xe2,0x86,0x06,0xb4,0x1e,0x5f,0x77,0x8d,0xb6,0x7d,0x37,0x44,0x90,0x9d,0x9f,0xe5,0x5c,0x7c,0xf4,0xe9,0x41,0x0f,0x0b,0x35,0x6c,0x95, + 0x38,0xa8,0x93,0x74,0x46,0xcb,0x31,0xda,0x09,0x9f,0xdc,0x0f,0x92,0xca,0xaf,0xf4,0xe1,0x4b,0xfa,0x30,0x9d,0x98,0xf3,0x32,0x29,0x7b,0xe1,0x67,0x4d,0x27,0x76,0xf0, + 0xff,0xe2,0x31,0xfc,0x47,0x81,0x3d,0xfb,0x84,0x71,0x0f,0xf5,0x32,0xbe,0x03,0x47,0x55,0xb4,0xfc,0xbc,0x9c,0xfd,0x3c,0x18,0x86,0x1a,0x10,0x85,0xe9,0x22,0x86,0xc9, + 0x0b,0xc1,0x69,0x67,0x6d,0x02,0xdb,0xa2,0x68,0xff,0xfa,0x8f,0x84,0xfa,0x8e,0x62,0x88,0xc9,0x59,0x7f,0x8c,0x26,0xd7,0x25,0x1b,0xe5,0xd5,0xa7,0x34,0x88,0x26,0x4a, + 0x1a,0x91,0xd1,0xef,0x0f,0xf7,0x50,0xee,0x0c,0xf1,0x67,0x7e,0xa0,0x00,0x45,0xc9,0x2d,0x6b,0x57,0xe1,0x9f,0xcd,0x5c,0x46,0x81,0x6e,0xf3,0x5e,0x37,0x64,0xb8,0xae, + 0xdf,0xe9,0xbd,0x9e,0x28,0x92,0x54,0xb3,0x1b,0xe1,0xfd,0x32,0xcf,0x7c,0x8d,0x54,0xa6,0x1c,0x78,0x81,0xff,0x79,0xa4,0x86,0xf0,0x60,0xb5,0x62,0x19,0xcc,0x9c,0xbd, + 0xfe,0x96,0x3f,0x47,0xfe,0x9d,0x08,0x74,0x7e,0x82,0x8f,0xe0,0x8c,0x55,0x24,0xda,0xad,0x7e,0xbc,0xfa,0x9d,0x9f,0xe5,0x0a,0xb9,0x8e,0x1c,0xcc,0x69,0x55,0x7f,0x17, + 0xfc,0x6d,0x44,0x01,0x7c,0x3a,0x93,0xc7,0x28,0xef,0xd5,0x6b,0x67,0x65,0x2e,0xc4,0x95,0x25,0xa8,0x2b,0x66,0x1a,0xd3,0x8a,0x52,0x8d,0xaf,0xe5,0xa5,0xa2,0xd5,0x6c, + 0x82,0x61,0xac,0xa8,0x2a,0x7d,0x77,0xe2,0x3a,0x10,0xfd,0x39,0x18,0x65,0x22,0x21,0xd4,0x62,0x9b,0xf5,0x20,0xa7,0x44,0x16,0xda,0xf6,0xf9,0x18,0xc9,0xa7,0x7e,0x5f, + 0x09,0x87,0x9d,0xa3,0xb7,0x4c,0x80,0x6d,0x57,0x5a,0x5d,0x2e,0xf9,0x30,0xa8,0xae,0x2f,0x82,0x88,0xe0,0xf0,0xfa,0x35,0x54,0x51,0xcd,0x71,0x6d,0xb6,0x4c,0xf6,0x29, + 0xc1,0x6d,0x9e,0xee,0x20,0xdf,0xb8,0x75,0x01,0x0b,0x2e,0x4a,0x77,0x69,0x47,0xa6,0x8e,0x54,0x48,0x9d,0x1a,0xf3,0xc3,0x00,0xf0,0x62,0x6d,0xd8,0xfa,0xe3,0xed,0x08, + 0x7f,0x29,0x7d,0xf9,0x8d,0x14,0xca,0xfa,0xdd,0xcc,0x32,0x28,0xb9,0x98,0xe4,0xcc,0x41,0x69,0xcb,0xe7,0x5c,0x38,0x32,0x69,0x13,0xbe,0x1e,0xef,0x41,0x74,0xd6,0x4c, + + 0xd7,0xab,0xa6,0x26,0xbc,0x32,0x24,0x91,0xe9,0xa6,0x35,0xd6,0x92,0x3e,0x2f,0xb1,0x65,0x6a,0xe2,0xc1,0x51,0x00,0x80,0x14,0x3f,0x1e,0x55,0x7c,0x84,0xe5,0x1f,0xd8, + 0x51,0x25,0x34,0x1e,0x35,0xc8,0x8d,0xc4,0xb2,0x1f,0x72,0x43,0x3b,0x21,0x78,0x2f,0xd7,0xab,0xa6,0x26,0xbc,0x32,0x24,0x91,0xe9,0xa6,0x35,0xd6,0x92,0x3e,0x2f,0xb1, + 0x65,0x6a,0xe2,0xc1,0x51,0x00,0x80,0x14,0xd4,0xe0,0xaa,0x83,0x7b,0x1a,0xe0,0x27,0xae,0xda,0xcb,0xe1,0xca,0x37,0x72,0x3b,0x4d,0xe0,0x8d,0xbc,0xc4,0xde,0x87,0xd0, +}; + // bign-curve128v1 static const char _curve128v1_name[] = "1.2.112.0.2.0.34.101.45.3.1"; @@ -75,6 +219,146 @@ static const octet _curve128v1_yG[32] = { 0x9F, 0xD6, 0x16, 0xFB, 0x3C, 0xFC, 0xF7, 0x6B, }; +#define CURVE128V1_PRECOMP_W 6 +static const octet _curve128v1_precomp_Gs[64 * (2 + (1 << CURVE128V1_PRECOMP_W))] = { + 0x54,0xb8,0xeb,0xa1,0xfa,0xfe,0xf9,0x00,0x0b,0xa1,0x61,0x50,0x43,0x3f,0x05,0x68,0x89,0xf5,0x61,0x4e,0x6c,0xf2,0xb6,0xcb,0xdc,0x20,0x44,0x7a,0x68,0xb0,0x35,0x6a, + 0xa7,0x14,0x68,0x06,0x59,0x20,0x13,0x9d,0x94,0x33,0xe5,0xfe,0x56,0x20,0xfd,0x48,0x1e,0x61,0x75,0xc3,0x38,0x89,0x64,0x98,0x39,0xcf,0xdc,0xb5,0xcb,0x42,0x60,0x97, + 0xe5,0x4f,0x30,0x13,0x36,0xf9,0xa0,0xd4,0xe2,0x36,0x2b,0xa5,0x08,0x39,0x8c,0xb8,0x5d,0x99,0x9a,0x1d,0x87,0x2a,0x8f,0xb9,0xe1,0x12,0x0c,0x85,0x31,0x6e,0x8b,0xd2, + 0x65,0x10,0x99,0x33,0xbf,0xc6,0x2a,0xfc,0x08,0x99,0x2f,0x86,0x18,0xb5,0x8e,0xdf,0x3b,0x36,0x84,0xfc,0x6d,0x77,0x26,0x48,0x56,0x49,0xaf,0x36,0x42,0x74,0x0f,0x75, + 0xa0,0x4e,0xfe,0xc4,0x37,0x6b,0x19,0x1d,0x37,0xa7,0xc7,0xb7,0xbb,0xb8,0x16,0x47,0x61,0xf1,0x6f,0x04,0x6d,0x54,0xa5,0x6d,0xc0,0x0b,0x1c,0xaa,0xb4,0x10,0xa5,0x72, + 0xc4,0x78,0xc9,0x3a,0xc5,0x44,0x6a,0x62,0x00,0xdd,0x0e,0x87,0x71,0x85,0xad,0xd9,0x52,0xa2,0xcc,0x61,0x3a,0x18,0x0e,0xa3,0x26,0x2c,0x74,0x4b,0xe9,0xab,0x8b,0xb7, + 0x86,0x53,0x63,0x7d,0x2d,0x39,0x57,0x49,0xf6,0x89,0x68,0x4a,0xd0,0xbb,0xd1,0x42,0x1d,0x1e,0x62,0x73,0x04,0xc7,0xa7,0x1b,0xd7,0xe1,0xa3,0x7d,0x27,0x07,0xf2,0xe9, + 0xd3,0xde,0x28,0x88,0xac,0x06,0xdc,0x11,0x4e,0xef,0xcf,0x9e,0xa8,0x65,0x29,0x7d,0x81,0x21,0xb4,0xed,0xc4,0x4b,0x3a,0x8b,0x52,0xef,0x2d,0xac,0xfa,0x36,0xa0,0x78, + 0xea,0x0f,0xf5,0x87,0x9b,0x8f,0xcb,0x98,0x83,0xab,0x64,0x34,0x7c,0x59,0xf3,0xfa,0xaf,0xc4,0x5f,0xcc,0xf4,0x47,0x2b,0x21,0x32,0x5e,0x3d,0x8d,0x28,0xdf,0x67,0x58, + 0xe8,0xcc,0x46,0x2a,0x8f,0xbe,0xd2,0x6e,0xc6,0x08,0xa9,0x4e,0x3d,0x29,0xd9,0x40,0x1a,0x50,0x7e,0x49,0xad,0x4c,0xab,0x31,0x1e,0xa1,0x2c,0xed,0xc8,0xcd,0x9b,0x88, + 0xbb,0x8f,0x4f,0x42,0x55,0x8c,0x69,0xc5,0x83,0x4c,0x52,0x56,0x01,0x39,0x1e,0xa9,0x0a,0xcb,0x35,0x73,0x7e,0xfb,0x23,0xfd,0xe0,0xf4,0x42,0x01,0x59,0x3a,0x0b,0x8f, + 0x9d,0xc2,0x8c,0xac,0x42,0xbf,0x42,0x5a,0x51,0x18,0x61,0x25,0x3c,0x0b,0x35,0xc3,0xdc,0x92,0xa2,0x5b,0x2d,0x44,0xf0,0x52,0xc2,0x5c,0x28,0x07,0x0d,0x05,0xc9,0x1a, + 0x82,0xc3,0xd2,0xbc,0x4c,0xae,0xd1,0x26,0xb3,0x60,0x71,0x26,0xbf,0x06,0xe6,0x8d,0x3f,0x8a,0x8e,0xde,0x4f,0xe3,0x92,0x64,0x1e,0x55,0xee,0xfa,0x88,0x22,0xfd,0xee, + 0xdf,0x0e,0x8c,0x80,0x8c,0xa9,0x7f,0xb0,0xdf,0x6e,0x85,0xca,0xa1,0x5d,0x53,0x39,0x40,0x64,0x60,0x5f,0xc4,0x32,0x64,0x85,0xb0,0x85,0xa5,0x22,0x90,0x8a,0x14,0xd1, + 0xf5,0xf2,0xab,0x2d,0x79,0x07,0xfc,0xa1,0xeb,0xe5,0x3a,0x36,0x38,0x4d,0xfe,0x0f,0x32,0x4d,0x19,0x45,0x05,0xc6,0x5a,0xd0,0xfd,0x0a,0xc8,0x71,0xbf,0xb9,0x97,0x82, + 0xdf,0xb2,0xe5,0xe8,0x41,0x1f,0x74,0x09,0x07,0x4a,0x33,0xff,0x0d,0xf5,0xf2,0xc6,0x37,0x47,0xf2,0x0a,0xad,0xf7,0xe4,0x75,0x3e,0x4e,0x2b,0x44,0xa3,0x94,0x53,0x01, + 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0xf5,0xf2,0xab,0x2d,0x79,0x07,0xfc,0xa1,0xeb,0xe5,0x3a,0x36,0x38,0x4d,0xfe,0x0f,0x32,0x4d,0x19,0x45,0x05,0xc6,0x5a,0xd0,0xfd,0x0a,0xc8,0x71,0xbf,0xb9,0x97,0x82, + 0x64,0x4c,0x1a,0x17,0xbe,0xe0,0x8b,0xf6,0xf8,0xb5,0xcc,0x00,0xf2,0x0a,0x0d,0x39,0xc8,0xb8,0x0d,0xf5,0x52,0x08,0x1b,0x8a,0xc1,0xb1,0xd4,0xbb,0x5c,0x6b,0xac,0xfe, + 0x82,0xc3,0xd2,0xbc,0x4c,0xae,0xd1,0x26,0xb3,0x60,0x71,0x26,0xbf,0x06,0xe6,0x8d,0x3f,0x8a,0x8e,0xde,0x4f,0xe3,0x92,0x64,0x1e,0x55,0xee,0xfa,0x88,0x22,0xfd,0xee, + 0x64,0xf0,0x73,0x7f,0x73,0x56,0x80,0x4f,0x20,0x91,0x7a,0x35,0x5e,0xa2,0xac,0xc6,0xbf,0x9b,0x9f,0xa0,0x3b,0xcd,0x9b,0x7a,0x4f,0x7a,0x5a,0xdd,0x6f,0x75,0xeb,0x2e, + 0xbb,0x8f,0x4f,0x42,0x55,0x8c,0x69,0xc5,0x83,0x4c,0x52,0x56,0x01,0x39,0x1e,0xa9,0x0a,0xcb,0x35,0x73,0x7e,0xfb,0x23,0xfd,0xe0,0xf4,0x42,0x01,0x59,0x3a,0x0b,0x8f, + 0xa6,0x3c,0x73,0x53,0xbd,0x40,0xbd,0xa5,0xae,0xe7,0x9e,0xda,0xc3,0xf4,0xca,0x3c,0x23,0x6d,0x5d,0xa4,0xd2,0xbb,0x0f,0xad,0x3d,0xa3,0xd7,0xf8,0xf2,0xfa,0x36,0xe5, + 0xea,0x0f,0xf5,0x87,0x9b,0x8f,0xcb,0x98,0x83,0xab,0x64,0x34,0x7c,0x59,0xf3,0xfa,0xaf,0xc4,0x5f,0xcc,0xf4,0x47,0x2b,0x21,0x32,0x5e,0x3d,0x8d,0x28,0xdf,0x67,0x58, + 0x5b,0x32,0xb9,0xd5,0x70,0x41,0x2d,0x91,0x39,0xf7,0x56,0xb1,0xc2,0xd6,0x26,0xbf,0xe5,0xaf,0x81,0xb6,0x52,0xb3,0x54,0xce,0xe1,0x5e,0xd3,0x12,0x37,0x32,0x64,0x77, + 0x86,0x53,0x63,0x7d,0x2d,0x39,0x57,0x49,0xf6,0x89,0x68,0x4a,0xd0,0xbb,0xd1,0x42,0x1d,0x1e,0x62,0x73,0x04,0xc7,0xa7,0x1b,0xd7,0xe1,0xa3,0x7d,0x27,0x07,0xf2,0xe9, + 0x70,0x20,0xd7,0x77,0x53,0xf9,0x23,0xee,0xb1,0x10,0x30,0x61,0x57,0x9a,0xd6,0x82,0x7e,0xde,0x4b,0x12,0x3b,0xb4,0xc5,0x74,0xad,0x10,0xd2,0x53,0x05,0xc9,0x5f,0x87, + 0xa0,0x4e,0xfe,0xc4,0x37,0x6b,0x19,0x1d,0x37,0xa7,0xc7,0xb7,0xbb,0xb8,0x16,0x47,0x61,0xf1,0x6f,0x04,0x6d,0x54,0xa5,0x6d,0xc0,0x0b,0x1c,0xaa,0xb4,0x10,0xa5,0x72, + 0x7f,0x86,0x36,0xc5,0x3a,0xbb,0x95,0x9d,0xff,0x22,0xf1,0x78,0x8e,0x7a,0x52,0x26,0xad,0x5d,0x33,0x9e,0xc5,0xe7,0xf1,0x5c,0xd9,0xd3,0x8b,0xb4,0x16,0x54,0x74,0x48, + 0xe5,0x4f,0x30,0x13,0x36,0xf9,0xa0,0xd4,0xe2,0x36,0x2b,0xa5,0x08,0x39,0x8c,0xb8,0x5d,0x99,0x9a,0x1d,0x87,0x2a,0x8f,0xb9,0xe1,0x12,0x0c,0x85,0x31,0x6e,0x8b,0xd2, + 0xde,0xee,0x66,0xcc,0x40,0x39,0xd5,0x03,0xf7,0x66,0xd0,0x79,0xe7,0x4a,0x71,0x20,0xc4,0xc9,0x7b,0x03,0x92,0x88,0xd9,0xb7,0xa9,0xb6,0x50,0xc9,0xbd,0x8b,0xf0,0x8a, + 0x54,0xb8,0xeb,0xa1,0xfa,0xfe,0xf9,0x00,0x0b,0xa1,0x61,0x50,0x43,0x3f,0x05,0x68,0x89,0xf5,0x61,0x4e,0x6c,0xf2,0xb6,0xcb,0xdc,0x20,0x44,0x7a,0x68,0xb0,0x35,0x6a, + 0x9c,0xea,0x97,0xf9,0xa6,0xdf,0xec,0x62,0x6b,0xcc,0x1a,0x01,0xa9,0xdf,0x02,0xb7,0xe1,0x9e,0x8a,0x3c,0xc7,0x76,0x9b,0x67,0xc6,0x30,0x23,0x4a,0x34,0xbd,0x9f,0x68, + + 0x95,0x09,0x8f,0x82,0xb3,0x3b,0xf5,0x07,0xc8,0xd0,0xad,0x2c,0x0c,0x09,0x83,0x55,0xb3,0x5b,0xc9,0xad,0x1d,0x26,0x11,0x36,0x1e,0xd2,0x05,0xd9,0xe3,0x19,0x84,0x2d, + 0xb9,0xd9,0x30,0xb6,0x89,0xc7,0xfd,0x93,0x32,0x81,0xc5,0x6c,0x75,0xe1,0x9d,0xb6,0xb7,0xa9,0xab,0xff,0x88,0x4d,0x0a,0x05,0xb1,0x8a,0x23,0xe4,0x27,0x6f,0xd9,0x19, + 0x95,0x09,0x8f,0x82,0xb3,0x3b,0xf5,0x07,0xc8,0xd0,0xad,0x2c,0x0c,0x09,0x83,0x55,0xb3,0x5b,0xc9,0xad,0x1d,0x26,0x11,0x36,0x1e,0xd2,0x05,0xd9,0xe3,0x19,0x84,0x2d, + 0x8a,0x25,0xcf,0x49,0x76,0x38,0x02,0x6c,0xcd,0x7e,0x3a,0x93,0x8a,0x1e,0x62,0x49,0x48,0x56,0x54,0x00,0x77,0xb2,0xf5,0xfa,0x4e,0x75,0xdc,0x1b,0xd8,0x90,0x26,0xe6, +}; + // bign-curve192v1 static const char _curve192v1_name[] = "1.2.112.0.2.0.34.101.45.3.2"; @@ -128,6 +412,212 @@ static const octet _curve192v1_yG[48] = 0x9E, 0x9E, 0x2E, 0xA8, 0x24, 0x82, 0x43, 0x5D, }; +#define CURVE192V1_PRECOMP_W 6 +static const octet _curve192v1_precomp_Gs[96 * (2 + (1 << CURVE192V1_PRECOMP_W))] = { + 0x71,0x04,0x54,0x0c,0x4b,0x76,0x74,0x0b,0xdf,0xdb,0x73,0xbf,0x64,0x03,0x2e,0x29,0x93,0x8b,0x8f,0x1d,0x44,0x0e,0x7b,0x4c,0x9e,0x07,0xb9,0xa5,0x73,0xf2,0xc6,0x05, + 0x20,0x1f,0x9c,0xc5,0x2e,0x20,0x65,0x08,0x0c,0xa5,0xa2,0x71,0xcc,0xd5,0x3a,0x1a,0x09,0xcc,0x24,0x42,0xd1,0x70,0x8f,0x78,0xab,0x85,0x34,0x97,0xfc,0xfb,0x7e,0x86, + 0x15,0x3d,0xc5,0x5f,0x8a,0xa4,0x19,0xe5,0x1c,0x97,0x89,0x0c,0x47,0xff,0x0a,0xb3,0xb5,0x79,0x09,0x0c,0x4d,0xe7,0x8f,0xc7,0x59,0xbe,0x5c,0xc3,0x51,0x4f,0x18,0xb5, + 0x2d,0xf8,0x48,0xc5,0xa9,0x87,0xe0,0x58,0x30,0x08,0x4b,0x06,0x3e,0xd2,0xa8,0xa7,0x5e,0x31,0x31,0x5d,0x8d,0x02,0x4b,0x10,0xc7,0x9e,0x99,0x49,0xb3,0x54,0x2b,0x7e, + 0x09,0x7a,0x6f,0xab,0x5a,0x04,0x0a,0x11,0x67,0x19,0x6d,0x8c,0x1a,0x12,0x8c,0x7d,0x1b,0xfe,0x41,0x33,0x3d,0xa3,0xcd,0x3e,0x65,0xba,0x06,0xa9,0xeb,0x1c,0x1f,0xf4, + 0x97,0xa0,0x50,0x9d,0x1c,0xbe,0x7b,0xcc,0xcb,0x6e,0xfb,0xb0,0x89,0xff,0x69,0x40,0x6e,0x67,0xcd,0x54,0x19,0x92,0x94,0xe8,0x38,0x11,0xbc,0xf0,0x26,0xe7,0x05,0x4e, + 0x20,0x7c,0x69,0x24,0x76,0xcb,0xe3,0x75,0xad,0x7d,0xdb,0xa2,0x8b,0xec,0x9a,0x67,0xf8,0xa1,0x31,0xf2,0xbc,0x01,0xd1,0xd9,0x53,0x1b,0x1b,0x03,0x1d,0x4d,0x27,0xe0, + 0x7f,0x9d,0x4b,0x26,0x86,0x97,0x12,0x2a,0xc1,0xb9,0x99,0x1e,0xc5,0xe4,0x0a,0x91,0x06,0x65,0x8e,0x4c,0xeb,0x0f,0x32,0x1a,0xad,0x85,0xf9,0x4b,0x4d,0xe9,0x76,0xd5, + 0x23,0x0e,0x9e,0xbe,0x1d,0x42,0x7e,0xd1,0x45,0xf9,0x5a,0x61,0x99,0x51,0xe4,0x21,0xa8,0xb8,0x93,0x10,0x53,0x91,0x13,0xa3,0xbb,0x22,0xd4,0xaf,0x9c,0x06,0xff,0xe2, + 0x8c,0xb7,0x83,0xc9,0xce,0x58,0x4c,0x16,0xfa,0x13,0xcc,0x3d,0xcf,0x2a,0x49,0x9d,0xc3,0xc3,0xf5,0x0e,0xb8,0x54,0xef,0xce,0xdf,0x9d,0x2f,0xba,0x94,0x81,0xde,0x17, + 0x2d,0xc7,0x55,0xc6,0xaf,0xe9,0x40,0x15,0x40,0x51,0x91,0x13,0xe9,0xc9,0xe8,0xa8,0x8d,0x19,0x8d,0x7a,0x05,0xab,0x1b,0xa9,0x95,0x7a,0x8a,0x92,0xf8,0xb6,0x77,0x49, + 0x7a,0x13,0x09,0x56,0xb9,0x37,0x70,0x5e,0x10,0xc8,0x31,0xb2,0x80,0xd7,0x1c,0x39,0xad,0x29,0x4e,0x03,0xd8,0x56,0x73,0x78,0x22,0x81,0xd1,0x4b,0x9b,0x72,0x8c,0x09, + 0x5d,0x3d,0x98,0x63,0x91,0x9f,0x45,0xbc,0xdb,0xa4,0x35,0xe6,0x9e,0xcf,0xaa,0xef,0xf6,0x11,0x27,0x61,0x36,0x0a,0x8d,0xb0,0x9d,0xb5,0xba,0x7c,0xfd,0xf1,0x7a,0x44, + 0xc7,0xa2,0x94,0xbb,0xcd,0x6c,0x82,0x7d,0x2e,0xb2,0x92,0xe6,0x7c,0x89,0x88,0xcc,0x47,0xb8,0x1f,0x95,0x0a,0x98,0x9c,0xc8,0x45,0x7d,0xb0,0x8b,0xfd,0x31,0x8c,0x8b, + 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0x22,0x91,0xe1,0xe0,0xc8,0xc3,0xe5,0xbe,0xb5,0x19,0x83,0x70,0x20,0x70,0xfd,0x78,0x45,0x00,0x17,0xf4,0x11,0x31,0x5d,0x72,0x16,0xbd,0x0e,0x50,0xcd,0x47,0x6a,0xd8, + 0x92,0xbd,0xa0,0xe3,0xa9,0x0b,0x4e,0x93,0x95,0x71,0xe3,0xe6,0xc7,0xb0,0x06,0x28,0xe2,0x33,0xbb,0x59,0x88,0x52,0xe6,0xfb,0x98,0xbd,0xad,0x5c,0x52,0x92,0x34,0xa6, + 0x6e,0xfb,0xa4,0x2b,0x55,0x6d,0x35,0xe5,0x20,0x75,0x76,0x13,0xf0,0xef,0xbf,0x6f,0xc7,0xfb,0x0f,0xfc,0x89,0x07,0x42,0x2f,0xbe,0xe3,0x4f,0xc2,0x2d,0x41,0xa7,0xfe, + 0xb4,0x95,0x0e,0xaa,0xe7,0x7d,0x5f,0x5c,0x1a,0xaf,0x6a,0x3a,0x63,0xc0,0xfc,0x51,0xaa,0x54,0xf1,0x07,0xdd,0xad,0xe1,0x3a,0x80,0x09,0x1f,0xf9,0x84,0xff,0x52,0x21, + 0xe1,0x7c,0xbc,0x8c,0xc9,0x39,0xa2,0x07,0x48,0xd0,0x87,0x47,0xf5,0xdd,0x25,0xaa,0xd6,0x0b,0x10,0xc9,0xb3,0x76,0x5e,0xd5,0x13,0x08,0x7d,0x29,0x0b,0x86,0x3f,0xdb, + 0xf4,0xa6,0x95,0x08,0x36,0x2d,0x40,0x8c,0x4f,0x92,0xac,0xf5,0x04,0xe5,0x46,0x50,0x51,0x36,0x96,0x87,0xaf,0x9f,0x77,0x77,0xb7,0x15,0x9e,0x5f,0x57,0xa8,0xc1,0x8b, + 0xfc,0x82,0xf5,0x08,0x4e,0x2b,0x01,0x31,0x8a,0x75,0x4d,0x3c,0x0b,0x0a,0x21,0x82,0x5a,0x49,0x78,0x14,0x5e,0x98,0x2f,0xc5,0x46,0x96,0x97,0x5a,0xee,0xfe,0xc1,0x52, + 0xc4,0x8e,0x9a,0xa4,0xbd,0xa3,0xa4,0x98,0x44,0xeb,0x42,0x54,0xa6,0xac,0xab,0x72,0xfa,0x4a,0x76,0x46,0xa8,0xd8,0x42,0x28,0x3e,0x62,0xb0,0xc3,0x05,0x4e,0xfa,0xfe, + 0x68,0x95,0x7c,0x7f,0xf7,0x72,0xc2,0xc6,0x1d,0x91,0x8f,0x0f,0x38,0x3b,0x0d,0x1e,0x0c,0x06,0xef,0xac,0x5d,0xa2,0xe5,0x71,0xab,0x4c,0xfb,0xfd,0x10,0x5c,0x91,0xa0, + 0xae,0xb0,0x90,0x2e,0xc5,0xb3,0x92,0x14,0x0c,0x58,0x55,0xca,0x94,0xf0,0xe4,0x15,0xce,0x3d,0x94,0x8f,0xdf,0x71,0x13,0x98,0x40,0x8f,0xc8,0x9c,0xaf,0xb3,0x0d,0x80, + 0x63,0x0d,0x0c,0x0e,0xb5,0xe4,0x55,0xd2,0x0f,0xe3,0xfa,0xce,0x9b,0xd7,0x92,0xad,0x27,0x0c,0x96,0x29,0xfa,0x4e,0xff,0xf3,0x20,0x1c,0x04,0x45,0x19,0x95,0x72,0xea, + 0xb2,0x10,0xe2,0x21,0x74,0xa2,0xfe,0xe0,0xef,0x96,0x06,0x31,0xe6,0x71,0xbb,0x39,0x89,0x9f,0xa4,0xdc,0xc7,0xb8,0x8b,0xba,0xc1,0xea,0xbd,0xdf,0x4a,0xcd,0xea,0x66, + 0x16,0xf7,0x2f,0xc1,0xd3,0xe4,0x0b,0xd6,0xd8,0x05,0x39,0x4d,0xeb,0x5f,0x22,0xad,0x1d,0xba,0xb8,0x73,0x21,0x22,0xdc,0x23,0x2d,0x13,0x73,0xd0,0x9a,0xba,0xda,0xe9, + 0x0f,0xc8,0xb6,0x03,0xb1,0x5f,0xf0,0x89,0x77,0x09,0x40,0x87,0xd7,0xf7,0x6d,0xe2,0x2f,0x7d,0x47,0x59,0xe6,0x60,0xf5,0x96,0x27,0x3f,0x82,0x8f,0xe3,0xae,0x1d,0x5a, + 0xa5,0xa6,0x03,0x2c,0x0f,0xcd,0x52,0x4f,0x86,0x54,0xc5,0x91,0x07,0xe6,0x70,0x11,0xaf,0xb6,0x99,0xc5,0x41,0x8e,0x3a,0x56,0x6e,0x0c,0xea,0x10,0x3a,0x5d,0x5d,0x46, + 0xf6,0x2c,0x3a,0x58,0x39,0xb7,0x68,0x50,0xfb,0x71,0x0b,0x17,0xed,0xc8,0x9e,0xec,0x33,0x8c,0x1f,0x0e,0xa0,0x4e,0xb2,0x18,0xf8,0x37,0x76,0x59,0xab,0x9c,0x32,0x26, + 0x6d,0x87,0x93,0x0c,0xdd,0x0a,0x69,0x51,0x38,0x3f,0x00,0x07,0x7b,0xe1,0xc2,0xc5,0x6f,0xb9,0xfd,0xb3,0x0e,0x93,0x9a,0xd5,0xea,0xb9,0x1d,0x03,0x3f,0x2e,0x30,0x05, + 0xd8,0xdc,0xc8,0x21,0xc1,0x91,0xf4,0x55,0x97,0xf9,0xff,0x45,0x6d,0x72,0xe5,0xfd,0xc3,0x05,0xfb,0x40,0xc4,0x09,0x87,0x74,0x9c,0x7f,0x3b,0xbf,0xde,0x2f,0xd8,0x50, + 0xfd,0xa7,0x8f,0xbb,0x6d,0x0e,0xaa,0xa1,0x31,0xd6,0xc1,0xa1,0x4a,0x9c,0xc8,0xd6,0x8e,0x42,0xfd,0x8b,0x80,0x87,0x4a,0xe5,0xa0,0x7f,0xdc,0x0c,0xfe,0xde,0x82,0x7b, + 0x5d,0x3d,0x98,0x63,0x91,0x9f,0x45,0xbc,0xdb,0xa4,0x35,0xe6,0x9e,0xcf,0xaa,0xef,0xf6,0x11,0x27,0x61,0x36,0x0a,0x8d,0xb0,0x9d,0xb5,0xba,0x7c,0xfd,0xf1,0x7a,0x44, + 0xc7,0xa2,0x94,0xbb,0xcd,0x6c,0x82,0x7d,0x2e,0xb2,0x92,0xe6,0x7c,0x89,0x88,0xcc,0x7c,0x46,0xe0,0x6a,0xf5,0x67,0x63,0x37,0xba,0x82,0x4f,0x74,0x02,0xce,0x73,0x74, + 0xa9,0x35,0x78,0xc6,0xc2,0x3f,0x2b,0xd3,0xcc,0x7e,0x2b,0xa4,0x46,0xaa,0x4a,0x45,0xea,0xd6,0xb8,0xf7,0xdc,0xb1,0x57,0xa9,0x66,0x69,0x2c,0xe6,0x86,0xd0,0x23,0x16, + 0x8c,0xb7,0x83,0xc9,0xce,0x58,0x4c,0x16,0xfa,0x13,0xcc,0x3d,0xcf,0x2a,0x49,0x9d,0xc3,0xc3,0xf5,0x0e,0xb8,0x54,0xef,0xce,0xdf,0x9d,0x2f,0xba,0x94,0x81,0xde,0x17, + 0x2d,0xc7,0x55,0xc6,0xaf,0xe9,0x40,0x15,0x40,0x51,0x91,0x13,0xe9,0xc9,0xe8,0xa8,0x36,0xe5,0x72,0x85,0xfa,0x54,0xe4,0x56,0x6a,0x85,0x75,0x6d,0x07,0x49,0x88,0xb6, + 0x85,0xec,0xf6,0xa9,0x46,0xc8,0x8f,0xa1,0xef,0x37,0xce,0x4d,0x7f,0x28,0xe3,0xc6,0x52,0xd6,0xb1,0xfc,0x27,0xa9,0x8c,0x87,0xdd,0x7e,0x2e,0xb4,0x64,0x8d,0x73,0xf6, + 0x20,0x7c,0x69,0x24,0x76,0xcb,0xe3,0x75,0xad,0x7d,0xdb,0xa2,0x8b,0xec,0x9a,0x67,0xf8,0xa1,0x31,0xf2,0xbc,0x01,0xd1,0xd9,0x53,0x1b,0x1b,0x03,0x1d,0x4d,0x27,0xe0, + 0x7f,0x9d,0x4b,0x26,0x86,0x97,0x12,0x2a,0xc1,0xb9,0x99,0x1e,0xc5,0xe4,0x0a,0x91,0xbd,0x99,0x71,0xb3,0x14,0xf0,0xcd,0xe5,0x52,0x7a,0x06,0xb4,0xb2,0x16,0x89,0x2a, + 0xdc,0xf1,0x61,0x41,0xe2,0xbd,0x81,0x2e,0xba,0x06,0xa5,0x9e,0x66,0xae,0x1b,0xde,0x57,0x47,0x6c,0xef,0xac,0x6e,0xec,0x5c,0x44,0xdd,0x2b,0x50,0x63,0xf9,0x00,0x1d, + 0x2d,0xf8,0x48,0xc5,0xa9,0x87,0xe0,0x58,0x30,0x08,0x4b,0x06,0x3e,0xd2,0xa8,0xa7,0x5e,0x31,0x31,0x5d,0x8d,0x02,0x4b,0x10,0xc7,0x9e,0x99,0x49,0xb3,0x54,0x2b,0x7e, + 0x09,0x7a,0x6f,0xab,0x5a,0x04,0x0a,0x11,0x67,0x19,0x6d,0x8c,0x1a,0x12,0x8c,0x7d,0xa8,0x00,0xbe,0xcc,0xc2,0x5c,0x32,0xc1,0x9a,0x45,0xf9,0x56,0x14,0xe3,0xe0,0x0b, + 0x68,0x5f,0xaf,0x62,0xe3,0x41,0x84,0x33,0x34,0x91,0x04,0x4f,0x76,0x00,0x96,0xbf,0x91,0x98,0x32,0xab,0xe6,0x6d,0x6b,0x17,0xc7,0xee,0x43,0x0f,0xd9,0x18,0xfa,0xb1, + 0x71,0x04,0x54,0x0c,0x4b,0x76,0x74,0x0b,0xdf,0xdb,0x73,0xbf,0x64,0x03,0x2e,0x29,0x93,0x8b,0x8f,0x1d,0x44,0x0e,0x7b,0x4c,0x9e,0x07,0xb9,0xa5,0x73,0xf2,0xc6,0x05, + 0x20,0x1f,0x9c,0xc5,0x2e,0x20,0x65,0x08,0x0c,0xa5,0xa2,0x71,0xcc,0xd5,0x3a,0x1a,0xba,0x32,0xdb,0xbd,0x2e,0x8f,0x70,0x87,0x54,0x7a,0xcb,0x68,0x03,0x04,0x81,0x79, + 0xea,0xc2,0x3a,0xa0,0x75,0x5b,0xe6,0x1a,0xe3,0x68,0x76,0xf3,0xb8,0x00,0xf5,0x4c,0x4a,0x86,0xf6,0xf3,0xb2,0x18,0x70,0x38,0xa6,0x41,0xa3,0x3c,0xae,0xb0,0xe7,0x4a, + + 0x6c,0xff,0xa6,0xe0,0xe6,0x61,0x72,0x74,0xa3,0x0b,0x19,0x27,0x79,0xc7,0xdd,0x40,0xc9,0xe6,0x98,0x0a,0xed,0x90,0xf7,0xbe,0xbf,0x1c,0x4d,0x9d,0x30,0x62,0xa6,0xee, + 0x05,0x64,0x2b,0x98,0xd9,0xda,0x2a,0x84,0x9c,0xa9,0x4d,0x5b,0x44,0x14,0x67,0x58,0x2d,0x6e,0xcd,0x4f,0x91,0xd9,0xb3,0xbd,0x46,0x63,0x8f,0xbc,0xcb,0x37,0xbe,0x3f, + 0xbd,0xc1,0xff,0x99,0xe2,0x16,0xd6,0x09,0x31,0x8f,0xd7,0xc6,0xaf,0x86,0xcb,0x47,0xaa,0x31,0x13,0x4a,0x01,0x52,0xe8,0x8d,0xeb,0x5e,0xd6,0x36,0x5d,0x53,0x69,0x6d, + 0x6c,0xff,0xa6,0xe0,0xe6,0x61,0x72,0x74,0xa3,0x0b,0x19,0x27,0x79,0xc7,0xdd,0x40,0xc9,0xe6,0x98,0x0a,0xed,0x90,0xf7,0xbe,0xbf,0x1c,0x4d,0x9d,0x30,0x62,0xa6,0xee, + 0x05,0x64,0x2b,0x98,0xd9,0xda,0x2a,0x84,0x9c,0xa9,0x4d,0x5b,0x44,0x14,0x67,0x58,0x96,0x90,0x32,0xb0,0x6e,0x26,0x4c,0x42,0xb9,0x9c,0x70,0x43,0x34,0xc8,0x41,0xc0, + 0x42,0x3e,0x00,0x66,0x1d,0xe9,0x29,0xf6,0xce,0x70,0x28,0x39,0x50,0x79,0x34,0xb8,0x55,0xce,0xec,0xb5,0xfe,0xad,0x17,0x72,0x14,0xa1,0x29,0xc9,0xa2,0xac,0x96,0x92, +}; + // bign-curve256v1 static const char _curve256v1_name[] = "1.2.112.0.2.0.34.101.45.3.3"; @@ -191,16 +681,302 @@ static const octet _curve256v1_yG[64] = 0x81, 0x76, 0x03, 0xE4, 0x7A, 0xFF, 0x26, 0xA8, }; +#define CURVE256V1_PRECOMP_W 6 +static const octet _curve256v1_precomp_Gs[128 * (2 + (1 << CURVE256V1_PRECOMP_W))] = { + 0xad,0x39,0xac,0x2c,0x86,0xd6,0x73,0xd3,0x0d,0xa0,0xf7,0x30,0x08,0x43,0x74,0x8c,0x5d,0x14,0x32,0x6e,0xa6,0x2f,0xbd,0x87,0x27,0xd0,0x13,0x06,0xf8,0xf6,0x22,0xaa, + 0xee,0xb0,0xf4,0xc5,0xf3,0x5d,0x32,0xfd,0xaf,0x33,0xfc,0x4c,0xd2,0x42,0x1e,0xbe,0xaa,0x4a,0x34,0x57,0x74,0x0e,0x29,0x13,0xea,0x0a,0x1d,0x80,0x14,0x96,0xa9,0xfb, + 0xee,0x3e,0xda,0x6e,0xf6,0x84,0x9a,0xcf,0x61,0x44,0x7b,0xf5,0x40,0xe4,0xdf,0xd0,0xc2,0x71,0xf9,0x2c,0xc3,0x89,0x49,0x2c,0xf0,0x5f,0xd3,0xad,0xb5,0x48,0x63,0xc6, + 0xf4,0x80,0xeb,0x25,0x22,0xc4,0x24,0xc6,0xd0,0x6b,0x80,0x16,0x39,0xb6,0xc7,0xf7,0x32,0xe7,0x1f,0x65,0x54,0x23,0xe6,0x30,0x8b,0x36,0xde,0x2d,0x52,0x73,0xb5,0xc9, + 0xcc,0x1a,0x34,0x30,0x00,0x03,0xa0,0xe3,0xbf,0x25,0x9f,0x75,0xac,0x11,0xe1,0xb7,0x86,0x9b,0x49,0x2f,0x4d,0xc6,0xb1,0x96,0x67,0xbb,0xe8,0x87,0xad,0xd2,0xed,0x80, + 0x07,0xc6,0x8d,0x6c,0xaf,0xaf,0x98,0x76,0xf4,0x97,0xe1,0x4f,0x64,0x98,0x98,0xfa,0x58,0xe1,0x7b,0xdf,0xfd,0xc4,0xe2,0xaa,0x17,0xb5,0xca,0x28,0x8b,0x9b,0x7e,0xc3, + 0x39,0xef,0x7d,0x00,0x5c,0x36,0x09,0x08,0xbd,0xdf,0x74,0xa2,0x42,0x0a,0xda,0xcb,0xa9,0x5f,0xfa,0x42,0x12,0xc4,0xbb,0x0d,0x87,0x8d,0x81,0x3f,0xc9,0xf1,0x53,0x94, + 0xe6,0x5f,0xdb,0xb0,0x34,0x42,0x55,0x7c,0x87,0x74,0xda,0xd1,0x32,0x02,0xf4,0x8e,0xf3,0x77,0x4c,0xa1,0xff,0x26,0x02,0x83,0x98,0x1f,0x31,0x18,0x35,0x5a,0x99,0xdc, + 0x92,0xda,0xff,0xda,0xcd,0xce,0x01,0x03,0x24,0x8a,0xd5,0xc0,0xf0,0x73,0x08,0xd5,0x5f,0x63,0x19,0xe3,0x18,0xe2,0xf5,0xc7,0xd1,0x1e,0xe3,0x43,0xed,0x58,0xed,0x9a, + 0xe2,0xc7,0x49,0x8d,0xe8,0x74,0x9d,0x36,0xb9,0x0a,0x8c,0x65,0xac,0x69,0xea,0x0d,0xad,0x94,0x8f,0xef,0x09,0x16,0xe3,0xfa,0xa3,0x5a,0xfe,0x88,0x31,0x0e,0x67,0xaf, + 0xa4,0x93,0x79,0x9b,0x5c,0xf2,0xe5,0xb8,0xe8,0xce,0xc9,0x68,0xfb,0x8c,0x47,0x83,0x86,0x72,0x53,0xf1,0x3f,0x6e,0x2f,0x41,0xd7,0x83,0xc4,0x6c,0x56,0xf4,0x69,0x68, + 0x8c,0xb8,0xb7,0x39,0xe1,0x27,0x80,0x69,0xf3,0xc7,0x30,0xe0,0x97,0x08,0xf2,0xa1,0x28,0x1e,0xab,0xf3,0xdf,0xff,0x2c,0x3f,0xa7,0x71,0x89,0x6e,0x35,0x6a,0xaf,0x96, + 0x7b,0x9c,0x28,0xf0,0x3c,0x4e,0x0b,0x04,0x29,0x59,0x6a,0x52,0x6e,0x0b,0xe7,0xe6,0x94,0x9e,0x99,0xd0,0x62,0xc9,0xbd,0x30,0x9a,0x42,0xd8,0xe4,0x6e,0x16,0xae,0x2d, + 0x9c,0xcb,0x0d,0x19,0xaa,0x4e,0xb5,0xeb,0xe5,0x8c,0x90,0xf5,0xfa,0x18,0xca,0x5e,0x27,0xb0,0x93,0x66,0x80,0x2e,0xa9,0x01,0xd1,0xeb,0x85,0x6a,0x4a,0x67,0xd2,0xc7, + 0x01,0x73,0x63,0x1a,0x88,0xa2,0x5e,0xf2,0xa2,0x3e,0x7b,0x37,0xac,0xfe,0xfb,0xc5,0xe8,0xcd,0x88,0x19,0x93,0xa2,0x11,0x57,0x85,0xe5,0x83,0x79,0x31,0x71,0x1a,0xa1, + 0x85,0xd3,0x64,0x4e,0xd8,0x43,0xf2,0x20,0xe1,0x4e,0xea,0x5d,0xf9,0xe2,0xff,0xfe,0xc9,0xd0,0x63,0xf8,0x44,0x2a,0x81,0xf3,0xeb,0x79,0xdb,0x59,0x3b,0x07,0x7d,0x90, + 0x2d,0x92,0x0c,0x64,0xcb,0x56,0x8f,0xe7,0xd2,0xf7,0xc7,0xe1,0xe2,0xda,0x27,0x04,0xda,0x5a,0x32,0x50,0x2f,0x13,0x2e,0x3a,0x9b,0x1e,0x04,0x06,0xd4,0xae,0xb0,0x2c, + 0xd2,0x8b,0x9e,0x11,0x4f,0x24,0x67,0xd6,0xa3,0x08,0x88,0x4f,0x2b,0x93,0xd7,0x11,0xf8,0xd8,0xe8,0x9d,0x1d,0x91,0x67,0xd3,0x12,0xc6,0xbd,0x4b,0xbb,0xdb,0xbf,0xce, + 0x6b,0x7c,0x5f,0xae,0xe6,0x77,0xba,0xbe,0x2f,0x63,0x55,0xb8,0xb8,0x2f,0x61,0xc5,0x73,0x10,0xa4,0x6d,0xbb,0xeb,0xb4,0x4f,0x35,0x7b,0xf1,0x98,0x45,0xb5,0x7e,0x56, + 0x25,0xc2,0xd5,0x2e,0x8e,0x47,0xce,0x61,0x6e,0x44,0x1f,0x47,0xe3,0xc4,0xdc,0xe1,0x4d,0x21,0xd8,0xf4,0x0b,0x07,0xd8,0x63,0xdb,0x1c,0xac,0xfb,0x26,0x47,0xe7,0x63, + 0x51,0x00,0x09,0xe1,0xbb,0xd4,0x1c,0x93,0xc3,0x12,0xe9,0x62,0x78,0x61,0x19,0xcf,0x26,0x5f,0x96,0x8e,0xa4,0x99,0x8e,0x04,0x01,0x20,0x0f,0x96,0x57,0x66,0x2f,0x78, + 0xda,0x56,0x4e,0xb0,0xb6,0x60,0xfd,0xb0,0xd6,0x62,0x1e,0x02,0x9e,0x58,0xa4,0xf9,0x20,0xb0,0xf6,0x44,0xfb,0x04,0xdc,0xec,0x61,0x81,0xa9,0xb7,0x2f,0xda,0xad,0xa2, + 0x33,0xd6,0x68,0x0e,0x2e,0x8c,0xfc,0xa4,0xdb,0x32,0x7e,0x46,0xe4,0xdb,0xe8,0x37,0x61,0x4c,0xa7,0x77,0x70,0x61,0x1b,0x8d,0x75,0x57,0xc8,0x93,0xa9,0x68,0xde,0x2b, + 0x66,0xd4,0xcd,0xbd,0xdb,0x12,0xfe,0x59,0xcf,0x33,0xd5,0xaa,0x81,0x43,0x3b,0x45,0x04,0x72,0x8c,0xbb,0x23,0x93,0x9c,0x0a,0xd2,0x51,0xbb,0x61,0xd8,0xb9,0xb4,0x05, + 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******************************************************************************* Загрузка стандартных параметров ******************************************************************************* */ +bool_t bignPrecomp = TRUE; err_t bignStdParams(bign_params* params, const char* name) { if (!memIsValid(params, sizeof(bign_params))) return ERR_BAD_INPUT; + if (strEq(name, _curve96v1_name)) + { + params->l = 96; + memCopy(params->p, _curve96v1_p, 24); + memCopy(params->a, _curve96v1_a, 24); + memCopy(params->seed, _curve96v1_seed, 8); + memCopy(params->b, _curve96v1_b, 24); + memCopy(params->q, _curve96v1_q, 24); + memCopy(params->yG, _curve96v1_yG, 24); + params->precomp.w = bignPrecomp ? CURVE96V1_PRECOMP_W : 0; + params->precomp.Gs = bignPrecomp ? _curve96v1_precomp_Gs : NULL; + return ERR_OK; + } if (strEq(name, _curve128v1_name)) { params->l = 128; @@ -210,6 +986,8 @@ err_t bignStdParams(bign_params* params, const char* name) memCopy(params->b, _curve128v1_b, 32); memCopy(params->q, _curve128v1_q, 32); memCopy(params->yG, _curve128v1_yG, 32); + params->precomp.w = bignPrecomp ? CURVE128V1_PRECOMP_W : 0; + params->precomp.Gs = bignPrecomp ? _curve128v1_precomp_Gs : NULL; return ERR_OK; } if (strEq(name, _curve192v1_name)) @@ -221,6 +999,8 @@ err_t bignStdParams(bign_params* params, const char* name) memCopy(params->b, _curve192v1_b, 48); memCopy(params->q, _curve192v1_q, 48); memCopy(params->yG, _curve192v1_yG, 48); + params->precomp.w = bignPrecomp ? CURVE192V1_PRECOMP_W : 0; + params->precomp.Gs = bignPrecomp ? _curve192v1_precomp_Gs : NULL; return ERR_OK; } if (strEq(name, _curve256v1_name)) @@ -232,6 +1012,8 @@ err_t bignStdParams(bign_params* params, const char* name) memCopy(params->b, _curve256v1_b, 64); memCopy(params->q, _curve256v1_q, 64); memCopy(params->yG, _curve256v1_yG, 64); + params->precomp.w = bignPrecomp ? CURVE256V1_PRECOMP_W : 0; + params->precomp.Gs = bignPrecomp ? _curve256v1_precomp_Gs : NULL; return ERR_OK; } return ERR_FILE_NOT_FOUND; @@ -255,7 +1037,7 @@ err_t bignStart(void* state, const bign_params* params) void* stack; /* вложенный стек */ // pre ASSERT(memIsValid(params, sizeof(bign_params))); - ASSERT(params->l == 128 || params->l == 192 || params->l == 256); + ASSERT(params->l == 96 || params->l == 128 || params->l == 192 || params->l == 256); ASSERT(memIsValid(state, bignStart_keep(params->l, 0))); // определить размерности no = O_OF_B(2 * params->l); @@ -272,7 +1054,8 @@ err_t bignStart(void* state, const bign_params* params) // создать кривую и группу, выполнить минимальную проверку order ec = (ec_o*)state; if (!ecpCreateJ(ec, f, params->a, params->b, stack) || - !ecCreateGroup(ec, 0, params->yG, params->q, no, 1, stack) || + !ecCreateGroup(ec, 0, params->yG, params->q, no, 1, + params->precomp.w, params->precomp.Gs, stack) || wwBitSize(ec->order, n) != params->l * 2 || zzIsEven(ec->order, n)) return ERR_BAD_PARAMS; diff --git a/src/crypto/dstu.c b/src/crypto/dstu.c index 9ced877a..9683ed32 100644 --- a/src/crypto/dstu.c +++ b/src/crypto/dstu.c @@ -491,7 +491,7 @@ static err_t _dstuCreateEc( stack = A + f->no; if (!ec2CreateLD(ec, f, A, params->B, stack) || !ecCreateGroup(ec, params->P, params->P + ec->f->no, params->n, - ec->f->no, params->c, stack)) + ec->f->no, params->c, 0, NULL, stack)) { blobClose(state); return ERR_BAD_PARAMS; diff --git a/src/crypto/g12s.c b/src/crypto/g12s.c index 76c35004..be51cd58 100644 --- a/src/crypto/g12s.c +++ b/src/crypto/g12s.c @@ -653,7 +653,7 @@ static err_t g12sCreateEc( ec = (ec_o*)state; if (!ecpCreateJ(ec, f, params->a, params->b, stack) || !ecCreateGroup(ec, params->xP, params->yP, params->q, - params->l / 8, params->n, stack)) + params->l / 8, params->n, 0, NULL, stack)) { blobClose(state); return ERR_BAD_PARAMS; diff --git a/src/math/ec.c b/src/math/ec.c index b84a5ced..417c93b2 100644 --- a/src/math/ec.c +++ b/src/math/ec.c @@ -6,7 +6,7 @@ \author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}] \created 2014.03.04 \version 2015.11.09 -\license This program is released under the GNU General Public License +\license This program is released under the GNU General Public License version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ @@ -35,14 +35,15 @@ bool_t ecIsOperable2(const ec_o* ec) wwIsValid(ec->A, ec->f->n) && wwIsValid(ec->B, ec->f->n) && ec->d >= 3 && - ec->froma != 0 && - ec->toa != 0 && - ec->neg != 0 && - ec->add != 0 && - ec->adda != 0 && - ec->sub != 0 && - ec->suba != 0 && - ec->dbl != 0 && + ec->froma != 0 && + ec->toa != 0 && + ec->neg != 0 && + ec->nega != 0 && + ec->add != 0 && + ec->adda != 0 && + ec->sub != 0 && + ec->suba != 0 && + ec->dbl != 0 && ec->dbla != 0; } @@ -53,8 +54,9 @@ bool_t ecIsOperable(const ec_o* ec) ec->deep >= ec->f->deep; } -bool_t ecCreateGroup(ec_o* ec, const octet xbase[], const octet ybase[], - const octet order[], size_t order_len, u32 cofactor, void* stack) +bool_t ecCreateGroup(ec_o* ec, const octet xbase[], const octet ybase[], + const octet order[], size_t order_len, u32 cofactor, + size_t w, const octet Gs[], void* stack) { ASSERT(ecIsOperable(ec)); ASSERT(memIsValid(order, order_len)); @@ -62,9 +64,9 @@ bool_t ecCreateGroup(ec_o* ec, const octet xbase[], const octet ybase[], ASSERT(memIsNullOrValid(ybase, ec->f->no)); // корректное описание? order_len = memNonZeroSize(order, order_len); - if (order_len == 0 || + if (order_len == 0 || W_OF_O(order_len) > ec->f->n + 1 || - cofactor == 0 || + cofactor == 0 || (u32)(word)cofactor != cofactor) return FALSE; // установить базовую точку @@ -78,9 +80,13 @@ bool_t ecCreateGroup(ec_o* ec, const octet xbase[], const octet ybase[], return FALSE; // установить порядок и кофактор wwFrom(ec->order, order, order_len); - wwSetZero(ec->order + W_OF_O(order_len), + wwSetZero(ec->order + W_OF_O(order_len), ec->f->n + 1 - W_OF_O(order_len)); ec->cofactor = (word)cofactor; + // предвычисления + ec->precomp_w = w; + ec->precomp_Gs = (const word *)Gs; + //TODO: выделить память под precomp_Gs в ec->descr и форсировать предвычисления, если Gs==NULL // все нормально return TRUE; } @@ -104,8 +110,8 @@ bool_t ecIsOperableGroup(const ec_o* ec) Кратная точка Для определения b = da (d-кратное точки a) используется оконный NAF с -длиной окна w. В функции ecMulWNAF() реализован алгоритм 3.35 из -[Hankerson D., Menezes A., Vanstone S. Guide to Elliptic Curve Cryptography, +длиной окна w. В функции ecMulWNAF() реализован алгоритм 3.35 из +[Hankerson D., Menezes A., Vanstone S. Guide to Elliptic Curve Cryptography, Springer, 2004]. Предварительно рассчитываются малые кратные a: сначала 2a, а затем @@ -122,7 +128,7 @@ Springer, 2004]. 3) c3(l, w) = 1(P <- 2A) + (2^{w-2} - 2)(P <- P + P) + l/(w + 1)(P <- P + P), без учета общего во всех стратегиях слагаемого l(P <- 2P). -Здесь +Здесь - (P <- P + A) -- время работы функций ec->adda / ec->suba; - (A <- 2A) -- время работы каскада (ec->dbla, ec->toa)*; - (A <- A + A) -- время работы каскада (ec->adda, ec->toa)*; @@ -134,29 +140,33 @@ Springer, 2004]. В практических диапазонах размерностей при использовании наиболее эффективных -координат (якобиановых для кривых над GF(p) и Лопеса -- Дахаба для кривых -над GF(2^m)) первые две стратегии являются проигрышными. Реализована только -третья стратегия. +координат (якобиановых для кривых над GF(p) и Лопеса -- Дахаба для кривых +над GF(2^m)) первые две стратегии являются проигрышными. Реализована только +третья стратегия. -Оптимальная длина окна выбирается как решение следующей оптимизационной +Оптимальная длина окна выбирается как решение следующей оптимизационной задачи: (2^{w - 2} - 2) + l / (w + 1) -> min. -\todo Усилить вторую стратегию. Рассчитать малые кратные в проективных -координатах, а затем быстро перейти к аффинным координатам с помощью +\todo Усилить вторую стратегию. Рассчитать малые кратные в проективных +координатах, а затем быстро перейти к аффинным координатам с помощью трюка Монтгомери [Algorithm 11.15 Simultaneous inversion, CohenFrey, p. 209]: U_1 <- Z_1 for t = 2,..., T: U_t <- U_{t-1} Z_t V <- U_T^{-1} - for t = T,..., 2: + for t = T,..., 2: Z_t^{-1} <- V U_{t-1} V <- V Z_t Z_1^{-1} <- V ******************************************************************************* */ +size_t ecW = 3; static size_t ecNAFWidth(size_t l) { +#if 0 + return ecW + 1; +#else if (l >= 336) return 6; else if (l >= 120) @@ -164,9 +174,10 @@ static size_t ecNAFWidth(size_t l) else if (l >= 40) return 4; return 3; +#endif } -bool_t ecMulA(word b[], const word a[], const ec_o* ec, const word d[], +bool_t FAST(ecMulAOrig)(word b[], const word a[], const ec_o* ec, const word d[], size_t m, void* stack) { const size_t n = ec->f->n; @@ -236,16 +247,771 @@ bool_t ecMulA(word b[], const word a[], const ec_o* ec, const word d[], return ecToA(b, t, ec, stack); } -size_t ecMulA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t m) +size_t FAST(ecMulAOrig_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t m) { const size_t naf_width = ecNAFWidth(B_OF_W(m)); const size_t naf_count = SIZE_1 << (naf_width - 2); - return O_OF_W(2 * m + 1) + - O_OF_W(ec_d * n) + - O_OF_W(ec_d * n * naf_count) + + return O_OF_W(2 * m + 1) + + O_OF_W(ec_d * n) + + O_OF_W(ec_d * n * naf_count) + + ec_deep; +} + +bool_t sm_mult_add(word pre[], const word p[], const word dblP + [], const word w, const ec_o* ec, void* stack); +bool_t SAFE(ecMulAOrig)(word b[], const word a[], const ec_o* ec, const word d[], + size_t m, void* stack) +{ + const size_t point_size = ec->f->n * ec->d; + + //window width of recording + //todo resolve width by used sm_mult algorithm and l size + const size_t window_width = ecNAFWidth(B_OF_W(m)); + + //set size of small multiples |{+-1, +-3, ..., +-(2^w - 1)}| = 2^w + const size_t odd_recording_set_size = SIZE_1 << window_width; + + //2^w, required for positive/negative decoding of recording + const word hi_bit = WORD_1 << window_width; + + //number of elements in actual odd recording of d + const size_t odd_recording_size = wwOddRecording_size(m, window_width); + + register int i; + register word w; + register word sign; + + word delta = WORD_1; + word b_flag; + + // переменные в stack + word* odd_recording; /* Odd Recording */ + word* t; /* 2 вспомогательных точки */ + word* pre; /* pre[i] = (odd_recording_size элементов) */ + word* q; /* вспомогательная точка */ + word* temp; /* вспомогательное число */ + // pre + ASSERT(ecIsOperable(ec)); + + // раскладка stack + odd_recording = (word*)stack; + t = odd_recording + W_OF_B(odd_recording_size * (window_width + 1)); + pre = t + 2 * point_size; + q = pre + odd_recording_set_size * point_size; + temp = q + point_size; + stack = temp + m; + + ASSERT(window_width >= 2); + + //t[0] <- 2a + ecDblA(t, a, ec, stack); + + // расчет pre[i]: pre[2i] = pre[2i - 2] + 2a, pre[2i + 1] = -pre[2i], i > 0 + // pre[0] <- a, pre[1] <- -a + sm_mult_add(pre, a, t, window_width, ec, stack); + + // переход к нечетной кратности + delta += d[0] & WORD_1; + zzAddW(temp, d, m, delta); + + //1, 0, -1 + b_flag = wwCmp2(temp, m, ec->order, ec->f->n); + //-1 -> 0 + b_flag = wordEq0M(b_flag, WORD_1); + + //recalculate temp + zzSubW2(temp, m, (delta * 2) & b_flag); + + // save point, current sequence in stack: t[0] <- 2a, t[1] <- -2a, pre[0] = a, pre[1] = -a => t[0]=2a, t[1]=-2a, t[2]=a, t[3]=-a + ecNeg(t + point_size, t, ec, stack); + //if b_flag = 11111111_2 (binary) => need addition, add delta*a, else sub delta*a, delta = 1, 2; + //t += (((delta – 2) & 2) - (~b_flag)) * point_size; + b_flag = ~b_flag; + delta -= 2; + delta &= 2; + delta -= b_flag; + delta *= point_size; + t += delta; + + // расчет Odd_Recording + ASSERT(window_width >= 3); + wwOddRecording(odd_recording, W_OF_B(odd_recording_size * (window_width + 1)), + temp, m, odd_recording_size, window_width); + + // q <- odd_recording[k-1] * a + w = wwGetBits(odd_recording, (odd_recording_size - 1) * (window_width + 1), window_width + 1); + + //calculate index + ASSERT((w & 1) && (w & hi_bit) == 0); + w ^= WORD_1; + //save + wwCopy(q, pre + w * point_size, point_size); + + for (i = odd_recording_size - 2; i >= 0; --i) { + //Q <- 2^odd_recording_width * Q + w = window_width; + while (w) { + ecDbl(q, q, ec, stack); + --w; + } + + w = wwGetBits(odd_recording, i * (window_width + 1), window_width + 1); + // calculate index + sign = w & hi_bit; + w ^= sign; + ASSERT((w & 1) && (w & hi_bit) == 0); + sign >>= window_width; + sign = ~sign; + sign &= WORD_1; + w ^= sign; + // add + ecAdd(q, q, pre + w * point_size, ec, stack); + } + + // correction + ecAdd(q, q, t, ec, stack); + + // cleanup + w = 0; + i = 0; + t = NULL; + sign = 0; + delta = 0; + b_flag = 0; + + // к аффинным координатам + return ecToA(b, q, ec, stack); +} + +size_t SAFE(ecMulAOrig_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t m) +{ + const size_t point_size = n * ec_d; + const size_t odd_recording_width = ecNAFWidth(B_OF_W(m)); + const size_t odd_recording_count = SIZE_1 << odd_recording_width; + const size_t odd_recording_size = wwOddRecording_size(m, odd_recording_width); + + return O_OF_W(W_OF_B(odd_recording_size * (odd_recording_width + 1))) + + O_OF_W(2 * point_size) + + O_OF_W(odd_recording_count * point_size) + + O_OF_W(point_size) + + O_OF_W(m) + ec_deep; } +bool_t FAST(ecMulAPrecompA)(word b[], const word a[], const ec_o* ec, const word d[], + size_t m, void* stack) +{ + const size_t n = ec->f->n; + const size_t naf_width = ecNAFWidth(B_OF_W(m)); + const size_t naf_count = SIZE_1 << (naf_width - 2); + const word naf_hi = WORD_1 << (naf_width - 1); + register size_t naf_size; + register size_t i; + register word w; + // переменные в stack + word* naf; /* NAF */ + word* t; /* вспомогательная точка */ + word* pre; /* pre[i] = (2i + 1)a (naf_count элементов) */ + // pre + ASSERT(ecIsOperable(ec)); + // раскладка stack + naf = (word*)stack; + // расчет NAF + ASSERT(naf_width >= 3); + naf_size = wwNAF(naf, d, m, naf_width); + // d == O => b <- O + if (naf_size == 0) + return FALSE; + t = naf + 2 * m + 1; + if(a == ec->base && ec->precomp_Gs && naf_width <= ec->precomp_w+1) + { + pre = (word *)ec->precomp_Gs + ((2 * n) << (ec->precomp_w - 1)); + stack = t + ec->d * n; + } else + { + pre = t + ec->d * n; + stack = pre + naf_count * 2 * n; + ec->smulsa(pre, t, a, naf_width - 1, ec, stack); + } + + // t <- a[naf[l - 1]] + w = wwGetBits(naf, 0, naf_width); + ASSERT((w & 1) == 1 && (w & naf_hi) == 0); + ecFromA(t, pre + (w >> 1) * 2 * n, ec, stack); + // цикл по символам NAF + i = naf_width; + while (--naf_size) + { + w = wwGetBits(naf, i, naf_width); + if (w & 1) + { + // t <- 2 t + ecDbl(t, t, ec, stack); + // t <- t \pm pre[naf[w]] + if (w & naf_hi) + ecSubA(t, t, pre + ((w ^ naf_hi) >> 1) * 2 * n, ec, stack); + else + ecAddA(t, t, pre + (w >> 1) * 2 * n, ec, stack); + // к следующему разряду naf + i += naf_width; + } + else + ecDbl(t, t, ec, stack), ++i; + } + // очистка + w = 0; + i = 0; + // к аффинным координатам + return ecToA(b, t, ec, stack); +} + +size_t FAST(ecMulAPrecompA_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t m) +{ + //TODO: сделать a_is_base аргументом функции + bool_t a_is_base = FALSE; + const size_t naf_width = ecNAFWidth(B_OF_W(m)); + const size_t naf_count = SIZE_1 << (naf_width - 2); + return O_OF_W(2 * m + 1) + + O_OF_W(ec_d * n) + + (a_is_base ? 0 : O_OF_W(2 * n * naf_count)) + + ec_deep; +} + +static void ecNegPrecompA(word c[], const size_t w, const ec_o* ec) +{ + const size_t na = ec->f->n * 2; + word *nci; + word *ci; + ci = nci = c + (na << (w - 1)); + + for(; nci != c;) + { + nci -= na; + ecNegA(nci, ci, ec); + ci += na; + } +} + +static size_t ecSafeMulAWidth(const size_t l) { + //todo calculate actual breakpoints + if (l <= 256) + { + return 4; + } + return 5; +} + +bool_t SAFE(ecMulAPrecompA)(word b[], const word a[], const ec_o* ec, const word d[], + size_t m, void* stack) +{ + const size_t n = ec->f->n * ec->d; + const size_t na = ec->f->n * 2; + const size_t order_len = ec->f->n + 1; + + /* + * todo если есть предвычисленные малые кратные для точки a, + * то имеет смысл w = max(ecSafeMulAWidth(...), ec->precomp_w); + */ + const size_t w = ecSafeMulAWidth(wwBitSize(ec->order, order_len)); + + + /* Текущая цифра кратности */ + register word t; + /* Индекс малого кратного */ + register size_t v; + /* Флаг нечётности */ + register word f; + /* Флаг четности d */ + register word d_is_even; + /* исправленная кратность dd = ((d & 1) ? d : -d) \mod ec->order */ + word* dd; + /* Текущая кратная точка */ + word *q; + + /* Предвычисленные в следующем порядке малые кратные: + [1-2^w]a, [3-2^w]a, .., [-1]a, [1]a, [3]a, .., [2^w-1]a, */ + word *c; + size_t j, k; + word* check_stack; + + // pre + ASSERT(ecIsOperable(ec)); + ASSERT(3 <= w && w + 1 < B_PER_W); + ASSERT(m <= order_len); //todo добавить этот assert в описание + + // раскладка stack + q = (word*)stack; + dd = q + n; + c = dd + order_len; + check_stack = c + (na << w); +#ifdef _DEBUG + *check_stack = 0xdeadbeef; + stack = (void*)(check_stack + 1); +#else + stack = (void*)check_stack; +#endif + + /* Расчёт малых кратных */ + if(a == ec->base && ec->precomp_Gs && w <= ec->precomp_w) + { + c = (word *)ec->precomp_Gs + (na << (ec->precomp_w-1)) - (na << (w-1)); + } else + { + word *ci; + ci = c + (na << (w - 1)); + + ec->smulsa(ci, NULL, a, w, ec, stack); + ecNegPrecompA(c, w, ec); + } + + /* Переход к нечетной кратности dd = ((d & 1) ? d : -d) \mod ec->order */ + wwSetZero(dd, order_len); + wwCopy(dd, d, m); //todo регулярно ли разрешать m переменной длины, или всегда должно быть m == order_len? + d_is_even = WORD_1 - (d[0] & 1); + zzSetSignMod(dd, dd, ec->order, order_len, d_is_even); + + /* Каноническое разложение a по степеням 2^w: + a = a_0 + a_1 2^w + .. + a_i 2^{wi} + .. + a_k 2^{wk} + 0 <= a_i < 2^w + B_PER_W * order_len <= wk + */ + + k = B_PER_W * order_len; + ASSERT(w < k); + if(k % w != 0) + j = k - (k % w); + else + j = k - w; + + + /* + Индекс, по которому находится необходимое малое кратное в списке предвычисленных малых кратных + t - значение канонического разложения на текущем шаге + f - флаг нечетности значения канонического разложения на предыдущей итерации + */ +#define SMULT_IDX(t, f) ((t >> 1) | (f << (w - 1))) + + /* Старшая часть кратности: a_k + 1.1) a_k - нечётное: + a = .. + a_{k-1} 2^{wk-w} + a_k 2^{wk} + t := a_k + f := 0 + 1.2) a_k - чётное: + a = .. + (a_{k-1} - 2^w) 2^{wk-w} + (a_k + 1) 2^{wk} + t := a_k + 1 + f := -2^w + */ + t = wwGetBits(d, j, k - j); + v = SMULT_IDX(t, 1); + ecFromA(q, c + v * na, ec, stack); + f = t & 1; + + + /* a_{k-1} .. a_1 */ + for (; (j -= w) != 0;) { + /* Q <- 2^(w-1) * Q */ + for(k = w - 1; k--;) + ecDbl(q, q, ec, stack); + + /* Внутренняя часть кратности: a_i + f - флаг нечётности с предыдущего шага + 2.1) a_i - нечётное: + a = .. + a_{i-1} 2^{wi-w} + (a_i + f) 2^{wi} + .. + t := a_i + f + f := 0 + 2.2) a_i - чётное: + a = .. + (a_{i-1} - 2^w) 2^{wi-w} + (a_i + 1 + f) 2^wi + .. + t := a_i + 1 + f + f := -2^w + */ + t = wwGetBits(dd, j, w); + v = SMULT_IDX(t, f); + ec->dbl_adda(q, q, c + v * na, FALSE, ec, stack); + f = t & 1; + } + + /* Q <- 2^(w-1) * Q */ + for(k = w - 1; k--;) + ecDbl(q, q, ec, stack); + + t = wwGetBits(dd, 0, w); + v = SMULT_IDX(t, f); + ec->dbl_adda(q, q, c + v * na, FALSE, ec, stack); + +#undef SMULT_IDX + +#ifdef _DEBUG + ASSERT(*check_stack == 0xdeadbeef); +#endif + + //к аффинным координатам + ecToA(b, q, ec, stack); + //переход к исходной кратности + ec->set_signa(b, b, d_is_even, ec); + //todo очистка остальных переменных + t = v = f = d_is_even = j = k = 0; + //предусмотреть d == 0 + return WORD_1 - wwIsZero(dd, order_len); +} + +size_t SAFE(ecMulAPrecompA_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t ec_order_len) +{ + const size_t na = n * 2; + const size_t w = ecSafeMulAWidth(B_OF_W(ec_order_len)); + + //TODO: сделать a_is_base аргументом функции + bool_t a_is_base = FALSE; + + return O_OF_W(n * ec_d + n + 1 + (na << w)) + ec_deep +#ifdef _DEBUG + + O_OF_W(1) +#endif + ; +} + + +bool_t FAST(ecMulAPrecompJ)(word b[], const word a[], const ec_o* ec, const word d[], + size_t m, void* stack) +{ + const size_t n = ec->f->n; + const size_t naf_width = ecNAFWidth(B_OF_W(m)); + const size_t naf_count = SIZE_1 << (naf_width - 2); + const word naf_hi = WORD_1 << (naf_width - 1); + register size_t naf_size; + register size_t i; + register word w; + // переменные в stack + word* naf; /* NAF */ + word* t; /* вспомогательная точка */ + word* pre; /* pre[i] = (2i + 1)a (naf_count элементов) */ + // pre + ASSERT(ecIsOperable(ec)); + // раскладка stack + naf = (word*)stack; + // расчет NAF + ASSERT(naf_width >= 3); + naf_size = wwNAF(naf, d, m, naf_width); + // d == O => b <- O + if (naf_size == 0) + return FALSE; + t = naf + 2 * m + 1; + if(a == ec->base && naf_width <= ec->precomp_w+1) + { + // precomputed point in affine coordinates + //TODO: convert to jacobian coordinates + ASSERT(0); + pre = (word *)ec->precomp_Gs + ((2 * n) << (ec->precomp_w - 1)); + stack = t + ec->d * n; + } else + { + pre = t + ec->d * n; + stack = pre + naf_count * ec->d * n; + ec->smulsj(pre, t, a, naf_width - 1, ec, stack); + } + // t <- a[naf[l - 1]] + w = wwGetBits(naf, 0, naf_width); + ASSERT((w & 1) == 1 && (w & naf_hi) == 0); + wwCopy(t, pre + (w >> 1) * ec->d * n, ec->d * n); + // цикл по символам NAF + i = naf_width; + while (--naf_size) + { + w = wwGetBits(naf, i, naf_width); + if (w & 1) + { + // t <- 2 t + ecDbl(t, t, ec, stack); + // t <- t \pm pre[naf[w]] + if (w & naf_hi) + ecSub(t, t, pre + ((w ^ naf_hi) >> 1) * ec->d * n, ec, stack); + else + ecAdd(t, t, pre + (w >> 1) * ec->d * n, ec, stack); + // к следующему разряду naf + i += naf_width; + } + else + ecDbl(t, t, ec, stack), ++i; + } + // очистка + w = 0; + i = 0; + // к аффинным координатам + return ecToA(b, t, ec, stack); +} + +size_t FAST(ecMulAPrecompJ_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t m) +{ + //TODO: сделать a_is_base аргументом функции + bool_t a_is_base = FALSE; + const size_t naf_width = ecNAFWidth(B_OF_W(m)); + const size_t naf_count = SIZE_1 << (naf_width - 2); + return O_OF_W(2 * m + 1) + + O_OF_W(ec_d * n) + + O_OF_W(ec_d * n) + + (a_is_base ? 0 : O_OF_W(ec_d * n * naf_count)) + + ec_deep; +} + +static void ecNegPrecompJ(word c[], const size_t w, const ec_o* ec, void* stack) +{ + const size_t nj = ec->f->n * 3; + word *nci; + word *ci; + ci = nci = c + (nj << (w - 1)); + + for(; nci != c;) + { + nci -= nj; + ecNeg(nci, ci, ec, stack); + ci += nj; + } +} + +static size_t ecSafeMulJWidth(const size_t l) { + //todo calculate actual breakpoints + if (l <= 256) + { + return 5; + } + return 6; +} + +bool_t SAFE(ecMulAPrecompJ)(word b[], const word a[], const ec_o* ec, const word d[], + size_t m, void* stack) +{ + const size_t n = ec->f->n * ec->d; + const size_t order_len = ec->f->n + 1; + + const size_t w = ecSafeMulJWidth(wwBitSize(ec->order, order_len)); + + /* Текущая цифра кратности */ + register word t; + /* Индекс малого кратного */ + register size_t v; + /* Флаг нечётности */ + register word f; + /* Флаг четности d */ + register word d_is_even; + /* исправленная кратность dd = ((d & 1) ? d : -d) \mod ec->order */ + word* dd; + /* Текущая кратная точка */ + word* q; + + /* Предвычисленные в следующем порядке малые кратные: + [1-2^w]a, [3-2^w]a, .., [-1]a, [1]a, [3]a, .., [2^w-1]a, */ + word* c; + size_t j, k; + word* check_stack; + + // pre + ASSERT(ecIsOperable(ec)); + ASSERT(3 <= w && w + 1 < B_PER_W); + ASSERT(m <= order_len); //todo добавить этот assert в описание + + // раскладка stack + q = (word*)stack; + dd = q + n; + c = dd + order_len; + check_stack = c + (n << w); +#ifdef _DEBUG + *check_stack = 0xdeadbeef; + stack = (void*)(check_stack + 1); +#else + stack = (void*)check_stack; +#endif + + /* Расчёт малых кратных */ + if (a == ec->base && ec->precomp_Gs && w <= ec->precomp_w) + { + // precomputed point in affine coordinates + //TODO: convert to jacobian coordinates + ASSERT(0); + c = (word*)ec->precomp_Gs + (n << (ec->precomp_w - 1)) - (n << (w - 1)); + } + else + { + word* ci; + ci = c + (n << (w - 1)); + + ec->smulsj(ci, NULL, a, w, ec, stack); + ecNegPrecompJ(c, w, ec, stack); + } + + /* Переход к нечетной кратности dd = ((d & 1) ? d : -d) \mod ec->order */ + wwSetZero(dd, order_len); + wwCopy(dd, d, m); //todo регулярно ли разрешать m переменной длины, или всегда должно быть m == order_len? + d_is_even = WORD_1 - (d[0] & 1); + zzSetSignMod(dd, dd, ec->order, order_len, d_is_even); + + /* Каноническое разложение a по степеням 2^w: + a = a_0 + a_1 2^w + .. + a_i 2^{wi} + .. + a_k 2^{wk} + 0 <= a_i < 2^w + B_PER_W * order_len <= wk + */ + + k = B_PER_W * order_len; + ASSERT(w < k); + if (k % w != 0) + j = k - (k % w); + else + j = k - w; + + + /* + Индекс, по которому находится необходимое малое кратное в списке предвычисленных малых кратных + t - значение канонического разложения на текущем шаге + f - флаг нечетности значения канонического разложения на предыдущей итерации + */ +#define SMULT_IDX(t, f) ((t >> 1) | (f << (w - 1))) + + /* Старшая часть кратности: a_k + 1.1) a_k - нечётное: + a = .. + a_{k-1} 2^{wk-w} + a_k 2^{wk} + t := a_k + f := 0 + 1.2) a_k - чётное: + a = .. + (a_{k-1} - 2^w) 2^{wk-w} + (a_k + 1) 2^wk + t := a_k + 1 + f := -2^w + */ + t = wwGetBits(dd, j, k - j); + v = SMULT_IDX(t, 1); + wwCopy(q, c + v * n, n); + f = t & 1; + + /* a_{k-1} .. a_1 */ + for (; (j -= w) != 0;) { + /* Q <- 2^w * Q */ + for(k = w; k--;) + ecDbl(q, q, ec, stack); + + /* Внутренняя часть кратности: a_i + f - флаг нечётности с предыдущего шага + 2.1) a_i - нечётное: + a = .. + a_{i-1} 2^{wi-w} + (a_i + f) 2^{wi} + .. + t := a_i + f + f := 0 + 2.2) a_i - чётное: + a = .. + (a_{i-1} - 2^w) 2^{wi-w} + (a_i + 1 + f) 2^wi + .. + t := a_i + 1 + f + f := -2^w + */ + t = wwGetBits(dd, j, w); + v = SMULT_IDX(t, f); + ecAdd(q, q, c + v * n, ec, stack); + f = t & 1; + } + + /* Q <- 2^w * Q */ + for(k = w; k--;) + ecDbl(q, q, ec, stack); + + t = wwGetBits(dd, 0, w); + v = SMULT_IDX(t, f); + ecAdd(q, q, c + v * n, ec, stack); + +#undef SMULT_IDX + +#ifdef _DEBUG + ASSERT(*check_stack == 0xdeadbeef); +#endif + + //к аффинным координатам + ecToA(b, q, ec, stack); + //переход к исходной кратности + ec->set_signa(b, b, d_is_even, ec, stack); + //todo очистка остальных переменных + t = v = f = d_is_even = j = k = 0; + //предусмотреть d == 0 + return WORD_1 - wwIsZero(dd, order_len); +} + +size_t SAFE(ecMulAPrecompJ_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t ec_order_len) +{ + //TODO: сделать a_is_base аргументом функции + bool_t a_is_base = FALSE; + const size_t w = ecSafeMulJWidth(B_OF_W(ec_order_len)); + const size_t order_len = n + 1; + + return O_OF_W(n * ec_d) + + + O_OF_W(order_len) + + + O_OF_W((n * ec_d) << w) + + ec_deep +#ifdef _DEBUG + + O_OF_W(1) +#endif + ; +} + + +bool_t ecPrecomp = FALSE; +bool_t ecPrecompA = FALSE; +bool_t ecSafe = TRUE; +bool_t ecMulA(word b[], const word a[], const ec_o* ec, const word d[], + size_t m, void* stack) +{ + return ecSafe + ? (ecPrecomp + ? (ecPrecompA + ? SAFE(ecMulAPrecompA)(b, a, ec, d, m, stack) + : SAFE(ecMulAPrecompJ)(b, a, ec, d, m, stack) + ) + : SAFE(ecMulAOrig)(b, a, ec, d, m, stack) + ): (ecPrecomp + ? (ecPrecompA + ? FAST(ecMulAPrecompA)(b, a, ec, d, m, stack) + : FAST(ecMulAPrecompJ)(b, a, ec, d, m, stack) + ) + : FAST(ecMulAOrig)(b, a, ec, d, m, stack) + ); +} +size_t ecMulA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t m) +{ + return ecSafe + ? (ecPrecomp + ? (ecPrecompA + ? SAFE(ecMulAPrecompA_deep)(n, ec_d, ec_deep, m) + : SAFE(ecMulAPrecompJ_deep)(n, ec_d, ec_deep, m) + ) + : SAFE(ecMulAOrig_deep)(n, ec_d, ec_deep, m) + ): (ecPrecomp + ? (ecPrecompA + ? FAST(ecMulAPrecompA_deep)(n, ec_d, ec_deep, m) + : FAST(ecMulAPrecompJ_deep)(n, ec_d, ec_deep, m) + ) + : FAST(ecMulAOrig_deep)(n, ec_d, ec_deep, m) + ); +} + +/* +Вычисление малых кратных P, -P, 3P, -3P, ... , -(2^w - 1)P +Вычисление через сложение P + 2P, 3P + 2P, ... +На входе pre[0] = P +todo продумать общий интерфейс для вычисления малых кратных +[2n]p - в афинных координатах, +[3n]dblP - в проективных координатах + +*/ +bool_t sm_mult_add(word pre[], const word p[], const word dblP + [], const word w, const ec_o* ec, void* stack) { + const size_t point_size = ec->f->n * ec->d; + + //set size of small multiples |{+-1, +-3, ..., +-(2^w - 1)}| = 2^w + const size_t odd_recording_set_size = SIZE_1 << w; + + register int i; + + ecFromA(pre, p, ec, stack); + ecNeg(pre + point_size, pre, ec, stack); + + + for (i = 1; (unsigned)i <= odd_recording_set_size / 2 - 1; ++i) { + ecAdd(pre + 2 * i * point_size, pre + (2 * i - 2) * point_size, dblP, ec, stack); + ecNeg(pre + (2 * i + 1) * point_size, pre + 2 * i * point_size, ec, stack); + } + +} + /* ******************************************************************************* Имеет порядок? @@ -255,17 +1021,35 @@ size_t ecMulA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t m) bool_t ecHasOrderA(const word a[], const ec_o* ec, const word q[], size_t m, void* stack) { - const size_t n = ec->f->n; + const size_t na = ec->f->n * 2; + const size_t order_len = ec->f->n + 1; + register bool_t f; // переменные в stack word* b = (word*)stack; - stack = b + ec->d * n; - // q a == O? - return !ecMulA(b, a, ec, q, m, stack); + word* qq = b + na; + stack = qq + order_len; + + wwSetZero(qq, order_len); + zzSubW(qq, q, m, WORD_1); + //todo обсудить - добавить поддержку d >= q в SAFE(ecMulA) и вернуться к q a == O? + + // - ((q - 1) a) == a? +#ifdef SAFE_FAST + if (!ecMulA(b, a, ec, qq, m, stack)) + return FALSE; + ecNegA(b, b, ec); + return wwEq(b, a, na); +#else + f = ecMulA(b, a, ec, qq, m, stack); + ecNegA(b, b, ec); + f &= wwEq(b, a, na); + return f; +#endif } size_t ecHasOrderA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t m) { - return O_OF_W(ec_d * n) + ecMulA_deep(n, ec_d, ec_deep, m); + return O_OF_W(2 * n + n + 1) + ecMulA_deep(n, ec_d, ec_deep, m); } /* @@ -283,7 +1067,7 @@ Elliptic Curve Cryptography, Springer, 2004] (interleaving with NAF). ******************************************************************************* */ -bool_t ecAddMulA(word b[], const ec_o* ec, void* stack, size_t k, ...) +bool_t FAST(ecAddMulAOrig)(word b[], const ec_o* ec, void* stack, size_t k, ...) { const size_t n = ec->f->n; register word w; @@ -390,7 +1174,7 @@ bool_t ecAddMulA(word b[], const ec_o* ec, void* stack, size_t k, ...) return ecToA(b, t, ec, stack); } -size_t ecAddMulA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t k, ...) +size_t FAST(ecAddMulAOrig_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t k, ...) { size_t i, ret; va_list marker; @@ -410,3 +1194,238 @@ size_t ecAddMulA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t k, ...) ret += ec_deep; return ret; } + +bool_t FAST(ecAddMulAPrecompA)(word b[], const ec_o* ec, void* stack, size_t k, ...) +{ + const size_t n = ec->f->n; + register word w; + size_t i, naf_max_size = 0; + va_list marker; + // переменные в stack + word* t; /* проективная точка */ + size_t* m; /* длины d[i] */ + size_t* naf_width; /* размеры NAF-окон */ + size_t* naf_size; /* длины NAF */ + size_t* naf_pos; /* позиция в NAF-представлении */ + word** naf; /* NAF */ + word** pre; /* предвычисленные точки */ + // pre + ASSERT(ecIsOperable(ec)); + ASSERT(k > 0); + // раскладка stack + t = (word*)stack; + m = (size_t*)(t + ec->d * n); + naf_width = m + k; + naf_size = naf_width + k; + naf_pos = naf_size + k; + naf = (word**)(naf_pos + k); + pre = naf + k; + stack = pre + k; + // обработать параметры (a[i], d[i], m[i]) + va_start(marker, k); + for (i = 0; i < k; ++i) + { + const word* a; + const word* d; + size_t naf_count, j; + // a <- a[i] + a = va_arg(marker, const word*); + // d <- d[i] + d = va_arg(marker, const word*); + // прочитать m[i] + m[i] = va_arg(marker, size_t); + // подправить m[i] + m[i] = wwWordSize(d, m[i]); + // расчет naf[i] + naf_width[i] = ecNAFWidth(B_OF_W(m[i])); + naf_count = SIZE_1 << (naf_width[i] - 2); + ASSERT(naf_count > 1); + naf[i] = (word*)stack; + stack = naf[i] + 2 * m[i] + 1; + naf_size[i] = wwNAF(naf[i], d, m[i], naf_width[i]); + if (naf_size[i] > naf_max_size) + naf_max_size = naf_size[i]; + naf_pos[i] = 0; + // резервируем память для pre[i] + pre[i] = (word*)stack; + stack = pre[i] + ec->d * n * naf_count; +#if 1 + if(a == ec->base && ec->precomp_Gs && naf_width[i] <= ec->precomp_w+1) + { + pre[i] = (word *)ec->precomp_Gs + ((2 * n) << (ec->precomp_w - 1)); + } else + { + ec->smulsa(pre[i], NULL, a, naf_width[i] - 1, ec, stack); + } +#else + // pre[i][0] <- a[i] + ecFromA(pre[i], a, ec, stack); + // расчет pre[i][j]: t <- 2a[i], pre[i][j] <- t + pre[i][j - 1] + ecDblA(t, pre[i], ec, stack); + ecAddA(pre[i] + ec->d * n, t, pre[i], ec, stack); + for (j = 2; j < naf_count; ++j) + ecAdd(pre[i] + j * ec->d * n, t, pre[i] + (j - 1) * ec->d * n, ec, + stack); +#endif + } + va_end(marker); + // t <- O + ecSetO(t, ec); + // основной цикл + for (; naf_max_size; --naf_max_size) + { + // t <- 2 t + ecDbl(t, t, ec, stack); + // цикл по (a[i], naf[i]) + for (i = 0; i < k; ++i) + { + word naf_hi; + // символы naf[i] не начались? + if (naf_size[i] < naf_max_size) + continue; + // прочитать очередной символ naf[i] + w = wwGetBits(naf[i], naf_pos[i], naf_width[i]); + // обработать символ + naf_hi = WORD_1 << (naf_width[i] - 1); + if (w & 1) + { + // t <- t \pm pre[i][naf[i][w]] + if (w & naf_hi) + ecSubA(t, t, pre[i] + ((w ^ naf_hi) >> 1) * 2 * n, ec, stack); + else + ecAddA(t, t, pre[i] + (w >> 1) * 2 * n, ec, stack); + // к следующему символу naf[i] + naf_pos[i] += naf_width[i]; + } + else + ++naf_pos[i]; + } + } + // очистка + w = 0; + // к аффинным координатам + return ecToA(b, t, ec, stack); +} + +size_t FAST(ecAddMulAPrecompA_deep)(size_t n, size_t ec_d, size_t ec_deep, size_t k, ...) +{ + size_t i, ret; + va_list marker; + ret = O_OF_W(ec_d * n); + ret += 4 * sizeof(size_t) * k; + ret += 2 * sizeof(word**) * k; + va_start(marker, k); + for (i = 0; i < k; ++i) + { + size_t m = va_arg(marker, size_t); + size_t naf_width = ecNAFWidth(B_OF_W(m)); + size_t naf_count = SIZE_1 << (naf_width - 2); + ret += O_OF_W(2 * m + 1); + ret += O_OF_W(ec_d * n * naf_count); + } + va_end(marker); + ret += ec_deep + 40*1024; + return ret; +} + +bool_t ecAddMulA(word b[], const ec_o* ec, void* stack, size_t k, ...) { + word const *a1, *d1, *a2, *d2, *a3, *d3; + size_t m1, m2, m3; + va_list marker; + ASSERT(k == 2 || k == 3); + va_start(marker, k); + a1 = va_arg(marker, const word*); + d1 = va_arg(marker, const word*); + m1 = va_arg(marker, size_t); + a2 = va_arg(marker, const word*); + d2 = va_arg(marker, const word*); + m2 = va_arg(marker, size_t); + if(k == 3){ + a3 = va_arg(marker, const word*); + d3 = va_arg(marker, const word*); + m3 = va_arg(marker, size_t); + } + va_end(marker); + + return (k == 2) + ? (ecPrecomp + ? FAST(ecAddMulAPrecompA)(b, ec, stack, 2, a1, d1, m1, a2, d2, m2) + : FAST(ecAddMulAOrig)(b, ec, stack, 2, a1, d1, m1, a2, d2, m2) + ) + : (ecPrecomp + ? FAST(ecAddMulAPrecompA)(b, ec, stack, 3, a1, d1, m1, a2, d2, m2, a3, d3, m3) + : FAST(ecAddMulAOrig)(b, ec, stack, 3, a1, d1, m1, a2, d2, m2, a3, d3, m3) + ) + ; +} + +size_t ecAddMulA_deep(size_t n, size_t ec_d, size_t ec_deep, size_t k, ...) { + return ecPrecomp + ? FAST(ecAddMulAPrecompA_deep)(n, ec_d, ec_deep, k) + : FAST(ecAddMulAOrig_deep)(n, ec_d, ec_deep, k) + ; +} + +void ecDblAddA(word c[], const word a[], const word b[], bool_t neg_b, const struct ec_o* ec, void* stack) { + //todo SAFE - memcpy b to another buffer and apply (-1)^(1+neg_b) to it? + ecDbl(c, a, ec, stack); + if (neg_b) { + ecSubA(c, c, b, ec, stack); + } + else + { + ecAddA(c, c, b, ec, stack); + } +} + +void ecSmallMultAdd2J(word* c, word d[], const word a[], const size_t w, const ec_o* ec, void* stack) { + const size_t n = ec->f->n * ec->d; + size_t k = SIZE_1 << (w - 1); + if(!d) + { + d = (word*)stack; + stack = (word*)(d + n); + } + ecDblA(d, a, ec, stack); + ecFromA(c, a, ec, stack); + ecAddA(c + n, d, a, ec, stack); + for (--k; --k;) { + c += n; + ecAdd(c + n, d, c, ec, stack); + } +} + +size_t ecSmallMultAdd2J_deep() +{ + //TODO: da? + return 0; +} + +void ecSmallMultAdd2A(word* c, word d[], const word a[], const size_t w, const ec_o* ec, void* stack) { + const size_t n = ec->f->n * ec->d; + const size_t na = ec->f->n * 2; + size_t k = SIZE_1 << (w - 1); + word* p = (word*)stack; + stack = (void*)(p + n); + if(!d) + { + d = (word*)stack; + stack = (void*)(d + na); + } + + ecDblA(p, a, ec, stack); + ecToA(d, p, ec, stack); + wwCopy(c, a, na); + ecFromA(p, a, ec, stack); + for (; --k;) { + c += na; + //TODO: ecAddAA + ecAddA(p, p, d, ec, stack); + ecToA(c, p, ec, stack); + } +} + +size_t ecSmallMultAdd2A_deep(size_t n, size_t ec_d) +{ + return O_OF_W(ec_d * n); +} diff --git a/src/math/ec2.c b/src/math/ec2.c index 61cf7deb..9f596a2e 100644 --- a/src/math/ec2.c +++ b/src/math/ec2.c @@ -6,7 +6,7 @@ \author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}] \created 2012.06.26 \version 2014.07.15 -\license This program is released under the GNU General Public License +\license This program is released under the GNU General Public License version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ @@ -532,6 +532,16 @@ static size_t ec2SubALD_deep(size_t n, size_t f_deep) return O_OF_W(2 * n) + ec2AddALD_deep(n, f_deep); } +static void ec2SetSignA(word b[], const word a[], bool_t neg, const struct ec_o* ec) +{ + //todo SAFE? + if (neg) + ec2SetSignA(b, a, neg, ec); + else + wwCopy(b, a, 2 * ec->f->n); +} + + bool_t ec2CreateLD(ec_o* ec, const qr_o* f, const octet A[], const octet B[], void* stack) { @@ -557,12 +567,17 @@ bool_t ec2CreateLD(ec_o* ec, const qr_o* f, const octet A[], const octet B[], ec->froma = ec2FromALD; ec->toa = ec2ToALD; ec->neg = ec2NegLD; + ec->nega = ec2NegA; ec->add = ec2AddLD; ec->adda = ec2AddALD; ec->sub = ec2SubLD; ec->suba = ec2SubALD; ec->dbl = ec2DblLD; ec->dbla = ec2DblALD; + ec->dbl_adda = ecDblAddA; + ec->set_signa = ec2SetSignA; + ec->smulsa = ecSmallMultAdd2A; + ec->smulsj = ecSmallMultAdd2J; ec->deep = utilMax(8, ec2ToALD_deep(f->n, f->deep), ec2NegLD_deep(f->n, f->deep), diff --git a/src/math/ecp.c b/src/math/ecp.c index c53dd045..fffc16eb 100644 --- a/src/math/ecp.c +++ b/src/math/ecp.c @@ -6,7 +6,7 @@ \author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}] \created 2012.06.26 \version 2016.07.05 -\license This program is released under the GNU General Public License +\license This program is released under the GNU General Public License version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ @@ -25,7 +25,7 @@ version 3. See Copyright Notices in bee2/info.h. Общие положения Ссылки на все реализованные алгоритмы имеются на сайте -http://www.hyperelliptic.org/efd. Там же можно найти соглашения по +http://www.hyperelliptic.org/EFD. Там же можно найти соглашения по обозначению сложности алгоритмов. В этих обозначениях фигурируют следующие формальные выражения: add -- сложение или вычитание \mod p, @@ -52,8 +52,9 @@ version 3. See Copyright Notices in bee2/info.h. #define ecpSeemsOnA(a, ec)\ (zmIsIn(ecX(a), (ec)->f) && zmIsIn(ecY(a, (ec)->f->n), (ec)->f)) +//wwIsZero для случая a == O (особая точка) #define ecpSeemsOn3(a, ec)\ - (ecpSeemsOnA(a, ec) && zmIsIn(ecZ(a, (ec)->f->n), (ec)->f)) + (wwIsZero(ecZ(a, (ec)->f->n), (ec)->f->n) || ecpSeemsOnA(a, ec) && zmIsIn(ecZ(a, (ec)->f->n), (ec)->f)) /* ******************************************************************************* @@ -81,11 +82,11 @@ on a 16-bit Microcomputer. Public Key Cryptography, 1998]. \todo Сравнить dbl-1998-hnm2 с dbl-2001-b, сложность которого 3M +5S + 8add + 1*4 + 2*8 + 1*3. -В функции ecpDblAJ() выполняется удвоение P <- 2A. Реализован алгоритм +В функции ecpDblAJ() выполняется удвоение P <- 2A. Реализован алгоритм mdbl-2007-bl [Bernstein-Lange, 2007]. Сложность алгоритма: 1M + 5S + 7add + 1*8 + 3*2 + 1*3 \approx 6M. -В функции ecpAddJ() выполняется сложение P <- P + P. Реализован алгоритм +В функции ecpAddJ() выполняется сложение P <- P + P. Реализован алгоритм add-2007-bl [Bernstein-Lange, 2007]. Сложность алгоритма: 11M + 5S + 9add + 4*2 \approx 16M. @@ -98,16 +99,16 @@ Guide to Elliptic Curve Cryptography, Springer, 2004]. Сложность алгоритма: 8M + 3S + 6add + 1*2 \approx 11M. -В функции ecpTplJ() выполняется утроение P <- 3P. Реализован алгоритм +В функции ecpTplJ() выполняется утроение P <- 3P. Реализован алгоритм tpl-2007-bl [Bernstein-Lange, 2007]. Сложность алгоритма 5M + 10S + 1*A + 15add + 2*4 + 1*6 + 1*8 + 1*16 + 1*3 \approx 15M. -В функции ecpTplJA3() выполняется утроение P <- 3P для случая A = -3. -Реализован алгоритм tpl-2007-bl-2 [Bernstein-Lange, 2007]. +В функции ecpTplJA3() выполняется утроение P <- 3P для случая A = -3. +Реализован алгоритм tpl-2007-bl-2 [Bernstein-Lange, 2007]. Сложность алгоритма 7M + 7S + 13add + 2*4 + 1*8 + 1*12 + 1*16 + 1*3 \approx 14M. -Целевые функции ci(l), определенные в описании реализации ecMul() в ec.c, +Целевые функции ci(l), определенные в описании реализации ecMul() в ec.c, принимают следующий вид: c1(l) = l/3 11; c2(l, w) = 103 + (2^{w-2} - 2)102 + l/(w + 1) 11; @@ -148,6 +149,7 @@ static bool_t ecpFromAJ(word b[], const word a[], const ec_o* ec, void* stack) } // [2n]b <- [3n]a (A <- P) +//todo регуляризовать, так как используется в SAFE(ecMulA) static bool_t ecpToAJ(word b[], const word a[], const ec_o* ec, void* stack) { const size_t n = ec->f->n; @@ -496,7 +498,7 @@ static void ecpAddJ(word c[], const word a[], const word b[], const ec_o* ec, static size_t ecpAddJ_deep(size_t n, size_t f_deep) { - return O_OF_W(4 * n) + + return O_OF_W(4 * n) + utilMax(2, f_deep, ecpDblJ_deep(n, f_deep)); @@ -692,7 +694,7 @@ static void ecpTplJ(word b[], const word a[], const ec_o* ec, void* stack) qrSqr(ecZ(b, n), ecZ(b, n), ec->f, stack); zmSub(ecZ(b, n), ecZ(b, n), t2, ec->f); zmSub(ecZ(b, n), ecZ(b, n), t7, ec->f); - // t2 <- (t4 + t6)^2 - t5 - t7 - t3 [U] + // t2 <- (t4 + t6)^2 - t5 - t7 - t3 [U] zmAdd(t2, t4, t6, ec->f); qrSqr(t2, t2, ec->f, stack); zmSub(t2, t2, t5, ec->f); @@ -772,7 +774,7 @@ static void ecpTplJA3(word b[], const word a[], const ec_o* ec, void* stack) qrSqr(ecZ(b, n), ecZ(b, n), ec->f, stack); zmSub(ecZ(b, n), ecZ(b, n), t2, ec->f); zmSub(ecZ(b, n), ecZ(b, n), t7, ec->f); - // t2 <- (t4 + t6)^2 - t5 - t7 - t3 [U] + // t2 <- (t4 + t6)^2 - t5 - t7 - t3 [U] zmAdd(t2, t4, t6, ec->f); qrSqr(t2, t2, ec->f, stack); zmSub(t2, t2, t5, ec->f); @@ -802,7 +804,152 @@ size_t ecpTplJA3_deep(size_t n, size_t f_deep) return O_OF_W(7 * n) + f_deep; } -bool_t ecpCreateJ(ec_o* ec, const qr_o* f, const octet A[], const octet B[], +/* +* Формулы описаны в статье https://eprint.iacr.org/2008/051.pdf (стр 7) +* Схема вычисления описана в статье https://eprint.iacr.org/2008/052.pdf (стр 33) со следующей ошибкой: +* Шаг 36 необходимо выполнять после шага 38, так как на шаге 38 значение T5 предполагается равным theta^3, +* в то время как это значение было установлено на шаге 33 и перезаписано на шаге 36 +* +* +*/ +void ecpDblAddA(word c[], const word a[], const word b[], bool_t neg_b, const struct ec_o* ec, void* stack) { + const size_t n = ec->f->n; + + //вспомогательные переменные + word* t1 = ecX(a); + word* t2 = ecY(a, n); + word* t3 = ecZ(a, n); + word* tx = ecX(b); + word* ty = ecY(b, n); + + // переменные в stack + word* t4 = (word*)stack; + word* t5 = t4 + n; + word* t6 = t5 + n; + stack = t6 + n; + + // pre + ASSERT(ecIsOperable(ec) && ec->d == 3); + ASSERT(ecpSeemsOn3(a, ec)); + ASSERT(ecpSeemsOnA(b, ec)); + ASSERT(wwIsSameOrDisjoint(a, c, 3 * n)); + //todo - P != Q? + + wwCopy(t1, ecX(a), n); + wwCopy(t2, ecY(a, n), n); + wwCopy(t3, ecZ(a, n), n); + + //3. t4 <- t3^2 + qrSqr(t4, t3, ec->f, stack); + //4. t5 <- tx * t4 + qrMul(t5, tx, t4, ec->f, stack); + //5. t5 <- t5 - t1 + qrSub(t5, t5, t1, ec->f); + //6. t6 <- t3 + t5 + qrAdd(t6, t3, t5, ec->f); + //7. t6 <- t6^2 + qrSqr(t6, t6, ec->f, stack); + //8. t6 <- t6 - t4 + qrSub(t6, t6, t4, ec->f); + //9. t4 <- t3 * t4 + qrMul(t4, t3, t4, ec->f, stack); + //10. t4 <- ty * t4 + qrMul(t4, ty, t4, ec->f, stack); + //10.1 t4 <- (-1)^neg_b * t4 + zmSetSign(t4, t4, ec->f, neg_b); + //11. t4 <- t4 - t2 + qrSub(t4, t4, t2, ec->f); + //12. t3 <- t5^2 + t3 = ecZ(c, n); + qrSqr(t3, t5, ec->f, stack); + //13. t6 <- t6 - t3 + qrSub(t6, t6, t3, ec->f); + //14. t1 <- t1 * t3 + qrMul(ecX(c), t1, t3, ec->f, stack); + t1 = ecX(c); + //15. t1 <- 4t1 + gfpDouble(t1, t1, ec->f); + gfpDouble(t1, t1, ec->f); + //16. t3 <- t3 * t5 + qrMul(t3, t3, t5, ec->f, stack); + //17. t2 <- t2 * t3 + qrMul(ecY(c, n), t2, t3, ec->f, stack); + t2 = ecY(c, n); + //18. t2 <- 8t2 + gfpDouble(t2, t2, ec->f); + gfpDouble(t2, t2, ec->f); + gfpDouble(t2, t2, ec->f); + //19. t5 <- t4^2 + qrSqr(t5, t4, ec->f, stack); + //20. t3 <- t5 - t3 + qrSub(t3, t5, t3, ec->f); + //21. t3 <- 4t3 + gfpDouble(t3, t3, ec->f); + gfpDouble(t3, t3, ec->f); + //22. t3 <- t3 - t1 + qrSub(t3, t3, t1, ec->f); + //23. t3 <- t3 - t1 + qrSub(t3, t3, t1, ec->f); + //24. t3 <- t3 - t1 + qrSub(t3, t3, t1, ec->f); + //25. t4 <- t3 + t4 + qrAdd(t4, t3, t4, ec->f); + //26. t4 <- t4^2 + qrSqr(t4, t4, ec->f, stack); + //27. t4 <- t5 - t4 + qrSub(t4, t5, t4, ec->f); + //28. t4 <- t4 - t2 + qrSub(t4, t4, t2, ec->f); + //29. t4 <- t4 - t2 + qrSub(t4, t4, t2, ec->f); + //30. t5 <- t3^2 + qrSqr(t5, t3, ec->f, stack); + //31. t4 <- t4 + t5 + qrAdd(t4, t4, t5, ec->f); + //32. t1 <- t1 * t5 + qrMul(t1, t1, t5, ec->f, stack); + //33. t5 <- t3 * t5 + qrMul(t5, t3, t5, ec->f, stack); + //34. t3 <- t3 * t6 + qrMul(t3, t3, t6, ec->f, stack); + //35. t2 <- t2 * t5 + qrMul(t2, t2, t5, ec->f, stack); + //шаг 36 после шага 38 + //37. t6 <- t4^2 + qrSqr(t6, t4, ec->f, stack); + //38. t6 <- t6 - t5 + qrSub(t6, t6, t5, ec->f); + //36. t5 <- 3t1 + gfpDouble(t5, t1, ec->f); + qrAdd(t5, t5, t1, ec->f); + //39. t5 <- t5 - t6 + qrSub(t5, t5, t6, ec->f); + //40. t4 <- t4 * t5 + qrMul(t4, t4, t5, ec->f, stack); + //41. t2 <- t4 - t2 + qrSub(t2, t4, t2, ec->f); + //42. t1 <- t1 - t5 + qrSub(t1, t1, t5, ec->f); +} + +size_t ecpDblAddA_deep(size_t n, size_t f_deep) { + return O_OF_W(3 * n) + f_deep; +} + +void ecpSetSignA(word b[], const word a[], bool_t neg, const struct ec_o* ec) { + const size_t n = ec->f->n; + // pre + ASSERT(ecIsOperable(ec)); + ASSERT(ecpSeemsOnA(a, ec)); + ASSERT(wwIsSameOrDisjoint(a, b, 2 * n)); + // (xb, yb) <- (xa, -1^(neg + 1) * ya) + qrCopy(ecX(b), ecX(a), ec->f); + zmSetSign(ecY(b, n), ecY(a, n), ec->f, neg); +} + + +bool_t ecpDivp = TRUE; +bool_t ecpCreateJ(ec_o* ec, const qr_o* f, const octet A[], const octet B[], void* stack) { register bool_t bA3; @@ -810,8 +957,8 @@ bool_t ecpCreateJ(ec_o* ec, const qr_o* f, const octet A[], const octet B[], // pre ASSERT(memIsValid(ec, sizeof(ec_o))); ASSERT(gfpIsOperable(f)); - ASSERT(memIsValid(A, f->no)); - ASSERT(memIsValid(B, f->no)); + ASSERT(memIsValid(A, f->no)); + ASSERT(memIsValid(B, f->no)); // обнулить memSetZero(ec, sizeof(ec_o)); // зафикисровать размерности @@ -837,6 +984,7 @@ bool_t ecpCreateJ(ec_o* ec, const qr_o* f, const octet A[], const octet B[], ec->froma = ecpFromAJ; ec->toa = ecpToAJ; ec->neg = ecpNegJ; + ec->nega = ecpNegA; ec->add = ecpAddJ; ec->adda = ecpAddAJ; ec->sub = ecpSubJ; @@ -844,6 +992,10 @@ bool_t ecpCreateJ(ec_o* ec, const qr_o* f, const octet A[], const octet B[], ec->dbl = bA3 ? ecpDblJA3 : ecpDblJ; ec->dbla = ecpDblAJ; ec->tpl = bA3 ? ecpTplJA3 : ecpTplJ; + ec->dbl_adda = ecpDblAddA; + ec->set_signa = ecpSetSignA; + ec->smulsa = ecpDivp ? ecpSmallMultDivpA : ecSmallMultAdd2A; + ec->smulsj = ecpDivp ? ecpSmallMultDivpJ : ecSmallMultAdd2J; ec->deep = utilMax(9, ecpToAJ_deep(f->n, f->deep), ecpAddJ_deep(f->n, f->deep), @@ -852,7 +1004,13 @@ bool_t ecpCreateJ(ec_o* ec, const qr_o* f, const octet A[], const octet B[], ecpSubAJ_deep(f->n, f->deep), bA3 ? ecpDblJA3_deep(f->n, f->deep) : ecpDblJ_deep(f->n, f->deep), ecpDblAJ_deep(f->n, f->deep), - bA3 ? ecpTplJA3_deep(f->n, f->deep) : ecpTplJ_deep(f->n, f->deep)); + bA3 ? ecpTplJA3_deep(f->n, f->deep) : ecpTplJ_deep(f->n, f->deep), + ecpDblAddA_deep(f->n, f->deep) + ); + ec->deep += utilMax(2, + ecpDivp ? ecpSmallMultDivpA_deep(TRUE, 6, f->n, f->deep) : ecSmallMultAdd2A_deep(f->n, ec->deep), + ecpDivp ? ecpSmallMultDivpJ_deep(TRUE, 6, f->n, f->deep) : ecSmallMultAdd2J_deep() + ); // настроить ec->hdr.keep = sizeof(ec_o) + O_OF_W(5 * f->n + 1); ec->hdr.p_count = 6; @@ -885,7 +1043,7 @@ size_t ecpCreateJ_deep(size_t n, size_t f_deep) /* ******************************************************************************* -Свойства кривой +Свойства кривой ******************************************************************************* */ @@ -903,7 +1061,7 @@ bool_t ecpIsValid(const ec_o* ec, void* stack) if (!ecIsOperable2(ec) || !gfpIsValid(ec->f, stack) || ec->deep < ec->f->deep || - !zmIsIn(ec->A, ec->f) || + !zmIsIn(ec->A, ec->f) || !zmIsIn(ec->B, ec->f)) return FALSE; // t1 <- 4 A^3 @@ -926,7 +1084,7 @@ bool_t ecpIsValid(const ec_o* ec, void* stack) size_t ecpIsValid_deep(size_t n, size_t f_deep) { - return O_OF_W(3 * n) + + return O_OF_W(3 * n) + utilMax(2, f_deep, gfpIsValid_deep(n)); @@ -976,8 +1134,8 @@ bool_t ecpSeemsValidGroup(const ec_o* ec, void* stack) size_t ecpSeemsValidGroup_deep(size_t n, size_t f_deep) { - return O_OF_W(4 * n + 3) + - utilMax(2, + return O_OF_W(4 * n + 3) + + utilMax(2, ecpIsOnA_deep(n, f_deep), zzSqr_deep(n)); } @@ -1073,7 +1231,7 @@ void ecpNegA(word b[], const word a[], const ec_o* ec) // pre ASSERT(ecIsOperable(ec)); ASSERT(ecpSeemsOnA(a, ec)); - ASSERT(wwIsSameOrDisjoint(a, b, 3 * n)); + ASSERT(wwIsSameOrDisjoint(a, b, 2 * n)); // (xb, yb) <- (xa, -ya) qrCopy(ecX(b), ecX(a), ec->f); zmNeg(ecY(b, n), ecY(a, n), ec->f); @@ -1103,7 +1261,7 @@ bool_t ecpAddAA(word c[], const word a[], const word b[], const ec_o* ec, else { // ya != yb или yb == 0 => a == -b => a + b == O - if (qrCmp(ecY(a, n), ecY(b, n), ec->f) != 0 || + if (qrCmp(ecY(a, n), ecY(b, n), ec->f) != 0 || qrIsZero(ecY(b, n), ec->f)) return FALSE; // t2 <- 3 xa^2 + A @@ -1210,7 +1368,7 @@ void ecpSWU(word b[], const word a[], const ec_o* ec, void* stack) word* x1 = t + n; word* x2 = x1 + n; word* y = x2 + n; - word* s = y + n; + word* s = y + n; stack = s + n; // pre ASSERT(ecIsOperable(ec)); @@ -1223,7 +1381,7 @@ void ecpSWU(word b[], const word a[], const ec_o* ec, void* stack) // s <- p - 2 wwCopy(s, ec->f->mod, n); zzSubW2(s, n, 2); - // x1 <- -B(1 + t + t^2)(A(t + t^2))^{p - 2} + // x1 <- -B(1 + t + t^2)(A(t + t^2))^{p - 2} qrSqr(x2, t, ec->f, stack); qrAdd(x2, x2, t, ec->f); qrMul(x1, x2, ec->A, ec->f, stack); @@ -1262,8 +1420,1052 @@ void ecpSWU(word b[], const word a[], const ec_o* ec, void* stack) size_t ecpSWU_deep(size_t n, size_t f_deep) { - return O_OF_W(5 * n) + + return O_OF_W(5 * n) + utilMax(2, f_deep, qrPower_deep(n, n, f_deep)); -} \ No newline at end of file +} + +#if 0 +/* +******************************************************************************* + +Вычисление малых кратных в афинных координатах с помощью полиномов деления. + +Входная точка [2n]a в афинных коордитанах + +w - ширина окна. Вообще говоря, зависит только от стойкости. (Сохранить значеие в кривой ec_o для предвычисленных малых кратных?) + +sm_mults - выходной массив малых кратных X3,Y3,X5,Y5... в афинных координатах + +\safe алгоритм регулярен + +******************************************************************************* +*/ +bool_t smMultsA_divPoly(word* sm_mults, const word a[], const word w, const ec_o* ec, void* stack) +{ + //todo проверки? + const word ec_f_n = ec->f->n; + const word aff_point_size = ec->f->n * 2; + size_t i; + size_t t; + word* x = ecX(a); + word* y = ecY(a, ec->f->n); + word* xx; + word* bx; + word* aa; + word* bb; + word* ax; + word* xxx; + word* dblYSq; + + word* tmp; + word* tmp2; + + word* W; //полиномы деления начиная с третьего, W[0] = W_3 + word* WW; //квадраты полиномов деления начиная c третьего + word* WWd2; //произведения W_{n}W_{n+2}, c n = 1 + word* WWd2_dblYSq; //произведения (2y)^2 W_{n}W_{n+2}, начиная с n = 2 + word* WWd2_dblYPow4; //значения (2y)^4 W_{n}W_{n+2}, начиная с n = 2 + word* WW_odd_inv; //обратные к нечетным квадратам полиномов деления: W_{n}^{-2}, n = 3, 5, ... + + const int W_idx_shift = -3; + const int WW_idx_shift = -3; + const int WWd2_idx_shift = -1; + const int WWd2_dblYSq_idx_shift = -2; + const int WWd2_dblYPow4_idx_shift = -2; + + + //раскладка в stack + xx = (word*)stack; + bx = xx + ec->f->n; + aa = bx + ec->f->n; + bb = aa + ec->f->n; + ax = bb + ec->f->n; + xxx = ax + ec->f->n; + dblYSq = xxx + ec->f->n; + tmp = dblYSq + ec->f->n; + tmp2 = tmp + ec->f->n; + + //todo посчитать количество элементов + W = tmp2 + ec->f->n * ; + WW = W + ec->f->n*; + WWd2 = WW + ec->f->n* ; + WWd2_dblYSq = WWd2 + ec->f->n* ; + WWd2_dblYPow4 = WWd2_dblYSq + ec->f->n* ; + WW_odd_inv = WWd2_dblYPow4 + ec->f->n*; + stack = WW_odd_inv + ec->f->n*; + + //Вспомогательные значения + qrSqr(xx, x, ec->f, stack); + qrMul(bx, ec->B, x, ec->f, stack); + qrSqr(aa, ec->A, ec->f, stack); + qrSqr(bb, ec->B, ec->f, stack); + qrMul(ax, ec->A, x, ec->f, stack); + qrMul(xxx, xx, x, ec->f, stack); + + gfpDouble(dblYSq, y, ec->f); + qrSqr(dblYSq, dblYSq, ec->f, stack); + + //Вычислить W_3 = 3 (x^2 + a)^2 − 4 (a^2 − 3 bx) + qrAdd(tmp, xx, ec->A, ec->f); // x^2 + a + qrSqr(tmp, tmp, ec->f, stack); // (x^2 + a)^2 + gfpDouble(tmp2, tmp, ec->f); // 2 (x^2 + a)^2 + qrAdd(W, tmp, tmp2, ec->f); // 3 (x^2 + a)^2 + + gfpDouble(tmp, bx, ec->f); //2 bx + qrAdd(tmp, tmp, bx, ec->f); //3 bx + qrSub(tmp, aa, tmp, ec->f); //a^2 − 3 bx + gfpDouble(tmp, tmp, ec->f); //2 (a^2 − 3 bx) + gfpDouble(tmp, tmp, ec->f); //4 (a^2 − 3 bx) + + qrSub(W, W, tmp, ec->f); //W_3 = 3 (x^2 + a)^2 − 4 (a^2 − 3 bx) + + //Вычислить W_4 + qrSqr(W + ec_f_n, xxx, ec->f, stack); //(x^3)^2 + + gfpDouble(tmp, xx, ec->f); //2 x^2 + gfpDouble(tmp, tmp, ec->f); //4 x^2 + qrAdd(tmp, tmp, xx, ec->f); //5 x^2 + qrSub(tmp, tmp, ec->A, ec->f); //5 x^2 - a + qrMul(tmp, bx, tmp, ec->f, stack); //bx (5 x^2 - a) + gfpDouble(tmp, tmp, ec->f); //2 bx (5 x^2 - a) + gfpDouble(tmp, tmp, ec->f); //4 bx (5 x^2 - a) + + qrAdd(W + ec->f->n, W + ec_f_n, tmp, ec->f); //(x^3)^2 + 4 bx (5 x^2 - a) + + qrSub(tmp, xxx, ax, ec->f); //x^3 - ax + qrMul(tmp, tmp, ax, ec->f, stack); //ax (x^3 - ax) + gfpDouble(tmp2, tmp, ec->f); //2 ax (x^3 - ax) + gfpDouble(tmp2, tmp2, ec->f); //4 ax (x^3 - ax) + qrAdd(tmp, tmp, tmp2, ec->f); //5 ax (x^3 - ax) + + qrAdd(W + ec_f_n, W + ec_f_n, tmp, ec->f); //(x^3)^2 + 4 bx (5 x^2 - a) + 5 ax (x^3 - ax) + + gfpDouble(tmp, bb, ec->f); //2 b^2 + gfpDouble(tmp, tmp, ec->f); //4 b^2 + gfpDouble(tmp, tmp, ec->f); //8 b^2 + + qrSub(W + ec_f_n, W + ec_f_n, tmp, ec->f); //(x^3)^2 + 4 bx (5 x^2 - a) + 5 ax (x^3 - ax) - 8 b^2 + + qrMul(tmp, aa, a, ec->f, stack); //a^3 + + qrSub(W + ec_f_n, W + ec_f_n, tmp, ec->f); //(x^3)^2 + 4 bx (5 x^2 - a) + 5 ax (x^3 - ax) - 8 b^2 - a^3 + + gfpDouble(W + ec_f_n, W + ec_f_n, ec->f); //W_4 = 2 ((x^3)^2 + 4 bx (5 x^2 - a) + 5 ax (x^3 - ax) - 8 b^2 - a^3) + + + //(2y)^2 + gfpDouble(dblYSq, y, ec->f); + qrSqr(dblYSq, dblYSq, ec->f, stack); + + //(W_3)^2 + qrSqr(WW, W, ec->f, stack); + + //(W_4)^2 + qrSqr(WW + ec_f_n, W + ec_f_n, ec->f, stack); + + //W_{1}W_{3} = W{3} + qrCopy(WWd2, W, ec->f); + + //W_{2}W_{4} = W{4} + qrCopy(WWd2 + ec_f_n, w + ec_f_n, ec->f); + + //[(2y)2W2W4] + qrMul(WWd2_dblYSq, WWd2 + ec_f_n, dblYSq, ec->f, stack); + + //[(2y)4W2W4] + qrMul(WWd2_dblYPow4, WWd2_dblYSq, dblYSq, ec->f, stack); + + //[W5] ← [(2y)4W2W4] −[W1W3] ·[W_{3}^2] + qrMul(tmp, WWd2, WW, ec->f, stack); + qrSub(W + 2 * ec_f_n, WWd2_dblYPow4, tmp, ec->f, stack); + + //[W5 ^2] ←([W5])2 + qrSqr(WW + 2 * ec_f_n, W + 2 * ec_f_n, ec->f, stack); + + //i 3 = .. 2^{w-1} + t = (SIZE_1 << (w - 1)); + for (i = 3; i <= t; ++i) + { + //[WnWn+2] ← (([Wn] + [Wn+2])^2 − [W2n] −[W2 n + 2]) / 2 + qrAdd(tmp, W + ec_f_n * (i + W_idx_shift), W + ec_f_n * (i + W_idx_shift + 2), ec->f, stack); + qrSqr(tmp, tmp, ec->f, stack); + qrSub(tmp, tmp, WW + ec_f_n * (i + WW_idx_shift), ec->f); + qrSub(tmp, tmp, WW + ec_f_n * (i + WW_idx_shift + 2), ec->f); + gfpHalf(WWd2 + ec_f_n * (i-1), tmp, ec->f); + + if (i == 3) + { + //[W2n] ← [WnWn+2] − [Wn−2Wn] · [W2 n + 1]: 1M + 1A + qrMul(tmp, WWd2 + ec_f_n * (i + WWd2_idx_shift - 2), WW + ec_f_n * (i + WW_idx_shift + 1), ec->f, stack); + qrSub(W + ec_f_n * (2 * i + W_idx_shift), WWd2 + ec_f_n * (i - 1), tmp, ec->f, stack); + } + else + { + //[W2n] ← [WnWn+2] · [W2 n−1] −[Wn−2Wn] ·[W2 n + 1] + qrMul(tmp, WWd2 + ec_f_n * (i + WWd2_idx_shift - 2), WW + ec_f_n * (i + WW_idx_shift + 1), ec->f, stack); + qrMul(tmp2, WWd2 + ec_f_n * (i + WWd2_idx_shift), WW + ec_f_n * (i + WW_idx_shift - 1), ec->f, stack); + qrSub(W + ec_f_n * (2 * i + W_idx_shift), tmp2, tmp, ec->f, stack); + } + + //i нечетное? + if (i & 1 == 1) + { + //[W2n+1] ← [WnWn+2] · [W2 n] − [(2y)4Wn−1Wn + 1] ·[W2 n + 1] + qrMul(tmp, WWd2 + ec_f_n * (i + WWd2_idx_shift), WW + ec_f_n * (i + WW_idx_shift), ec->f, stack); + qrMul(tmp2, WWd2_dblYPow4 + ec_f_n * (i + WWd2_dblYPow4_idx_shift - 1), WW + ec_f_n * (i + WW_idx_shift + 1), ec->f, stack); + qrSub(W + ec_f_n * (2*i + 1 + W_idx_shift), tmp, tmp2, ec->f); + } + else + { + //(a) [(2y)2WnWn + 2] ←[(2y)2] ·[WnWn + 2]: 1M + qrMul(WWd2_dblYSq + ec_f_n * (i + WWd2_dblYSq_idx_shift), dblYSq, WWd2 + ec_f_n * (i + WWd2_idx_shift), ec->f, stack); + + //(b)[(2y)4WnWn + 2] ←[(2y)2] ·[(2y)2WnWn + 2]: 1M + qrMul(WWd2_dblYPow4 + ec_f_n * (i + WWd2_dblYPow4_idx_shift), dblYSq, WWd2_dblYSq + ec_f_n * (i + WWd2_dblYSq_idx_shift), ec->f, stack); + + //(c) [W2n+1] ← [(2y)4WnWn + 2] ·[W2n] −[Wn−1Wn + 1] ·[W2 n + 1]: 2M + 1A + qrMul(tmp, WWd2_dblYPow4 + ec_f_n * (i + WWd2_dblYPow4_idx_shift), WW + ec_f_n * (i + WW_idx_shift), ec->f, stack); + qrMul(tmp2, WWd2 + ec_f_n * (i - 1 + WWd2_idx_shift), WW + ec_f_n * (i + WW_idx_shift + 1), ec->f, stack); + qrSub(W + ec_f_n * (2 * i + 1 + W_idx_shift), tmp, tmp2, ec->f); + } + + if (i != t) + { + //[W2 2n + 1] ←([W2n + 1])2 + qrSqr(WW + ec_f_n * (2 * i + 1 + WW_idx_shift), W + ec_f_n * (2 * i + 1 + W_idx_shift), ec->f, stack); + } + } + + //обратить квадраты нечетных малых кратных + for (i = 0; i < t; ++i) + { + //WW_odd_inv <- W_n^2, n = 3, 5, ... 2^w - 1 + qrCopy(WW_odd_inv + ec_f_n * i, WW + ec_f_n * (i * 2 + 3 + WW_idx_shift), ec->f); + } + //WW_odd_inv <- W_n^(-2), n = 3, 5, ... 2^w - 1 + qrMontInv(WW_odd_inv, WW_odd_inv, t - 1, ec->f, stack); + + for (int i = 3; i <= t + 1; i += 2) + { + //[X'n] ← x −[(2y)2 Wn−1Wn + 1] ·[W−2 n] + qrMul(tmp, WWd2_dblYSq + ec_f_n * (i - 1 + WWd2_dblYSq_idx_shift), WW_odd_inv + ec_f_n * ((i - 3) / 2), ec->f, stack); + qrSub(ecX(sm_mults + aff_point_size * ((i - 3) / 2)), x, tmp, ec->f); + } + + for (int i = t + 3; i <= t * 2 - 1; i += 2) + { + //tmp ←(([Wn−1] + [Wn + 1])2 −[W2 n−1] −[W2n + 1]) / 2 + qrAdd(tmp, W + ec_f_n * (i - 1 + W_idx_shift), W + ec_f_n * (i + 1 + W_idx_shift), ec->f, stack); + qrSqr(tmp, tmp, ec->f, stack); + qrSub(tmp, tmp, WW + ec_f_n * (i - 1 + WW_idx_shift), ec->f); + qrSub(tmp, tmp, WW + ec_f_n * (i + 1 + WW_idx_shift ), ec->f); + gfpHalf(tmp, tmp, ec->f); + + //[X'n] ← x −[(2y)2] · tmp ·[W−2 n] + qrMul(tmp, tmp, WW_odd_inv + ec_f_n * ((i - 3) / 2), ec->f, stack); + qrMul(tmp, dblYSq, tmp, ec->f, stack); + qrSub(ecX(sm_mults + aff_point_size * ((i - 3) / 2)), x, tmp, ec->f); + } + + for (i = 3; i <= t - 1; i += 2) + { + //. [Y'n] ← y ·[W2n] ·([W−2 n])2 + qrSqr(tmp, WW_odd_inv + ec_f_n * ((i - 3) / 2), ec->f, stack); + qrMul(tmp, tmp, W + ec_f_n * (2 * i + W_idx_shift), ec->f, stack); + qrMul(ecY(sm_mults + aff_point_size * ((i - 3) / 2), ec_f_n), tmp, y, ec->f, stack); + } + + for (i = t + 1; i <= t * 2 - 3; i += 2) + { + //[WnWn+2] ← (([Wn] + [Wn+2])^2 − [W2n] −[W2 n + 2]) / 2 + qrAdd(tmp, W + ec_f_n * (i + W_idx_shift), W + ec_f_n * (i + W_idx_shift + 2), ec->f, stack); + qrSqr(tmp, tmp, ec->f, stack); + qrSub(tmp, tmp, WW + ec_f_n * (i + WW_idx_shift), ec->f); + qrSub(tmp, tmp, WW + ec_f_n * (i + WW_idx_shift + 2), ec->f); + gfpHalf(WWd2 + ec_f_n * (i - 1), tmp, ec->f); + + //tmp2 ← [WnWn+2] · [W2 n−1] −[Wn−2Wn] ·[W2 n + 1] + qrMul(tmp, WWd2 + ec_f_n * (i + WWd2_idx_shift - 2), WW + ec_f_n * (i + WW_idx_shift + 1), ec->f, stack); + qrMul(tmp2, WWd2 + ec_f_n * (i + WWd2_idx_shift), WW + ec_f_n * (i + WW_idx_shift - 1), ec->f, stack); + qrSub(tmp2, tmp2, tmp, ec->f, stack); + + //[Y'n] ← y · tmp2 ·([W−2 n])2 + qrSqr(tmp, WW_odd_inv + ec_f_n * ((i - 3) / 2), ec->f, stack); + qrMul(tmp, tmp, tmp2, ec->f, stack); + qrMul(ecY(sm_mults + aff_point_size * ((i - 3) / 2), ec_f_n), tmp, y, ec->f, stack); + } + + i = t * 2 - 1; + //[Y'2w−1] ← y·([W2w−1]·[W2w + 1]·[W2 2w−2]−[W2w−3W2w−1]·[W2 2w])·([W−2 2w−1])2 + + //tmp <- [W2w−1]·[W2w + 1]·[W2 2w−2] + qrMul(tmp, W + ec_f_n * (i + W_idx_shift), W + ec_f_n * (i + W_idx_shift + 2), ec->f, stack); + qrMul(tmp, tmp, WW + ec_f_n * (i + WW_idx_shift - 1), ec->f, stack); + + //tmp2 <-[W_2w−3 W_2w−1]·[W2 2w] + qrMul(tmp2, WWd2 + ec_f_n * (i + WWd2_idx_shift - 2), WW + ec_f_n * (i + WW_idx_shift + 1), ec->f, stack); + + //tmp <- ([W 2w−1]·[W 2w + 1]·[W2 2w−2]−[W 2w−3 W 2w−1]·[W2 2w]) = tmp - tmp2 + qrSub(tmp, tmp, tmp2, ec->f); + + //[Y'2w−1] ← y·tmp·tmp2 + qrMul(tmp, tmp, tmp2, ec->f, stack); + qrMul(ecY(sm_mults + aff_point_size * ((i - 3) / 2), ec_f_n), tmp, y, ec->f, stack); + + //todo cleanup +} +#endif + +#ifdef _DEBUG +#define stack_walloc(p, k) \ + do { \ + *(word*)(stack) = (word)(k); \ + *((word*)(stack) + 1) = 0xfeedbeef; \ + (p) = (word*)(stack) + 2; \ + *((word*)(stack) + 2) = 0xbeeffeed; \ + stack = (word*)(stack) + 3 + (k); \ + *((word*)(stack) - 2) = 0xfeedbeef; \ + *((word*)(stack) - 1) = 0xbeeffeed; \ + } while(0) +#define stack_wfree(p) \ + do { \ + ASSERT(*((word*)(p) - 1) == 0xfeedbeef); \ + ASSERT(*((word*)(p)) != 0xbeeffeed); \ + ASSERT(stack == ((word*)(p) + 1 + (size_t)*((word*)(p)-2))); \ + ASSERT(*((word*)(p) + (size_t)*((word*)(p)-2) - 1) != 0xfeedbeef); \ + ASSERT(*((word*)(p) + (size_t)*((word*)(p)-2)) == 0xbeeffeed); \ + stack = (word*)(p) - 2; \ + } while(0) +#else +#define stack_walloc(p, k) \ + do { \ + (p) = (word*)(stack); \ + stack = (word*)(stack) + (k); \ + } while(0) +#define stack_wfree(p) +#endif + +void ecpSmallMultDivpA(word* c, word da[], const word a[], const size_t w, const ec_o* ec, void* stack) +{ + // размер координаты + const size_t n = ec->f->n; + // размер аффинной точки + const size_t na = n * 2; + // координата x базовой точки + const word* x = ecX(a); + // координата y базовой точки + const word* y = ecY(a, n); + + size_t i; + + // Основные этапы алгоритма: + // 0) Wᵢ, i=3,4,5 + // 1) for i=3,4..2ʷ⁻¹ + // 2) Wᵢ⁻², i=3,5..2ʷ-1 + // 3) 2P + // 4*) for i=3,5..2ʷ⁻¹-1 + // 4) for i=3,5..2ʷ⁻¹+1 + // 5) for i=2ʷ⁻¹+1,2ʷ⁻¹+3..2ʷ-1 + // 5*) for i=2ʷ⁻¹+3,2ʷ⁻¹+5..2ʷ-1 + // + // Таблица. Подвыражения на этапах. + // Подвыражение | 0) | 1) | 2) | 3) | 4) | 5) | + // -------------------------------------------------------------------------------------------------- + // Wᵢ | W[3,4,5] | R[i,i+2,2i+1] | | R[3,4] | R[*2i] | R[*i-1,i,*i+1,i+2] | + // | | W[2i,2i+1] | | | | | + // Wᵢ² | W[3,4,5] | R[i-1,i,i+1,'i+2] | R[i] | | | R[i-1,'i,i+1,'i+2] | + // | | W[2i,2i+1] | | | | | + // Wᵢ⁻² | | | W[i] | | R[i] | R[i] | + // Wᵢ₋₁ Wᵢ₊₁ | W[2,3] | W[i+1] | | | | R[i-1], W[i+1] | + // | | R[i-1,i(e),i+1] | | | | | + // (2y)² Wᵢ₋₁ Wᵢ₊₁ | W[3] | W[i(e)+1] | | | R[i] | | + // (2y)⁴ Wᵢ₋₁ Wᵢ₊₁ | W[3] | R[i(o)] | | | | | + // | | WR[i(e)+1] | | | | | + // + + // Выделяемая память + word* tmp; + word* tmp2; + // 2y + word* dy; + // (2y)⁻¹ + word* dyi; + // (2y)² + word* dy2; + // полиномы деления: Wᵢ, i=3,4..(2ʷ+1) + // этапы: 0), 1), 3), 4), 5) + // память: 2ʷ-1 + // Значения расчитываются на этапе 1) по индексам 2i и 2i+1. + // На этапе 1) значения считываются последовательно, по индексам i, i+2. + // На этапе 4) значения считываются по чётным индексам 2i. + // На этапе 5) значения считываются последовательно, по индексам i-1,i,i+1,i+2. + // Упростить кэширование не получается - необходимо выделять память под все значения. + word* pW; +#define W(i) (pW + ((i)-3) * n) + // квадраты: Wᵢ², i=3,4..2ʷ + // этапы: 2), 4), 5) + // память: 2ʷ-2[+1] + // Если на этапе 5) не используется gfpMul2 (вычисление произведения через квадраты), + // то на этапе 5) используются только значения по чётным индексам, поэтому память + // под квадраты по нечётным индексам можно переиспользовать под обратные (макрос W2i). + // Квадраты с нечётными индексами сгруппированы вместе для упрощения их обращения. + // Если требуется найти также двойную точки (da != NULL), то требуется также инвертировать + // значение 2y. Оно добавляется к квадратам по нечётным индексам для обращения. + // Квадраты по чётным индексам: W₂ᵢ², i=2,3..2ʷ⁻¹, - выделяются в pW2[0]. + // Квадраты по нечётным индексам: W₂ᵢ₋₁²[,2y], i=2,3..2ʷ⁻¹, - выделяются в pw2[1]. + word* pW2[2]; +#define W2(i) (pW2[(i)&1] + (((i)-3)>>1) * n) + // обратные нечётные квадраты: W₂ᵢ₋₁⁻², i=2,3..2ʷ⁻¹ + // этапы: 2), 4), 5) + // память: 2ʷ⁻¹-1 + // Обратные нечётные квадраты формируются на этапе 2) и используются на этапах 4) и 5). + word* pW2i; +#define W2i(i) (pW2i + (((i)-3)>>1) * n) + // произведения: Wᵢ₋₁ Wᵢ₊₁, i=2,3..2ʷ⁻¹+1 + // этапы: 0), 1), 5) + // память: 3 + // На этапе 1) значения формируются и используются последовательно с индексами i-1,i,i+1, + // поэтому можно выделять память лишь под 3 текущие значения. + // На этапе 5) происходит чтение по индексу i-1, и запись по индексу i+1, поэтому + // память можно выделять только под 1 значение. + // Макрос WW(i) имеет вид (i+D)%3, где D - константа. + // D выбрано как 2ʷ, чтобы WW(2ʷ⁻¹)=[(2ʷ⁻¹(1+2))%3]=0. + // Макрос WW переопределен перед этапом 5) так, чтобы WW(i)=0. + word* pWW; +#define WW(i) (pWW + (((i) + (SIZE_1 << w))%3) * n) + // произведения: (2y)² Wᵢ₋₁ Wᵢ₊₁, i=3,5..2ʷ⁻¹+1 + // этапы: 0), 1), 4) + // память: 2ʷ⁻² + // Значения формируются на этапах 0), 1), чтение - на этапе 4). Кэшировать нужно все значения. + word* pWW2; +#define WWy2(i) (pWW2 + (((i)-3) >> 1) * n) + // текущее произведение: (2y)⁴ Wᵢ₋₁ Wᵢ₊₁, i=3,5..(2ʷ⁻¹-1) + // этапы: 0), 1) + // память: 1 + // Запись на пред. шаге, чтение на текущем. Кэшировать можно только одно текущее значение. + word* pWW4; +#define WWy4(i) (pWW4) + + ASSERT(w >= 2); + + stack_walloc(dy2, n); + stack_walloc(tmp, n); + stack_walloc(tmp2, n); + stack_walloc(pW, n * ((SIZE_1 << w) - 1)); + stack_walloc(pW2[0], n * ((SIZE_1 << (w-1)) - 1)); + stack_walloc(pW2[1], n * ((SIZE_1 << (w-1)) - (da ? 0 : 1))); + stack_walloc(pW2i, n * ((SIZE_1 << (w-1)) - (da ? 0 : 1))); + stack_walloc(pWW, n * 3); + stack_walloc(pWW2, n * (SIZE_1 << (w-2))); + stack_walloc(pWW4, n); + dy = da ? pW2[1] + n * ((SIZE_1 << (w-1)) - 1) : dy2; + + // Этап 0) + + // [(2y)²] + gfpDouble(dy, y, ec->f); + qrSqr(dy2, dy, ec->f, stack); + + { + // вспомогательные значения + word* xx; + word* bx; + word* aa; + + xx = pWW; + bx = xx + n; + aa = bx + n; + + qrSqr(xx, x, ec->f, stack); // x ² + qrMul(bx, ec->B, x, ec->f, stack); // b x + qrSqr(aa, ec->A, ec->f, stack); // a ² + + // [W₃] + { + qrAdd(tmp, xx, ec->A, ec->f); // x² + a + qrSqr(tmp, tmp, ec->f, stack); // (x²+a) ² + gfpDouble(tmp2, tmp, ec->f); // 2 (x²+a)² + qrAdd(W(3), tmp, tmp2, ec->f); // 3 (x²+a)² + + gfpDouble(tmp, bx, ec->f); // 2 bx + qrAdd(tmp, tmp, bx, ec->f); // 3 bx + qrSub(tmp, aa, tmp, ec->f); // a² − 3bx + gfpDouble(tmp, tmp, ec->f); // 2 (a²−3bx) + gfpDouble(tmp, tmp, ec->f); // 4 (a²−3bx) + + qrSub(W(3), W(3), tmp, ec->f); // W₃ = 3(x²+a)² − 4(a²−3bx) + } + + // [W₄] + { + word* u = da ? ecY(da, n) : W(4); + gfpDouble(tmp, xx, ec->f); // 2 x² + gfpDouble(tmp, tmp, ec->f); // 4 x² + qrAdd(tmp, tmp, xx, ec->f); // 5 x² + qrSub(tmp, tmp, ec->A, ec->f); // 5x² - a + qrMul(tmp, bx, tmp, ec->f, stack); // bx (5x²-a) + gfpDouble(tmp, tmp, ec->f); // 2 bx(5x²-a) + gfpDouble(W(4), tmp, ec->f); // 4 bx(5x²-a) + + qrMul(tmp, xx, x, ec->f, stack); // x³ + qrSqr(tmp2, tmp, ec->f, stack); // x⁶ + qrAdd(W(4), tmp2, W(4), ec->f); // x⁶ + 4bx(5x²-a) + + qrMul(tmp2, ec->A, x, ec->f, stack); // a x + qrSub(tmp, tmp, tmp2, ec->f); // x³ - ax + qrMul(tmp, tmp, tmp2, ec->f, stack); // ax (x³-ax) + gfpDouble(tmp2, tmp, ec->f); // 2 ax(x³-ax) + gfpDouble(tmp2, tmp2, ec->f); // 4 ax(x³-ax) + qrAdd(tmp, tmp, tmp2, ec->f); // 5 ax(x³-ax) + qrAdd(W(4), W(4), tmp, ec->f); // x⁶+4bx(5x²-a) + 5ax(x³-ax) + + qrSqr(tmp, ec->B, ec->f, stack); // b ² + gfpDouble(tmp, tmp, ec->f); // 2 b² + gfpDouble(tmp, tmp, ec->f); // 4 b² + gfpDouble(tmp, tmp, ec->f); // 8 b² + qrSub(W(4), W(4), tmp, ec->f); // x⁶+4bx(5x²-a)+5ax(x³-ax) - 8b² + + qrMul(tmp2, aa, ec->A, ec->f, stack); // a² a + qrSub(u, W(4), tmp2, ec->f); // W₄/2 = x⁶+4bx(5x²-a)+5ax(x³-ax)-8b² - a³ + + gfpDouble(W(4), u, ec->f); // W₄ = 2 (x⁶+4bx(5x²-a)+5ax(x³-ax)-8b²-a³) + } + } + // [W₃²], [W₁W₃], [W₄²], [W₂W₄], [(2y)²W₂W₄], [(2y)⁴W₂W₄] + qrSqr(W2(3), W(3), ec->f, stack); // W₃² + qrCopy(WW(2), W(3), ec->f); // W₁W₃ = W₃ + qrSqr(W2(4), W(4), ec->f, stack); // W₄² + qrCopy(WW(3), W(4), ec->f); // W₂W₄ = W₄ + qrMul(WWy2(3), dy2, WW(3), ec->f, stack); // (2y)² W₂W₄ + qrMul(WWy4(3), dy2, WWy2(3), ec->f, stack); // (2y)² (2y)²W₂W₄ + + + // [W₅], [W₅²] + { + qrMul(tmp, WW(2), W2(3), ec->f, stack); // W₁W₃ W₃² + qrSub(W(5), WWy4(3), tmp, ec->f); // W₅ = (2y)⁴W₂W₄ − W₁W₃W₃² + if (w > 2) + qrSqr(W2(5), W(5), ec->f, stack); // W₅ ² + } + + // Этап 1) + // для i=3,4..2ʷ⁻¹: [W₂ᵢ], [W₂ᵢ₊₁], [Wᵢ Wᵢ₊₂] + for (i = 3; i <= SIZE_1 << (w - 1); ++i) + { + // [WᵢWᵢ₊₂] = ((Wᵢ + Wᵢ₊₂) ² - Wᵢ² - Wᵢ₊₂²) / 2 + gfpMul2(WW(i+1), W(i), W(i+2), W2(i), W2(i+2), ec->f, stack); + + // [W₂ᵢ] + if (i == 3) + { + qrMul(tmp, WW(i-1), W2(i+1), ec->f, stack); // (W₁W₃) W₄² + qrSub(W(2*i), WW(i+1), tmp, ec->f); // W₆ = W₃W₅ - W₁W₃W₄² + } + else + { + qrMul(tmp, WW(i-1), W2(i+1), ec->f, stack); // (Wᵢ₋₂Wᵢ) Wᵢ₊₁² + qrMul(W(2*i), WW(i+1), W2(i-1), ec->f, stack); // (WᵢWᵢ₊₂) Wᵢ₋₁² + qrSub(W(2*i), W(2*i), tmp, ec->f); // W₂ᵢ = (WᵢWᵢ₊₂)Wᵢ₋₁² - (Wᵢ₋₂Wᵢ)Wᵢ₊₁² + } + + // [W₂ᵢ²] + qrSqr(W2(2*i), W(2*i), ec->f, stack); // W₂ᵢ ² + + // [W₂ᵢ₊₁] + if ((i & 1) == 1) + { + qrMul(tmp, WWy4(i), W2(i+1), ec->f, stack); // (2y)⁴Wᵢ₋₁Wᵢ₊₁ Wᵢ₊₁² + qrMul(W(2*i+1), WW(i+1), W2(i), ec->f, stack); // WᵢWᵢ₊₂ Wᵢ² + qrSub(W(2*i+1), W(2*i+1), tmp, ec->f); // W₂ᵢ₊₁ = WᵢWᵢ₊₂Wᵢ² - (2y)⁴Wᵢ₋₁Wᵢ₊₁Wᵢ₊₁² + } + else + { + // [(2y)²WᵢWᵢ₊₂] + qrMul(WWy2(i+1), dy2, WW(i+1), ec->f, stack); // (2y)² WᵢWᵢ₊₂ + // [(2y)⁴WᵢWᵢ₊₂] + qrMul(WWy4(i+1), dy2, WWy2(i+1), ec->f, stack); // (2y)² (2y)²WᵢWᵢ₊₂ + qrMul(tmp, WW(i), W2(i+1), ec->f, stack); // Wᵢ₋₁Wᵢ₊₁ Wᵢ₊₁² + qrMul(W(2*i+1), WWy4(i+1), W2(i), ec->f, stack); // (2y)⁴WᵢWᵢ₊₂ Wᵢ² + qrSub(W(2*i+1), W(2*i+1), tmp, ec->f); // W₂ᵢ₊₁ = (2y)⁴WᵢWᵢ₊₂Wᵢ² - Wᵢ₋₁Wᵢ₊₁Wᵢ₊₁² + } + + if (i != SIZE_1 << (w - 1)) + // [W₂ᵢ₊₁²] + qrSqr(W2(2 * i + 1), W(2 * i + 1), ec->f, stack); // W₂ᵢ₊₁ ² + } + + + // [1]P + wwCopy(c, a, na); + c += na; + + // Этап 2) + // [Wᵢ⁻²][,2y], i=3,5..2ʷ-1 + qrMontInv(W2i(3), W2(3), da ? i - 1 : i - 2, ec->f, stack); + + // Этап 3) + // [2]P + if(da) + { + dyi = pW2i + n * ((SIZE_1 << (w - 1)) - 1); + // X₂ = x-W₁W₃/(2yW₂)² = x - W₃ / (2y)² + qrSqr(tmp, dyi, ec->f, stack); // (2y) ⁻² + qrMul(ecX(da), W(3), tmp, ec->f, stack); // W₃ / (2y)² + qrSub(ecX(da), x, ecX(da), ec->f); // x - W₃/(2y)² + // Y₂ = (W₄W₁²-W₀W₃²)/2/(2yW₂)³ = W₄ / 2 / (2y)³ + qrMul(tmp, tmp, dyi, ec->f, stack); // (2y) ⁻³ + qrMul(ecY(da, n), ecY(da, n), tmp, ec->f, stack); // W₄/2 / (2y)³ + } + + // Этап 4) + for (i = 3;;) + { + // i=3,5..2ʷ⁻¹+1: [Xᵢ] = x − (2y)²Wᵢ₋₁Wᵢ₊₁ Wᵢ⁻² + qrMul(tmp, WWy2(i), W2i(i), ec->f, stack); + qrSub(ecX(c), x, tmp, ec->f); + + if (i == (SIZE_1 << (w - 1)) + 1) break; + + // i=3,5..2ʷ⁻¹-1: [Yᵢ] = y W₂ᵢ Wᵢ⁻⁴ + qrSqr(tmp, W2i(i), ec->f, stack); + qrMul(tmp, W(2*i), tmp, ec->f, stack); + qrMul(ecY(c, n), y, tmp, ec->f, stack); + + i += 2, c += na; + } + // Этап 5) +#undef WW +#define WW(i) (pWW) + for (; i <= (SIZE_1 << w) - 1;) + { + // i=2ʷ⁻¹+1,2ʷ⁻¹+3..2ʷ-1: [Yᵢ] = y (WᵢWᵢ₊₂ Wᵢ₋₁² - Wᵢ₋₂Wᵢ Wᵢ₊₁²) Wᵢ⁻⁴ + qrMul(tmp, WW(i-1), W2(i+1), ec->f, stack); // Wᵢ₋₂Wᵢ Wᵢ₊₁² + // [WᵢWᵢ₊₂] + if (i != (SIZE_1 << w) - 1) + gfpMul2(WW(i+1), W(i), W(i+2), W2(i), W2(i+2), ec->f, stack); // Wᵢ Wᵢ₊₂ + else + // Wᵢ₊₂² undefined + qrMul(WW(i+1), W(i), W(i+2), ec->f, stack); // Wᵢ Wᵢ₊₂ + + if (i < 4) + //w == 2, W2^2 = 1 + wwCopy(tmp2, WW(i + 1), n); + else + qrMul(tmp2, WW(i+1), W2(i-1), ec->f, stack); // WᵢWᵢ₊₂ Wᵢ₋₁² + + qrSub(tmp2, tmp2, tmp, ec->f); // WᵢWᵢ₊₂Wᵢ₋₁² - Wᵢ₋₂WᵢWᵢ₊₁² + qrSqr(tmp, W2i(i), ec->f, stack); // Wᵢ⁻² ² + qrMul(tmp, tmp2, tmp, ec->f, stack); // (WᵢWᵢ₊₂Wᵢ₋₁²-Wᵢ₋₂WᵢWᵢ₊₁²) Wᵢ⁻⁴ + qrMul(ecY(c, n), y, tmp, ec->f, stack); // y (WᵢWᵢ₊₂Wᵢ₋₁²-Wᵢ₋₂WᵢWᵢ₊₁²)Wᵢ⁻⁴ + + if (i == (SIZE_1 << w) - 1) break; + i += 2, c += na; + + // i=2ʷ⁻¹+3,2ʷ⁻¹+5..2ʷ-1: [Xᵢ] = x − (2y)² Wᵢ₋₁ Wᵢ₊₁ Wᵢ⁻² + gfpMul2(tmp, W(i-1), W(i+1), W2(i-1), W2(i+1), ec->f, stack); // Wᵢ₋₁ Wᵢ₊₁ + qrMul(tmp, dy2, tmp, ec->f, stack); // (2y)² Wᵢ₋₁Wᵢ₊₁ + qrMul(tmp, W2i(i), tmp, ec->f, stack); // (2y)²Wᵢ₋₁Wᵢ₊₁ Wᵢ⁻² + qrSub(ecX(c), x, tmp, ec->f); // x − (2y)²Wᵢ₋₁Wᵢ₊₁Wᵢ⁻² + } +#ifdef _DEBUG + if (w == 2) { + //чтобы stack_wfree не ломался для w == 2, так как значение по адресу pWW + 2 * n не записывается + wwSetZero(pWW + 2 * n, n); + } +#endif // _DEBUG + + + stack_wfree(pWW4); + stack_wfree(pWW2); + stack_wfree(pWW); + stack_wfree(pW2i); + stack_wfree(pW2[1]); + stack_wfree(pW2[0]); + stack_wfree(pW); + stack_wfree(tmp2); + stack_wfree(tmp); + stack_wfree(dy2); + +#undef W +#undef W2 +#undef W2i +#undef WW +#undef WWy2 +#undef WWy4 + +} + +size_t ecpSmallMultDivpA_deep(bool_t da, const size_t w, size_t n, size_t f_deep) +{ + size_t const ww = SIZE_1 << w; + size_t r = n * (0 + + 1 // dy2 + + 1 // tmp + + 1 // tmp2 + + (ww - 1) // pW + + (ww/2 - 1) // pW2[0] + + (ww/2 - (da ? 0 : 1)) // pW2[1] + + (ww/2 - (da ? 0 : 1)) // pW2i + + 3 // pWW + + ww/4 // pWW2 + + 1 // pWW4 + ); +#ifdef _DEBUG + r += 3 * 10; +#endif + return O_OF_W(r) + + utilMax(2, + f_deep, + qrMontInv_deep(n, da ? ww/2 : ww/2 - 1, f_deep)); +; +} + +void ecpSmallMultDivpJ(word* c, word da[], const word a[], const size_t w, const ec_o* ec, void* stack) +{ + // размер координаты + const size_t n = ec->f->n; + // размер якобиевой точки + const size_t nj = n * ec->d; + // координата x базовой точки + const word* x = ecX(a); + // координата y базовой точки + const word* y = ecY(a, n); + + size_t i; + + // Основные этапы алгоритма: + // 0) Wᵢ, i=3,4,5 + // 1) for i=3,4..2ʷ⁻¹ + // 3) 2P + // 4*) for i=3,5..2ʷ⁻¹-1 + // 4) for i=3,5..2ʷ⁻¹+1 + // 5) for i=2ʷ⁻¹+1,2ʷ⁻¹+3..2ʷ-1 + // 5*) for i=2ʷ⁻¹+3,2ʷ⁻¹+5..2ʷ-1 + // + // Таблица. Подвыражения на этапах. + // Подвыражение | 0) | 1) | 3) | 4) | 5) | + // ------------------------------------------------------------------------------------------- + // Wᵢ | W[3,4,5] | R[i,i+2,2i+1] | R[3,4] | R[*2i] | R[*i-1,i,*i+1,i+2] | + // | | W[2i,2i+1] | | | | + // Wᵢ² | W[3,4,5] | R[i-1,i,i+1,'i+2] | | | R[i-1,'i,i+1,'i+2] | + // | | W[2i,2i+1] | | | | + // Wᵢ₋₁ Wᵢ₊₁ | W[2,3] | W[i+1] | | | R[i-1], W[i+1] | + // | | R[i-1,i(e),i+1] | | | | + // (2y)² Wᵢ₋₁ Wᵢ₊₁ | W[3] | W[i(e)+1] | | R[i] | | + // (2y)⁴ Wᵢ₋₁ Wᵢ₊₁ | W[3] | R[i(o)] | | | | + // | | WR[i(e)+1] | | | | + // + + // Выделяемая память + word* tmp; + word* tmp2; + // 2y + word* dy; + // (2y)² + word* dy2; + // полиномы деления: Wᵢ, i=3,4..(2ʷ+1) + // этапы: 0), 1), 3), 4), 5) + // память: 2ʷ-1 + // Значения расчитываются на этапе 1) по индексам 2i и 2i+1. + // На этапе 1) значения считываются последовательно, по индексам i, i+2. + // На этапе 4) значения считываются по чётным индексам 2i. + // На этапе 5) значения считываются последовательно, по индексам i-1,i,i+1,i+2. + // Упростить кэширование не получается - необходимо выделять память под все значения. + word* pW; +#define W(i) (pW + ((i)-3) * n) + // квадраты: Wᵢ², i=3,4..2ʷ + // этапы: 2), 4), 5) + // память: 2ʷ-2[+1] + // Квадраты с нечётными индексами сгруппированы вместе для упрощения их обращения. + // Если требуется найти также двойную точки (da != NULL), то требуется также инвертировать + // значение 2y. Оно добавляется к квадратам по нечётным индексам для обращения. + // Квадраты по чётным индексам: W₂ᵢ², i=2,3..2ʷ⁻¹, - выделяются в pW2[0]. + // Квадраты по нечётным индексам: W₂ᵢ₋₁²[,2y], i=2,3..2ʷ⁻¹, - выделяются в pw2[1]. + word* pW2[2]; +#define W2(i) (pW2[(i)&1] + (((i)-3)>>1) * n) + // произведения: Wᵢ₋₁ Wᵢ₊₁, i=2,3..2ʷ⁻¹+1 + // этапы: 0), 1), 5) + // память: 3 + // На этапе 1) значения формируются и используются последовательно с индексами i-1,i,i+1, + // поэтому можно выделять память лишь под 3 текущие значения. + // На этапе 5) происходит чтение по индексу i-1, и запись по индексу i+1, поэтому + // память можно выделять только под 1 значение. + // Макрос WW(i) имеет вид (i+D)%3, где D - константа. + // D выбрано как 2ʷ, чтобы WW(2ʷ⁻¹)=[(2ʷ⁻¹(1+2))%3]=0. + // Макрос WW переопределен перед этапом 5) так, чтобы WW(i)=0. + word* pWW; +#define WW(i) (pWW + (((i) + (SIZE_1 << w))%3) * n) + // произведения: (2y)² Wᵢ₋₁ Wᵢ₊₁, i=3,5..2ʷ⁻¹+1 + // этапы: 0), 1), 4) + // память: 2ʷ⁻² + // Значения формируются на этапах 0), 1), чтение - на этапе 4). Кэшировать нужно все значения. + word* pWW2; +#define WWy2(i) (pWW2 + (((i)-3) >> 1) * n) + // текущее произведение: (2y)⁴ Wᵢ₋₁ Wᵢ₊₁, i=3,5..(2ʷ⁻¹-1) + // этапы: 0), 1) + // память: 1 + // Запись на пред. шаге, чтение на текущем. Кэшировать можно только одно текущее значение. + word* pWW4; +#define WWy4(i) (pWW4) + + ASSERT(w >= 2); + + stack_walloc(dy2, n); + stack_walloc(tmp, n); + stack_walloc(tmp2, n); + stack_walloc(pW, n * ((SIZE_1 << w) - 1)); + stack_walloc(pW2[0], n * ((SIZE_1 << (w-1)) - 1)); + stack_walloc(pW2[1], n * ((SIZE_1 << (w-1)) - (da ? 0 : 1))); + stack_walloc(pWW, n * 3); + stack_walloc(pWW2, n * (SIZE_1 << (w-2))); + stack_walloc(pWW4, n); + dy = da ? pW2[1] + n * ((SIZE_1 << (w-1)) - 1) : dy2; + + // Этап 0) + + // [(2y)²] + gfpDouble(dy, y, ec->f); + qrSqr(dy2, dy, ec->f, stack); + + { + // вспомогательные значения + word* xx; + word* bx; + word* aa; + + xx = pWW; + bx = xx + n; + aa = bx + n; + + qrSqr(xx, x, ec->f, stack); // x ² + qrMul(bx, ec->B, x, ec->f, stack); // b x + qrSqr(aa, ec->A, ec->f, stack); // a ² + + // [W₃] + { + qrAdd(tmp, xx, ec->A, ec->f); // x² + a + qrSqr(tmp, tmp, ec->f, stack); // (x²+a) ² + gfpDouble(tmp2, tmp, ec->f); // 2 (x²+a)² + qrAdd(W(3), tmp, tmp2, ec->f); // 3 (x²+a)² + + gfpDouble(tmp, bx, ec->f); // 2 bx + qrAdd(tmp, tmp, bx, ec->f); // 3 bx + qrSub(tmp, aa, tmp, ec->f); // a² − 3bx + gfpDouble(tmp, tmp, ec->f); // 2 (a²−3bx) + gfpDouble(tmp, tmp, ec->f); // 4 (a²−3bx) + + qrSub(W(3), W(3), tmp, ec->f); // W₃ = 3(x²+a)² − 4(a²−3bx) + } + + // [W₄] + { + word* u = da ? ecY(da, n) : W(4); + gfpDouble(tmp, xx, ec->f); // 2 x² + gfpDouble(tmp, tmp, ec->f); // 4 x² + qrAdd(tmp, tmp, xx, ec->f); // 5 x² + qrSub(tmp, tmp, ec->A, ec->f); // 5x² - a + qrMul(tmp, bx, tmp, ec->f, stack); // bx (5x²-a) + gfpDouble(tmp, tmp, ec->f); // 2 bx(5x²-a) + gfpDouble(W(4), tmp, ec->f); // 4 bx(5x²-a) + + qrMul(tmp, xx, x, ec->f, stack); // x³ + qrSqr(tmp2, tmp, ec->f, stack); // x⁶ + qrAdd(W(4), tmp2, W(4), ec->f); // x⁶ + 4bx(5x²-a) + + qrMul(tmp2, ec->A, x, ec->f, stack); // a x + qrSub(tmp, tmp, tmp2, ec->f); // x³ - ax + qrMul(tmp, tmp, tmp2, ec->f, stack); // ax (x³-ax) + gfpDouble(tmp2, tmp, ec->f); // 2 ax(x³-ax) + gfpDouble(tmp2, tmp2, ec->f); // 4 ax(x³-ax) + qrAdd(tmp, tmp, tmp2, ec->f); // 5 ax(x³-ax) + qrAdd(W(4), W(4), tmp, ec->f); // x⁶+4bx(5x²-a) + 5ax(x³-ax) + + qrSqr(tmp, ec->B, ec->f, stack); // b ² + gfpDouble(tmp, tmp, ec->f); // 2 b² + gfpDouble(tmp, tmp, ec->f); // 4 b² + gfpDouble(tmp, tmp, ec->f); // 8 b² + qrSub(W(4), W(4), tmp, ec->f); // x⁶+4bx(5x²-a)+5ax(x³-ax) - 8b² + + qrMul(tmp2, aa, ec->A, ec->f, stack); // a² a + qrSub(u, W(4), tmp2, ec->f); // W₄/2 = x⁶+4bx(5x²-a)+5ax(x³-ax)-8b² - a³ + + gfpDouble(W(4), u, ec->f); // W₄ = 2 (x⁶+4bx(5x²-a)+5ax(x³-ax)-8b²-a³) + } + } + // [W₃²], [W₁W₃], [W₄²], [W₂W₄], [(2y)²W₂W₄], [(2y)⁴W₂W₄] + qrSqr(W2(3), W(3), ec->f, stack); // W₃² + qrCopy(WW(2), W(3), ec->f); // W₁W₃ = W₃ + qrSqr(W2(4), W(4), ec->f, stack); // W₄² + qrCopy(WW(3), W(4), ec->f); // W₂W₄ = W₄ + qrMul(WWy2(3), dy2, WW(3), ec->f, stack); // (2y)² W₂W₄ + qrMul(WWy4(3), dy2, WWy2(3), ec->f, stack); // (2y)² (2y)²W₂W₄ + + // [W₅], [W₅²] + { + qrMul(tmp, WW(2), W2(3), ec->f, stack); // W₁W₃ W₃² + qrSub(W(5), WWy4(3), tmp, ec->f); // W₅ = (2y)⁴W₂W₄ − W₁W₃W₃² + if (w > 2) + qrSqr(W2(5), W(5), ec->f, stack); // W₅ ² + } + + // Этап 1) + // для i=3,4..2ʷ⁻¹: [W₂ᵢ], [W₂ᵢ₊₁], [Wᵢ Wᵢ₊₂] + for (i = 3; i <= SIZE_1 << (w - 1); ++i) + { + // [WᵢWᵢ₊₂] = ((Wᵢ + Wᵢ₊₂) ² - Wᵢ² - Wᵢ₊₂²) / 2 + gfpMul2(WW(i+1), W(i), W(i+2), W2(i), W2(i+2), ec->f, stack); + + // [W₂ᵢ] + if (i == 3) + { + qrMul(tmp, WW(i-1), W2(i+1), ec->f, stack); // (W₁W₃) W₄² + qrSub(W(2*i), WW(i+1), tmp, ec->f); // W₆ = W₃W₅ - W₁W₃W₄² + } + else + { + qrMul(tmp, WW(i-1), W2(i+1), ec->f, stack); // (Wᵢ₋₂Wᵢ) Wᵢ₊₁² + qrMul(W(2*i), WW(i+1), W2(i-1), ec->f, stack); // (WᵢWᵢ₊₂) Wᵢ₋₁² + qrSub(W(2*i), W(2*i), tmp, ec->f); // W₂ᵢ = (WᵢWᵢ₊₂)Wᵢ₋₁² - (Wᵢ₋₂Wᵢ)Wᵢ₊₁² + } + + // [W₂ᵢ²] + qrSqr(W2(2*i), W(2*i), ec->f, stack); // W₂ᵢ ² + + // [W₂ᵢ₊₁] + if ((i & 1) == 1) + { + qrMul(tmp, WWy4(i), W2(i+1), ec->f, stack); // (2y)⁴Wᵢ₋₁Wᵢ₊₁ Wᵢ₊₁² + qrMul(W(2*i+1), WW(i+1), W2(i), ec->f, stack); // WᵢWᵢ₊₂ Wᵢ² + qrSub(W(2*i+1), W(2*i+1), tmp, ec->f); // W₂ᵢ₊₁ = WᵢWᵢ₊₂Wᵢ² - (2y)⁴Wᵢ₋₁Wᵢ₊₁Wᵢ₊₁² + } + else + { + // [(2y)²WᵢWᵢ₊₂] + qrMul(WWy2(i+1), dy2, WW(i+1), ec->f, stack); // (2y)² WᵢWᵢ₊₂ + // [(2y)⁴WᵢWᵢ₊₂] + qrMul(WWy4(i+1), dy2, WWy2(i+1), ec->f, stack); // (2y)² (2y)²WᵢWᵢ₊₂ + qrMul(tmp, WW(i), W2(i+1), ec->f, stack); // Wᵢ₋₁Wᵢ₊₁ Wᵢ₊₁² + qrMul(W(2*i+1), WWy4(i+1), W2(i), ec->f, stack); // (2y)⁴WᵢWᵢ₊₂ Wᵢ² + qrSub(W(2*i+1), W(2*i+1), tmp, ec->f); // W₂ᵢ₊₁ = (2y)⁴WᵢWᵢ₊₂Wᵢ² - Wᵢ₋₁Wᵢ₊₁Wᵢ₊₁² + } + + if (i != SIZE_1 << (w - 1)) + { + // [W₂ᵢ₊₁²] + qrSqr(W2(2 * i + 1), W(2 * i + 1), ec->f, stack); // W₂ᵢ₊₁ ² + } + } + + // [1]P + ecFromA(c, a, ec, stack); + c += nj; + + // Этап 3) + // [2]P + if(da) + { + // X₂ = x(2y)²W₂²-W₁W₃ = (2y)²x - W₃ + qrMul(ecX(da), dy2, x, ec->f, stack); // (2y)² x + qrSub(ecX(da), ecX(da), W(3), ec->f); // (2y)²x - W₃ + // Y₂ = (W₄W₁²-W₀W₃²)/2 = W₄/2 + // Z₂ = 2yW₂ = 2y + gfpDouble(ecZ(da, n), y, ec->f); + } + + // Этап 4) + for (i = 3;;) + { + // i=3,5..2ʷ⁻¹+1: [Xᵢ] = x Wᵢ² − (2y)²Wᵢ₋₁Wᵢ₊₁ + qrMul(ecX(c), x, W2(i), ec->f, stack); + qrSub(ecX(c), ecX(c), WWy2(i), ec->f); + + if (i == (SIZE_1 << (w - 1)) + 1) break; + + // i=3,5..2ʷ⁻¹-1: [Yᵢ] = y (Wᵢ₊₂ Wᵢ₋₁² - Wᵢ₋₂ Wᵢ₊₁²) + if (i < 4) + wwCopy(tmp, W(i+2), n); + else + qrMul(tmp, W(i+2), W2(i-1), ec->f, stack); + if (i < 5) + wwCopy(ecY(c, n), W2(i+1), n); + else + qrMul(ecY(c, n), W(i-2), W2(i+1), ec->f, stack); + qrSub(ecY(c, n), tmp, ecY(c, n), ec->f); + qrMul(ecY(c, n), y, ecY(c, n), ec->f, stack); + // [Zᵢ] = Wᵢ + wwCopy(ecZ(c, n), W(i), n); + + i += 2, c += nj; + } + // Этап 5) +#undef WW +#define WW(i) (pWW) + for (; i <= (SIZE_1 << w) - 1;) + { + // i=2ʷ⁻¹+1,2ʷ⁻¹+3..2ʷ-1: [Yᵢ] = y (Wᵢ₊₂ Wᵢ₋₁² - Wᵢ₋₂ Wᵢ₊₁²) + if (i < 4) + wwCopy(tmp, W(i+2), n); + else + qrMul(tmp, W(i+2), W2(i-1), ec->f, stack); + if (i < 5) + wwCopy(ecY(c, n), W2(i+1), n); + else + qrMul(ecY(c, n), W(i-2), W2(i+1), ec->f, stack); + + qrSub(ecY(c, n), tmp, ecY(c, n), ec->f); + qrMul(ecY(c, n), y, ecY(c, n), ec->f, stack); + // [Zᵢ] = Wᵢ + wwCopy(ecZ(c, n), W(i), n); + + if (i == (SIZE_1 << w) - 1) break; + i += 2, c += nj; + + // i=2ʷ⁻¹+3,2ʷ⁻¹+5..2ʷ-1: [Xᵢ] = x Wᵢ² − (2y)² Wᵢ₋₁ Wᵢ₊₁ + gfpMul2(tmp, W(i-1), W(i+1), W2(i-1), W2(i+1), ec->f, stack); // Wᵢ₋₁ Wᵢ₊₁ + qrMul(tmp, dy2, tmp, ec->f, stack); // (2y)² Wᵢ₋₁Wᵢ₊₁ + qrMul(ecX(c), x, W2(i), ec->f, stack); // x Wᵢ² + qrSub(ecX(c), ecX(c), tmp, ec->f); // x Wᵢ² − (2y)²Wᵢ₋₁Wᵢ₊₁ + } + + stack_wfree(pWW4); + stack_wfree(pWW2); + stack_wfree(pWW); + stack_wfree(pW2[1]); + stack_wfree(pW2[0]); + stack_wfree(pW); + stack_wfree(tmp2); + stack_wfree(tmp); + stack_wfree(dy2); + +#undef W +#undef W2 +#undef WW +#undef WWy2 +#undef WWy4 + +} + +size_t ecpSmallMultDivpJ_deep(bool_t da, const size_t w, size_t n, size_t f_deep) +{ + size_t const ww = SIZE_1 << w; + size_t r = n * (0 + + 1 // dy2 + + 1 // tmp + + 1 // tmp2 + + (ww - 1) // pW + + (ww/2 - 1) // pW2[0] + + (ww/2 - (da ? 0 : 1)) // pW2[1] + + 3 // pWW + + ww/4 // pWW2 + + 1 // pWW4 + ); +#ifdef _DEBUG + r += 3 * 9; +#endif + return O_OF_W(r) + f_deep; +} + +#undef stack_walloc +#undef stack_wfree diff --git a/src/math/qr.c b/src/math/qr.c index 44cb8f17..f5092190 100644 --- a/src/math/qr.c +++ b/src/math/qr.c @@ -183,3 +183,82 @@ size_t qrPower_deep(size_t n, size_t m, size_t r_deep) const size_t powers_count = SIZE_1 << (qrCalcSlideWidth(m) - 1); return O_OF_W(n + n * powers_count) + r_deep; } + +#if 0 +void qrMontInv(word c[], const word u[], size_t m, const qr_o* r, void* stack) +{ + ASSERT(qrIsOperable(r)); + ASSERT(wwIsValid(u, r->n *m)); + ASSERT(wwIsSameOrDisjoint(c, u, m * r->n)); + + size_t i; + word* p; + word* v; + + p = (word*)stack; + v = p + m * r->n; + stack = v + r->n; + + qrCopy(p, u, r); + for (i = 1; i < m; ++i) { + qrMul(p + i * r->n, p + (i - 1) * r->n, u + i * r->n, r, stack); + } + qrInv(v, p + (m - 1) * r->n, r, stack); + for (i = m - 1; i > 0; --i) { + qrMul(c + i * r->n, p + (i - 1) * r->n, v, r, stack); + qrMul(v, v, c + i * r->n, r, stack); + } + qrCopy(c, v, r); +} + +size_t qrMontInv_deep(size_t n, size_t m, size_t r_deep) { + return O_OF_W((m + 1) * n) + r_deep; +} +#else +void qrMontInv(word c[], const word a[], size_t m, const qr_o* r, void* stack) +{ + ASSERT(qrIsOperable(r)); + ASSERT(wwIsValid(a, m * r->n)); + ASSERT(wwIsSameOrDisjoint(c, a, m * r->n)); + + //счетчик: i = 0 .. m-1 + size_t i; + //набор нарастающих произведений: b[0] = a[0]; b[i+1] = b[i] * a[i+1] + word* b; + //обратный элемент: v = 1/b[i] + word* v; + + b = (word*)stack; + v = b + m * r->n; + stack = v + r->n; + + //b[0] = a[0] + i = 0; + qrCopy(b, a, r); + for (; ++i < m;) { + a += r->n; + //b[i+1] = b[i] * a[i+1] + qrMul(b + r->n, b, a, r, stack); + b += r->n; + } + //v = 1/b[m-1] = 1/(a[0] * .. * a[m-1]) + qrInv(v, b, r, stack); + for (c += (m - 1) * r->n; --i > 0;) { + //значение b[i] не используется, хранит значение a[i]/b[i] = 1/b[i-1] + qrMul(b, v, a, r, stack); + //c[i] = b[i-1]/b[i] = 1/a[i] + qrMul(c, b - r->n, v, r, stack); + //v = 1/b[i-1] + qrCopy(v, b, r); + c -= r->n; + b -= r->n; + a -= r->n; + } + //a[0] = 1/b[0] + qrCopy(c, v, r); +} + +size_t qrMontInv_deep(size_t n, size_t m, size_t r_deep) { + return O_OF_W((m + 1) * n) + r_deep; +} +#endif diff --git a/src/math/ww.c b/src/math/ww.c index b765fa4b..e9fa41e7 100644 --- a/src/math/ww.c +++ b/src/math/ww.c @@ -472,6 +472,51 @@ size_t wwNAF(word naf[], const word a[], size_t n, size_t w) naf_len = a_len = 0; return naf_size; } +/* + \remark Для данной реализации значение k всегда должно равняться (n * B_PER_W + w - 1) / w. +*/ +void wwOddRecording(word oddRecording[], size_t m, const word a[], size_t n, size_t k, size_t w) +{ + const word hi_bit = WORD_BIT_POS(w); + register word digit; + register word mask; + size_t i; + //pre + ASSERT(2 <= w && w < B_PER_W); + ASSERT(wwIsValid(a, n) & wwIsValid(oddRecording, m)); + ASSERT(wwIsDisjoint2(a, n, oddRecording, m)); + ASSERT(wwTestBit(a, 0)); + ASSERT(k * w >= n * B_PER_W); + ASSERT((k - 1) * w < n * B_PER_W); + ASSERT(m >= W_OF_B(k * (w + 1))); + + wwSetZero(oddRecording, m); + + for (i = 0; i < k - 1; ++i) + { + //digit <- a mod 2^(w+1) + digit = wwGetBits(a, i * w , w + 1); + + //digit <- digit - 2^w + mask = wordNeq0M(digit & hi_bit, hi_bit); + digit ^= mask; + digit |= WORD_1; + mask = ~mask & hi_bit; + digit ^= mask; + + wwSetBits(oddRecording, i * (w+1), (w+1), digit); + } + mask = B_PER_W * n - (k - 1) * w; + digit = wwGetBits(a, (k - 1) * w, mask); + digit |= WORD_1; + wwSetBits(oddRecording, (k - 1) * (w + 1), w+1, digit); + //очистка + digit = WORD_0; +} + +size_t wwOddRecording_size(size_t n, size_t w) { + return (n * B_PER_W + w - 1) / w; +} /* ******************************************************************************* diff --git a/src/math/zz/zz_add.c b/src/math/zz/zz_add.c index b5f8328a..e9f3d0b1 100644 --- a/src/math/zz/zz_add.c +++ b/src/math/zz/zz_add.c @@ -298,3 +298,35 @@ void zzNeg(word b[], const word a[], size_t n) zzAddW2(b, n, 1); } +void FAST(zzSetSign)(word b[], const word a[], size_t n, bool_t neg) { + size_t i; + + ASSERT(neg == FALSE || neg == TRUE); + ASSERT(wwIsSameOrDisjoint(a, b, n)); + + if (neg) + { + zzNeg(b, a, n); + } + else + { + wwCopy(b, a, n); + } +} + +void SAFE(zzSetSign)(word b[], const word a[], size_t n, bool_t neg) { + size_t i; + word xor_mask; + + ASSERT(neg == FALSE || neg == TRUE); + ASSERT(wwIsSameOrDisjoint(a, b, n)); + + //xor_mask <- neg ? WORD_MAX : WORD_0; + xor_mask = WORD_0 - (word)neg; + + for (i = 0; i < n; ++i) + b[i] = a[i] ^ xor_mask; + zzAddW2(b, n, (word)neg); + + xor_mask = 0; +} diff --git a/src/math/zz/zz_mod.c b/src/math/zz/zz_mod.c index c89499b0..d57a6765 100644 --- a/src/math/zz/zz_mod.c +++ b/src/math/zz/zz_mod.c @@ -186,6 +186,51 @@ void SAFE(zzNegMod)(word b[], const word a[], const word mod[], size_t n) mask = 0; } +void FAST(zzSetSignMod)(word b[], const word a[], const word mod[], size_t n, bool_t neg) +{ + ASSERT(wwIsSameOrDisjoint(a, b, n)); + ASSERT(wwIsDisjoint(b, mod, n)); + ASSERT(wwCmp(a, mod, n) < 0); + // a != 0 => b <- mod - a + if (wwIsZero(a, n)) + { + wwSetZero(b, n); + } + else if (neg) + { + zzSub(b, mod, a, n); + } + else { + wwCopy(b, a, n); + } +} + +void SAFE(zzSetSignMod)(word b[], const word a[], const word mod[], size_t n, bool_t neg) +{ + register word mask; + ASSERT(neg == TRUE || neg == FALSE); + ASSERT(wwIsSameOrDisjoint(a, b, n)); + ASSERT(wwIsDisjoint(b, mod, n)); + ASSERT(wwCmp(a, mod, n) < 0); + + // b <- a - mod + zzSub(b, a, mod, n); + + //mask <- neg ? WORD_0 : WORD_MAX; + mask = WORD_MAX + (word)neg; + // b <- b + mod & mask + zzAddAndW(b, mod, n, mask); + + zzSetSign(b, b, n, neg); + + // mask <- b == mod ? WORD_MAX : WORD_0 + mask = WORD_0 - (word)wwEq(b, mod, n); + // b <- b - mod & mask + zzSubAndW(b, mod, n, mask); + + mask = 0; +} + /* ******************************************************************************* Модулярная арифметика: мультипликативные операции diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt index ca158920..ca1d0e50 100644 --- a/test/CMakeLists.txt +++ b/test/CMakeLists.txt @@ -27,6 +27,7 @@ add_executable(testbee2 crypto/pfok_test.c math/pri_test.c math/zz_test.c + math/ww_test.c math/word_test.c math/ecp_test.c math/ecp_bench.c @@ -34,4 +35,4 @@ add_executable(testbee2 ) target_link_libraries(testbee2 bee2_static) -add_test(testbee2 testbee2) \ No newline at end of file +add_test(testbee2 testbee2) diff --git a/test/crypto/bake_test.c b/test/crypto/bake_test.c index e212088e..9f323cf8 100644 --- a/test/crypto/bake_test.c +++ b/test/crypto/bake_test.c @@ -11,13 +11,17 @@ version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ +#include #include #include #include #include #include +#include #include #include +#include +#include /* ******************************************************************************* @@ -349,3 +353,195 @@ bool_t bakeTest() // все нормально return TRUE; } + +typedef struct +{ + const octet* X; /*< дополнительное слово */ + size_t count; /*< размер X в октетах */ + size_t offset; /*< текущее смещение в X */ + octet state_ex[]; /*< состояние brngCTR */ +} brng_ctrx_st; + +static size_t brngCTRX_keep() +{ + return sizeof(brng_ctrx_st) + brngCTR_keep(); +} + +static void brngCTRXStart(const octet theta[32], const octet iv[32], + const void* X, size_t count, void* state) +{ + brng_ctrx_st* s = (brng_ctrx_st*)state; + ASSERT(memIsValid(s, sizeof(brng_ctrx_st))); + ASSERT(count > 0); + ASSERT(memIsValid(s->state_ex, brngCTR_keep())); + brngCTRStart(s->state_ex, theta, iv); + s->X = (const octet*)X; + s->count = count; + s->offset = 0; +} + +static void brngCTRXStepR(void* buf, size_t count, void* stack) +{ + brng_ctrx_st* s = (brng_ctrx_st*)stack; + octet* buf1 = (octet*)buf; + size_t count1 = count; + ASSERT(memIsValid(s, sizeof(brng_ctrx_st))); + // заполнить buf + while (count1) + if (count1 < s->count - s->offset) + { + memCopy(buf1, s->X + s->offset, count1); + s->offset += count1; + count1 = 0; + } + else + { + memCopy(buf1, s->X + s->offset, s->count - s->offset); + buf1 += s->count - s->offset; + count1 -= s->count - s->offset; + s->offset = 0; + } + // сгенерировать + brngCTRStepR(buf, count, s->state_ex); +} + +extern size_t testReps; +bool_t bakeBench() +{ + err_t codea; + err_t codeb; + bign_params params[1]; + octet randa[48]; + octet randb[48]; + octet echoa[64]; + octet echob[64]; + bake_settings settingsa[1]; + bake_settings settingsb[1]; + octet da[64]; + octet db[64]; + octet certdataa[5 /* Alice */ + 128 + 3 /* align */]; + octet certdatab[3 /* Bob */ + 128 + 5 /* align */]; + bake_cert certa[1]; + bake_cert certb[1]; + file_msg_st filea[1]; + file_msg_st fileb[1]; + const char pwd[] = "8086"; + octet keya[32]; + octet keyb[32]; + octet brng_state[1024]; + char params_oid[] = "1.2.112.0.2.0.34.101.45.3.0"; + + brngCTRXStart(beltH() + 128, beltH() + 128 + 64, + beltH(), 8 * 32, brng_state); + for(; params_oid[sizeof(params_oid) - 2]++ < '3'; ) + { + size_t reps; + size_t i; + tm_ticks_t ticks; + printf("bakeBench: %s\n", params_oid); + bignStdParams(params, params_oid); + memcpy(certdataa, "Alice", 5); + bignGenKeypair(da, certdataa + 5, params, brngCTRXStepR, brng_state); + memcpy(certdatab, "Bob", 3); + bignGenKeypair(db, certdatab + 3, params, brngCTRXStepR, brng_state); + + reps = testReps*1024*1024 / 8 / params->l / params->l; + + // настроить генераторы + ASSERT(prngEcho_keep() <= sizeof(echoa)); + // задать настройки + memSetZero(settingsa, sizeof(bake_settings)); + memSetZero(settingsb, sizeof(bake_settings)); + settingsa->kca = settingsa->kcb = TRUE; + settingsb->kca = settingsb->kcb = TRUE; + settingsa->rng = settingsb->rng = prngEchoStepR; + settingsa->rng_state = echoa; + settingsb->rng_state = echob; + // загрузить сертификаты + certa->data = certdataa; + certa->len = 5 + params->l / 2; + certb->data = certdatab; + certb->len = 3 + params->l / 2; + certa->val = certb->val = bakeTestCertVal; + // тест Б.2 + hexTo(randa, _bmqv_randa); + hexTo(randb, _bmqv_randb); + + for(i = 0, ticks = tmTicks(); i < reps; ++i) + { + fileMsgFlash(); + do + { + filea->i = filea->offset = 0; + fileb->i = fileb->offset = 0; + prngEchoStart(echoa, randa, strLen(_bmqv_randb) / 2); + prngEchoStart(echob, randb, strLen(_bmqv_randb) / 2); + codeb = bakeBMQVRunB(keyb, params, settingsb, db, certb, certa, + fileMsgRead, fileMsgWrite, fileb); + if(codeb != ERR_OK && codeb != ERR_FILE_NOT_FOUND) + return FALSE; + codea = bakeBMQVRunA(keya, params, settingsa, da, certa, certb, + fileMsgRead, fileMsgWrite, filea); + if(codea != ERR_OK && codea != ERR_FILE_NOT_FOUND) + return FALSE; + } while(codea == ERR_FILE_NOT_FOUND || codeb == ERR_FILE_NOT_FOUND); + } + ticks = tmTicks() - ticks; + printf("bakeBench::bakeBMQV : %3u cycles / rep [%5u reps / sec]\n", + (unsigned)(ticks / reps), + (unsigned)tmSpeed(reps, ticks)); + // тест Б.3 + hexTo(randa, _bsts_randa); + hexTo(randb, _bsts_randb); + for(i = 0, ticks = tmTicks(); i < reps; ++i) + { + fileMsgFlash(); + do + { + filea->i = filea->offset = 0; + fileb->i = fileb->offset = 0; + prngEchoStart(echoa, randa, strLen(_bsts_randb) / 2); + prngEchoStart(echob, randb, strLen(_bsts_randb) / 2); + codeb = bakeBSTSRunB(keyb, params, settingsb, db, certb, + bakeTestCertVal, fileMsgRead, fileMsgWrite, fileb); + if(codeb != ERR_OK && codeb != ERR_FILE_NOT_FOUND) + return FALSE; + codea = bakeBSTSRunA(keya, params, settingsa, da, certa, + bakeTestCertVal, fileMsgRead, fileMsgWrite, filea); + if(codea != ERR_OK && codea != ERR_FILE_NOT_FOUND) + return FALSE; + } while(codea == ERR_FILE_NOT_FOUND || codeb == ERR_FILE_NOT_FOUND); + } + ticks = tmTicks() - ticks; + printf("bakeBench::bakeBSTS : %3u cycles / rep [%5u reps / sec]\n", + (unsigned)(ticks / reps), + (unsigned)tmSpeed(reps, ticks)); + // тест Б.4 + hexTo(randa, _bpace_randa); + hexTo(randb, _bpace_randb); + for(i = 0, ticks = tmTicks(); i < reps; ++i) + { + fileMsgFlash(); + do + { + filea->i = filea->offset = 0; + fileb->i = fileb->offset = 0; + prngEchoStart(echoa, randa, strLen(_bpace_randb) / 2); + prngEchoStart(echob, randb, strLen(_bpace_randb) / 2); + codeb = bakeBPACERunB(keyb, params, settingsb, (const octet*)pwd, + strLen(pwd), fileMsgRead, fileMsgWrite, fileb); + if(codeb != ERR_OK && codeb != ERR_FILE_NOT_FOUND) + return FALSE; + codea = bakeBPACERunA(keya, params, settingsa, (const octet*)pwd, + strLen(pwd), fileMsgRead, fileMsgWrite, filea); + if(codea != ERR_OK && codea != ERR_FILE_NOT_FOUND) + return FALSE; + } while(codea == ERR_FILE_NOT_FOUND || codeb == ERR_FILE_NOT_FOUND); + } + ticks = tmTicks() - ticks; + printf("bakeBench::bakeBPACE : %3u cycles / rep [%5u reps / sec]\n", + (unsigned)(ticks / reps), + (unsigned)tmSpeed(reps, ticks)); + } + return 0; +} diff --git a/test/crypto/bign_test.c b/test/crypto/bign_test.c index b2a12ec1..06174af6 100644 --- a/test/crypto/bign_test.c +++ b/test/crypto/bign_test.c @@ -11,9 +11,11 @@ version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ +#include #include #include #include +#include #include #include #include @@ -384,3 +386,130 @@ bool_t bignTest() // все нормально return TRUE; } + +extern size_t testReps; +bool_t bignBench() +{ + bign_params params[1]; + octet oid_der[128]; + size_t oid_len; + octet privkey[64]; + octet pubkey[128]; + octet hash[64]; + octet sig[64 + 32]; + octet brng_state[1024]; + char params_oid[] = "1.2.112.0.2.0.34.101.45.3.0"; + // создать стек + ASSERT(sizeof(brng_state) >= brngCTRX_keep()); + // + for(; params_oid[sizeof(params_oid) - 2]++ < '3'; ) + { + size_t reps; + size_t i; + tm_ticks_t ticks; + printf("bignBench: %s\n", params_oid); + bignStdParams(params, params_oid); + reps = testReps*1024*1024 / params->l / params->l; + + // идентификатор объекта + oid_len = sizeof(oid_der); + bignOidToDER(oid_der, &oid_len, "1.2.112.0.2.0.34.101.31.81"); + // инициализировать ГПСЧ + brngCTRXStart(beltH() + 128, beltH() + 128 + 64, + beltH(), 8 * 32, brng_state); + // тест Г.1 + bignGenKeypair(privkey, pubkey, params, brngCTRXStepR, brng_state); + + for(i = 0, ticks = tmTicks(); i < reps; ++i) + bignDH(pubkey, params, privkey, pubkey, params->l / 4); + ticks = tmTicks() - ticks; + printf("bignBench::bignDH : %3u cycles / rep [%5u reps / sec]\n", + (unsigned)(ticks / reps), + (unsigned)tmSpeed(reps, ticks)); + + // тест Г.2 + beltHash(hash, beltH(), 13); + + for(i = 0, ticks = tmTicks(); i < reps; ++i) + bignSign(sig, params, oid_der, oid_len, hash, privkey, brngCTRXStepR, + brng_state); + ticks = tmTicks() - ticks; + printf("bignBench::bignSign : %3u cycles / rep [%5u reps / sec]\n", + (unsigned)(ticks / reps), + (unsigned)tmSpeed(reps, ticks)); + + for(i = 0, ticks = tmTicks(); i < reps; ++i) + bignVerify(params, oid_der, oid_len, hash, sig, pubkey); + ticks = tmTicks() - ticks; + printf("bignBench::bignVerify: %3u cycles / rep [%5u reps / sec]\n", + (unsigned)(ticks / reps), + (unsigned)tmSpeed(reps, ticks)); + } + + return TRUE; +} + +#include "bee2/math/ecp.h" +#include + +extern err_t bignStart(void* state, const bign_params* params); + +void bignPrintPrecomp() +{ + octet state[4*1024]; + octet stack[8*1024]; + size_t const w = 6; + size_t i, j, k; + word c[2*(2*64 + (64 << 6))]; + word *da, *nda; + word *nci; + word *ci; + octet *o; + ec_o *ec = (ec_o*)state; + size_t na; + bign_params params[1]; + char oid[] = "1.2.112.0.2.0.34.101.45.3.0"; + + for(k = 0; k < 4; ++k) + { + bignStdParams(params, oid); + oid[sizeof(oid)-2]++; + bignStart(state, params); + na = ec->f->n * 2; + nda = c + (na << w); + da = nda + na; + + { + ci = nci = c + (na << (w - 1)); + + ecSmallMultAdd2A(ci, da, ec->base, w, ec, stack); + for(; nci != c;) + { + nci -= na; + ecNegA(nci, ci, ec); + ci += na; + } + ecNegA(nda, da, ec); + } + + printf("#define CURVE%dV1_PRECOMP_W %d\n", (int)params->l, (int)w); + printf("static const octet _curve%dv1_precomp_Gs[%d * (2 + (1 << CURVE%dV1_PRECOMP_W))] = {\n", (int)params->l, (int)(sizeof(word) * na), (int)params->l); + o = (octet *)c; + for(i = 0; i++ < 2 + (1 << w);) + { + for(j = 0; j < na * sizeof(word);) + { + if(j % 32 == 0) + printf("", '\t');//"%c" + printf("0x%02x,", (int)*o++); + if(++j % 32 == 0) + printf("");//"\n" + else + printf("");//" " + } + if (0 == (i & ((1 << (w - 2)) - 1))) + printf("\n"); + } + printf("};\n\n"); + } +} diff --git a/test/math/ecp_bench.c b/test/math/ecp_bench.c index 65b4b31a..5c5914a3 100644 --- a/test/math/ecp_bench.c +++ b/test/math/ecp_bench.c @@ -4,8 +4,9 @@ \brief Benchmarks for elliptic curves over prime fields \project bee2/test \author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}] +\author (C) Vlad Semenov [semenov.vlad.by@gmail.com] \created 2013.10.17 -\version 2016.07.15 +\version 2020.12.20 \license This program is released under the GNU General Public License version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* @@ -34,47 +35,81 @@ static size_t _ecpBench_deep(size_t n, size_t f_deep, size_t ec_d, ecMulA_deep(n, ec_d, ec_deep, n); } +extern size_t testReps; +extern size_t ecW; +extern bool_t ecPrecompA; bool_t ecpBench() { // описание кривой bign_params params[1]; // состояние - octet state[6000]; + octet state[40*6000]; ec_o* ec; octet* combo_state; - word* pt; + word* pt, *pta; word* d; + size_t nj, reps; void* stack; + char params_oid[] = "1.2.112.0.2.0.34.101.45.3.0"; // загрузить параметры и создать описание кривой - ASSERT(bignStart_keep(128, _ecpBench_deep) <= sizeof(state)); - if (bignStdParams(params, "1.2.112.0.2.0.34.101.45.3.1") != ERR_OK || - bignStart(state, params) != ERR_OK) - return FALSE; - // раскладка состояния - ec = (ec_o*)state; - ec->tpl = 0; - combo_state = objEnd(ec, octet); - pt = (word*)(combo_state + prngCOMBO_keep()); - d = pt + 2 * ec->f->n; - stack = d + ec->f->n; - // создать генератор COMBO - prngCOMBOStart(combo_state, 23/*utilNonce32()*/); - // оценить число кратных точек в секунду - { - const size_t reps = 1000; - size_t i; - tm_ticks_t ticks; - // эксперимент - for (i = 0, ticks = tmTicks(); i < reps; ++i) + ASSERT(bignStart_keep(256, _ecpBench_deep) <= sizeof(state)); + for(; ++params_oid[sizeof(params_oid)-2] < '4';) { + if (bignStdParams(params, params_oid) != ERR_OK || + bignStart(state, params) != ERR_OK) + return FALSE; + printf("ecpBench: %s\n", params_oid); + // раскладка состояния + ec = (ec_o*)state; + ec->tpl = 0; + nj = ec->d * ec->f->n; + combo_state = objEnd(ec, octet); + pt = (word*)(combo_state + prngCOMBO_keep()); + d = pt + 2 * ec->f->n; + stack = d + ec->f->n; + reps = testReps*1024*1024 / params->l / params->l; + // оценить число кратных точек в секунду + pta = ec->base; + for(;;) { - prngCOMBOStepR(d, ec->f->no, combo_state); - ecMulA(pt, ec->base, ec, d, ec->f->n, stack); + size_t i; + tm_ticks_t ticks; + // создать генератор COMBO + prngCOMBOStart(combo_state, 23/*utilNonce32()*/); + // эксперимент + for (i = 0, ticks = tmTicks(); i < reps; ++i) + { + prngCOMBOStepR(d, ec->f->no, combo_state); + ecMulA(pt, pta, ec, d, ec->f->n, stack); + } + ticks = tmTicks() - ticks; + // печать результатов + printf("ecpBench::%s: %u cycles / mulpoint [%u mulpoints / sec]\n", + pta == ec->base ? "base": "rand", + (unsigned)(ticks / reps), + (unsigned)tmSpeed(reps, ticks)); + if(pta == pt) break; + pta = pt; + } + // скорость предвычислений + { + word *c = (word*)stack; + void *stack2 = (word*)(c + (nj << ecW) + nj+nj); + size_t i; + tm_ticks_t ticks; + // эксперимент + if(ecPrecompA) + for (i = 0, ticks = tmTicks(); i < reps; ++i) + ec->smulsa(c, pt, ec->base, ecW, ec, stack2); + else + for (i = 0, ticks = tmTicks(); i < reps; ++i) + ec->smulsj(c, pt, ec->base, ecW, ec, stack2); + ticks = tmTicks() - ticks; + // печать результатов + printf("ecpBench::%s: %u cycles / rep [%u reps / sec]\n", + ecPrecompA ? "smulsa" : "smulsj", + (unsigned)(ticks / reps), + (unsigned)tmSpeed(reps, ticks)); } - ticks = tmTicks() - ticks; - // печать результатов - printf("ecpBench: %u cycles / mulpoint [%u mulpoints / sec]\n", - (unsigned)(ticks / reps), - (unsigned)tmSpeed(reps, ticks)); } // все нормально return TRUE; diff --git a/test/math/ecp_test.c b/test/math/ecp_test.c index 20997a72..21d1b9ba 100644 --- a/test/math/ecp_test.c +++ b/test/math/ecp_test.c @@ -4,9 +4,10 @@ \brief Tests for elliptic curves over prime fields \project bee2/test \author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}] +\author (C) Vlad Semenov [semenov.vlad.by@gmail.com] \created 2017.05.29 -\version 2017.08.23 -\license This program is released under the GNU General Public License +\version 2020.12.20 +\license This program is released under the GNU General Public License version 3. See Copyright Notices in bee2/info.h. ******************************************************************************* */ @@ -16,6 +17,9 @@ version 3. See Copyright Notices in bee2/info.h. #include #include #include +#include +#include +#include /* ******************************************************************************* @@ -24,17 +28,17 @@ version 3. See Copyright Notices in bee2/info.h. */ static const size_t no = 32; -static char p[] = +static char p[] = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF43"; -static char a[] = +static char a[] = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF40"; -static char b[] = +static char b[] = "00000000000000000000000000000000000000000000000000000000000014B8"; -static char q[] = +static char q[] = "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D1229165911507C328526818EC4E11D"; -static char xbase[] = +static char xbase[] = "0000000000000000000000000000000000000000000000000000000000000000"; -static char ybase[] = +static char ybase[] = "B0E9804939D7C2E931D4CE052CCC6B6B692514CCADBA44940484EEA5F52D9268"; static u32 cofactor = 1; /* @@ -43,6 +47,309 @@ static u32 cofactor = 1; ******************************************************************************* */ +static bool_t qrMontInvTest(const qr_o* qr, void* stack) +{ + size_t m, i; + word *c = (word *)stack; + word *u = (c + 3 * qr->n); + word *v = (u + 3 * qr->n); + word *ci, *ui; + stack = (void *)(v + qr->n); + + // u := [2, 3, 4] + qrAdd(u, qr->unity, qr->unity, qr); + qrAdd(u + qr->n, u, qr->unity, qr); + qrAdd(u + 2 * qr->n, u + qr->n, qr->unity, qr); + + for(m = 0; m++ < 3;) + { + qrMontInv(c, u, m, qr, stack); + ci = c; + ui = u; + for(i = 0; i < m; ++i) + { + qrMul(v, ci, ui, qr, stack); + if(0 != qrCmp(v, qr->unity, qr)) + return FALSE; + ci += qr->n; + ui += qr->n; + } + + wwCopy(c, u, qr->n * m); + qrMontInv(c, c, m, qr, stack); + ci = c; + ui = u; + for(i = 0; i < m; ++i) + { + qrMul(v, ci, ui, qr, stack); + if(0 != qrCmp(v, qr->unity, qr)) + return FALSE; + ci += qr->n; + ui += qr->n; + } + } + + return TRUE; +} + +static bool_t ecMulADoubleAdd(word *c, word const *a, const ec_o *ec, word const *d, size_t m, void *stack) +{ + size_t i; + word b; + word *q = (word*)stack; + stack = (void*)(q + ec->d * ec->f->n); + + ecSetO(q, ec); + for(i = m * B_PER_W; i--; ) + { + ecDbl(q, q, ec, stack); + b = wwGetBits(d, i, 1); + if(b) + ecAddA(q, q, a, ec, stack); + } + return ecToA(c, q, ec, stack); +} + +static bool_t ecSmallMultTest(const ec_o* ec, void *stack) +{ + size_t const MIN_W = 2; + size_t const MAX_W = 7; + const size_t na = ec->f->n * 2; + const size_t n = ec->f->n * ec->d; + size_t w, i, f, di; + + word* bj = (word*)stack; + stack = (void*)(bj + n); + ecFromA(bj, ec->base, ec, stack); + + word* d = bj + n; + word* p = d + n; + word* sa = p + n; + word* ta = sa + na; + word* c = ta + na; + word* ci; + word b[1]; + + for(;;) + { + for(w = MIN_W; w <= MAX_W; ++w) + { + stack = (void*)(c + (na << (w - 1))); + + for(f = 0; f < 2; ++f) + { + if(f == 0) + ecSmallMultAdd2A(c, d, ec->base, w, ec, stack); + else + ecpSmallMultDivpA(c, d, ec->base, w, ec, stack); + + if(d) + { + ecDblA(p, ec->base, ec, stack); + ecToA(ta, p, ec, stack); + if(0 != wwCmp(d, ta, na)) + return FALSE; + } + + ci = c; + *b = 1; + for(i = SIZE_1 << (w - 1); i--;) + { + //if(!ecMulA(ta, ec->base, ec, b, 1, stack)) + // return FALSE; + if(!ecMulADoubleAdd(ta, ec->base, ec, b, 1, stack)) + return FALSE; + if(0 != wwCmp(ci, ta, na)) + return FALSE; + ci += na; + *b += 2; + } + } + } + + for(w = MIN_W; w <= MAX_W; ++w) + { + stack = (void*)(c + (n << (w - 1))); + + for(f = 0; f < 2; ++f) + { + if(f == 0) + ecSmallMultAdd2J(c, d, ec->base, w, ec, stack); + else + ecpSmallMultDivpJ(c, d, ec->base, w, ec, stack); + + if(d) + { + ecToA(sa, d, ec, stack); + ecAdd(p, bj, bj, ec, stack); + ecToA(ta, p, ec, stack); + if(0 != wwCmp(sa, ta, na)) + return FALSE; + } + + ci = c; + *b = 1; + for(i = SIZE_1 << (w - 1); i--;) + { + ecToA(sa, ci, ec, stack); + //if(!ecMulA(ta, ec->base, ec, b, 1, stack)) + // return FALSE; + if(!ecMulADoubleAdd(ta, ec->base, ec, b, 1, stack)) + return FALSE; + if(0 != wwCmp(sa, ta, na)) + return FALSE; + ci += n; + *b += 2; + } + } + } + + if(!d) break; + d = NULL; + } + + return TRUE; +} + +static bool_t ecMulTest(const ec_o* ec, void *stack) +{ + const size_t MIN_W = 2; + const size_t MAX_W = 7; + const size_t na = ec->f->n * 2; + + size_t w, k, m = ec->f->n; + size_t d0, dk, ik; + word* d = (word*)stack; + word* ba = d + m + 1; + word* sa = ba + na; + word* fa = sa + na; + bool_t sb, fb; + stack = (void*)(fa + na); + + ecDblA(sa, ec->base, ec, stack); + ecToA(ba, sa, ec, stack); + + { + wwSetZero(d, m + 1); + d[0] = 0x0f; + fb = ecMulA(fa, /*ba*/ec->base, ec, d, m + 1, stack); + sb = ecMulADoubleAdd(sa, /*ba*/ec->base, ec, d, m + 1, stack); + if(fb != sb) + return FALSE; + if(fb && (0 != wwCmp(sa, fa, na))) + return FALSE; + } + + { + zzSubW(d, ec->order, m + 1, 1); + fb = ecMulA(fa, /*ba*/ec->base, ec, d, m + 1, stack); + sb = ecMulADoubleAdd(sa, /*ba*/ec->base, ec, d, m + 1, stack); + if (fb != sb) + return FALSE; + if (fb && (0 != wwCmp(sa, fa, na))) + return FALSE; + } + + for(;;) + { + // w = MIN_W .. MAX_W + // d = d_0 + .. + d_k 2^{wk} + for(w = MIN_W; w <= MAX_W; ++w) + { + m = (3 * w + B_PER_W - 1) / B_PER_W; + const word ds[8] = {0, 1, 2, (1<<(w-1))-1, 1<<(w-1), (1<<(w-1))+1, (1<base) + break; + ba = ec->base; + } + + return TRUE; +} + + +//одна и та же точка в якобиевых координатах? +static bool_t ecIsSamePointJ(const word a[], const word b[], const ec_o* ec, void* stack) { + const size_t na = ec->f->n * 2; + const size_t n = ec->f->n * 3; + word* aa; + word* ba; + + if (!wwCmp(a, b, n)) + return TRUE; + + aa = (word*)stack; + ba = aa + na; + stack = ba + na; + + ecToA(aa, a, ec, stack); + ecToA(ba, b, ec, stack); + + return wwCmp(aa, ba, na) == 0; +} + +static bool_t ecpTestDblAddA(const ec_o* ec, void* stack) +{ const size_t n = ec->f->n * 3; + + size_t i; + + word* a = (word*)stack; + word* base_dbl = a + n; + word* actual = base_dbl + n; + word* expected = actual + n; + stack = (void*)(expected + n); + + ecDblA(base_dbl, ec->base, ec, stack); + wwCopy(a, base_dbl, n); + + ecDbl(expected, base_dbl, ec, stack); + ecAddA(expected, expected, ec->base, ec, stack); + + //a = [3,4,5...] * ec->base + //expected = [5,7, 7,9, ...] * ec->base + for (i = 0; i < 20; ++i) + { + ecAddA(a, a, ec->base, ec, stack); + + ecpDblAddA(actual, a, ec->base, TRUE, ec, stack); + + if (!ecIsSamePointJ(expected, actual, ec, stack)) + return FALSE; + + ecAdd(expected, expected, base_dbl, ec, stack); + + ecpDblAddA(actual, a, ec->base, FALSE, ec, stack); + + if (!ecIsSamePointJ(expected, actual, ec, stack)) + return FALSE; + } + return TRUE; +} + +extern err_t bignStart(void* state, const bign_params* params); + bool_t ecpTest() { // размерности @@ -53,7 +360,7 @@ bool_t ecpTest() const size_t ec_deep = ecpCreateJ_deep(n, f_deep); // состояние и стек octet state[2048]; - octet stack[2048]; + octet stack[30*4096]; octet t[96]; // поле и эк qr_o* f; @@ -73,7 +380,7 @@ bool_t ecpTest() return FALSE; // создать группу точек ec hexToRev(t, xbase), hexToRev(t + 32, ybase), hexToRev(t + 64, q); - if (!ecCreateGroup(ec, t, t + 32, t + 64, no, cofactor, stack)) + if (!ecCreateGroup(ec, t, t + 32, t + 64, no, cofactor, 0, NULL, stack)) return FALSE; // присоединить f к ec objAppend(ec, f, 0); @@ -91,8 +398,36 @@ bool_t ecpTest() return FALSE; // базовая точка имеет порядок q? ASSERT(ecHasOrderA_deep(n, ec->d, ec_deep, n) <= sizeof(stack)); + //TODO: ecHasOrderA uses ecMulA and ecNegA before they are tested if (!ecHasOrderA(ec->base, ec, ec->order, n, stack)) return FALSE; + // проверить алгоритм Монтгомери инвертирования элементов поля + if (!qrMontInvTest(ec->f, stack)) + return FALSE; + // проверить алгоритм расчета малых кратных + if (!ecSmallMultTest(ec, stack)) + return FALSE; + // проверить алгоритм удвоения и вычитания/сложения с афинной точкой + if (!ecpTestDblAddA(ec, stack)) + return FALSE; + // проверить алгоритм скалярного умножения + if (!ecMulTest(ec, stack)) + return FALSE; + + + { + bign_params params[1]; + char oid[] = "1.2.112.0.2.0.34.101.45.3.0"; + for(; ++oid[sizeof(oid)-2] < '4'; ) + { + bignStdParams(params, oid); + bignStart(ec, params); + if(!ecSmallMultTest(ec, stack)) + return FALSE; + if(!ecMulTest(ec, stack)) + return FALSE; + } + } // все нормально return TRUE; } diff --git a/test/math/ww_test.c b/test/math/ww_test.c new file mode 100644 index 00000000..34396c65 --- /dev/null +++ b/test/math/ww_test.c @@ -0,0 +1,104 @@ +/* +******************************************************************************* +\file ww_test.c +\brief Tests for arbitrary length words +\project bee2/test +\author (C) Sergey Agievich [agievich@{bsu.by|gmail.com}] +\author (C) Stanislav Poruchnik [PoruchnikStanislav@gmail.com] +\created 2017.05.21 +\version 2017.05.21 +\license This program is released under the GNU General Public License +version 3. See Copyright Notices in bee2/info.h. +******************************************************************************* +*/ + +#include +#include +#include +#include +#include +#include + +/* +******************************************************************************* +Тестирование +******************************************************************************* +*/ + +static size_t checkOddRecordingResult_deep(size_t n) { + return n; +} + +static bool_t checkOddRecordingResult(word* odd_recording, size_t m, const word* d, size_t n, size_t k, + size_t w, void* stack) { + int i = 0; + const word hi_bit = WORD_BIT_POS(w); + word digit; + word* result = (word*)stack; + stack = result + n; + + for (i = k - 1; i >= 0; --i) { + wwShHi(result, n, w); + digit = wwGetBits(odd_recording, i*(w + 1), w + 1); + if (digit & hi_bit) { + zzSubW2(result, n, digit ^ hi_bit); + } + else { + zzAddW2(result, n, digit); + } + } + return wwEq(d, result, n); +} + +size_t wwTestOddRecording_deep(size_t n, size_t w) { + size_t m = W_OF_B(wwOddRecording_size(n, w) * (w + 1)); + return prngCOMBO_keep() + n + m + checkOddRecordingResult_deep(n); +} + +bool_t wwTestOddRecording() +{ + octet state[128]; + octet* combo_state; + word* d; + word* odd_recording; + void* stack; + size_t n = 8; + size_t w = 5; + size_t k = wwOddRecording_size(n, w); + size_t m = W_OF_B(k * (w + 1)); + + //раскладка в стек + combo_state = (octet*)state; + d = (word*)(combo_state + prngCOMBO_keep()); + odd_recording = d + n; + stack = odd_recording + m; + + ASSERT(wwTestOddRecording_deep(n, w) <= sizeof(state)); + + // создать генератор COMBO + prngCOMBOStart(combo_state, utilNonce32()); + { + const size_t reps = 1000; + size_t i; + for (i = 0; i < reps; ++i) + { + //сгенерировать число и сделать нечетным + prngCOMBOStepR(d, n, combo_state); + d[0] |= 1; + + wwSetZero(odd_recording, m); + wwOddRecording(odd_recording, m, d, n, k, w); + + //проверка результата + if (!checkOddRecordingResult(odd_recording, m, d, n, k, w, stack)) { + return FALSE; + } + } + } + return TRUE; +} + +bool_t wwTest() +{ + return wwTestOddRecording(); +} diff --git a/test/math/zz_test.c b/test/math/zz_test.c index 484680b3..ee0cdae2 100644 --- a/test/math/zz_test.c +++ b/test/math/zz_test.c @@ -80,6 +80,32 @@ static bool_t zzTestAdd() !wwEq(c1, a, 1) || zzIsSumWEq(c, a, 1, b[0]) != wordEq(carry, 0)) return FALSE; + // zzNeg + zzNeg(c, a, n); + zzAdd(c1, a, c, n); + if (!wwIsZero(c1, n)) { + return FALSE; + } + // zzSetSign + zzSetSign(c, a, n, TRUE); + zzNeg(c1, a, n); + if (!wwEq(c, c1, n)) { + return FALSE; + } + zzSetSign(c, a, n, FALSE); + if (!wwEq(a, c, n)) { + return FALSE; + } + //FAST(zzSetSign) + FAST(zzSetSign)(c, a, n, TRUE); + zzNeg(c1, a, n); + if (!wwEq(c, c1, n)) { + return FALSE; + } + FAST(zzSetSign)(c, a, n, FALSE); + if (!wwEq(a, c, n)) { + return FALSE; + } } // все нормально return TRUE; @@ -276,6 +302,36 @@ static bool_t zzTestMod() if (!FAST(wwIsZero)(t1, n)) return FALSE; FAST(zzNegMod)(t1, t1, mod, n); + if (!FAST(wwIsZero)(t1, n)) + return FALSE; + // zzSetSign. + zzSetSignMod(t, a, mod, n, TRUE); + zzAddMod(t1, t, a, mod, n); + if (!wwIsZero(t1, n)) + return FALSE; + zzSetSignMod(t1, t1, mod, n, TRUE); + if (!wwIsZero(t1, n)) + return FALSE; + zzSetSignMod(t, a, mod, n, FALSE); + zzSubMod(t1, t, a, mod, n); + if (!wwIsZero(t1, n)) + return FALSE; + zzSetSignMod(t1, t1, mod, n, FALSE); + if (!wwIsZero(t1, n)) + return FALSE; + // FAST(zzSetSign) + FAST(zzSetSignMod)(t, a, mod, n, TRUE); + FAST(zzAddMod)(t1, t, a, mod, n); + if (!FAST(wwIsZero)(t1, n)) + return FALSE; + FAST(zzSetSignMod)(t1, t1, mod, n, TRUE); + if (!FAST(wwIsZero)(t1, n)) + return FALSE; + FAST(zzSetSignMod)(t, a, mod, n, FALSE); + FAST(zzSubMod)(t1, t, a, mod, n); + if (!FAST(wwIsZero)(t1, n)) + return FALSE; + FAST(zzSetSignMod)(t1, t1, mod, n, FALSE); if (!FAST(wwIsZero)(t1, n)) return FALSE; // zzDoubleMod / zzHalfMod diff --git a/test/test.c b/test/test.c index 04ade82d..f601473f 100644 --- a/test/test.c +++ b/test/test.c @@ -62,21 +62,26 @@ int testCore() ******************************************************************************* */ +extern bool_t wwTest(); extern bool_t priTest(); extern bool_t zzTest(); extern bool_t wordTest(); extern bool_t ecpTest(); extern bool_t ecpBench(); +bool_t fTest; +bool_t fBench; + int testMath() { bool_t code; int ret = 0; - printf("priTest: %s\n", (code = priTest()) ? "OK" : "Err"), ret |= !code; + //printf("priTest: %s\n", (code = priTest()) ? "OK" : "Err"), ret |= !code; printf("zzTest: %s\n", (code = zzTest()) ? "OK" : "Err"), ret |= !code; - printf("wordTest: %s\n", (code = wordTest()) ? "OK" : "Err"), ret |= !code; - printf("ecpTest: %s\n", (code = ecpTest()) ? "OK" : "Err"), ret |= !code; - code = ecpBench(), ret |= !code; + //printf("wordTest: %s\n", (code = wordTest()) ? "OK" : "Err"), ret |= !code; + //printf("wwTest: %s\n", (code = wwTest()) ? "OK" : "Err"), ret |= !code; + if(fTest) printf("ecpTest: %s\n", (code = ecpTest()) ? "OK" : "Err"), ret |= !code; + if(fBench) code = ecpBench(), ret |= !code; return ret; } @@ -100,23 +105,28 @@ extern bool_t bakeDemo(); extern bool_t bashTest(); extern bool_t bashBench(); extern bool_t botpTest(); +extern bool_t bignBench(); +extern bool_t bakeBench(); + int testCrypto() { bool_t code; int ret = 0; - printf("beltTest: %s\n", (code = beltTest()) ? "OK" : "Err"), ret |= !code; - printf("bashTest: %s\n", (code = bashTest()) ? "OK" : "Err"), ret |= !code; - code = beltBench(), ret |= !code; - code = bashBench(), ret |= !code; - printf("botpTest: %s\n", (code = botpTest()) ? "OK" : "Err"), ret |= !code; - printf("bignTest: %s\n", (code = bignTest()) ? "OK" : "Err"), ret |= !code; - printf("brngTest: %s\n", (code = brngTest()) ? "OK" : "Err"), ret |= !code; - printf("belsTest: %s\n", (code = belsTest()) ? "OK" : "Err"), ret |= !code; - printf("bakeTest: %s\n", (code = bakeTest()) ? "OK" : "Err"), ret |= !code; - printf("dstuTest: %s\n", (code = dstuTest()) ? "OK" : "Err"), ret |= !code; - printf("g12sTest: %s\n", (code = g12sTest()) ? "OK" : "Err"), ret |= !code; - printf("pfokTest: %s\n", (code = pfokTest()) ? "OK" : "Err"), ret |= !code; + //printf("beltTest: %s\n", (code = beltTest()) ? "OK" : "Err"), ret |= !code; + //printf("bashTest: %s\n", (code = bashTest()) ? "OK" : "Err"), ret |= !code; + //code = beltBench(), ret |= !code; + //code = bashBench(), ret |= !code; + //printf("botpTest: %s\n", (code = botpTest()) ? "OK" : "Err"), ret |= !code; + //if(fTest) printf("bignTest: %s\n", (code = bignTest()) ? "OK" : "Err"), ret |= !code; + //if(fBench) code = bignBench(), ret |= !code; + //printf("brngTest: %s\n", (code = brngTest()) ? "OK" : "Err"), ret |= !code; + //printf("belsTest: %s\n", (code = belsTest()) ? "OK" : "Err"), ret |= !code; + //if(fTest) printf("bakeTest: %s\n", (code = bakeTest()) ? "OK" : "Err"), ret |= !code; + //if(fBench) code = bakeBench(), ret |= !code; + //printf("dstuTest: %s\n", (code = dstuTest()) ? "OK" : "Err"), ret |= !code; + //printf("g12sTest: %s\n", (code = g12sTest()) ? "OK" : "Err"), ret |= !code; + //printf("pfokTest: %s\n", (code = pfokTest()) ? "OK" : "Err"), ret |= !code; return ret; } @@ -126,12 +136,187 @@ main ******************************************************************************* */ -int main() +size_t testReps = 2; +extern bool_t ecSafe; +extern bool_t ecPrecomp; +extern bool_t ecPrecompA; +extern bool_t bignPrecomp; +extern bool_t ecpDivp; +extern size_t ecW; + +#define countof(a) (sizeof(a)/sizeof(*(a))) + +int run() { int ret = 0; - ret |= testCore(); + printf( + "\n====================================" + "\n%s %s %s %s w=%d" + "\n====================================" + "\n" + , ecSafe ? "SAFE" : "FAST" + , bignPrecomp ? "WithBignPrecomp" : "NoBignPrecomp" + , ecPrecomp ? (ecPrecompA ? "PrecompA" : "PrecompJ") : "Orig" + , ecPrecomp ? (ecpDivp ? "Divp" : "Add2") : "" + , (int)ecW); + if (bignPrecomp && ecPrecomp && !ecPrecompA) { + //временно пропустить заведомо падающую конфигурацию по причине того, что + //bignPrecomp в афинных координатах, + + // precomputed point in affine coordinates + //TODO: convert to jacobian coordinates + printf("Skip configuration because of attempt to use bignPrecomp in affine coordinates for PrecompJ\n"); + return ret; + } ret |= testMath(); ret |= testCrypto(); return ret; } +int all() +{ + int ret = 0; + size_t i, j, k, l, m; + bool_t safe[] = {TRUE, FALSE, }; + bool_t precomp[] = { TRUE, FALSE, }; + bool_t with_precomp[] = {TRUE, FALSE, }; + bool_t divp[] = { FALSE, TRUE, }; + bool_t precompA[] = { TRUE, FALSE, }; + size_t MIN_W = 2; + size_t MAX_W = 3; + + fTest = TRUE; + fBench = TRUE; + + for(i = 0; i < countof(safe); ++i) + { + ecSafe = safe[i]; + for(j = 0; j < countof(precomp); ++j) + { + ecPrecomp = precomp[j]; + for(m = 0; m < countof(precompA); ++m) + { + ecPrecompA = precompA[m]; + for(k = 0; k < countof(with_precomp); ++k) + { + bignPrecomp = with_precomp[k]; + for(l = 0; l < countof(divp); ++l) + { + ecpDivp = divp[l]; + for(ecW = MIN_W; ecW++ < MAX_W;) + { + ret |= run(); + } + if(!ecPrecomp) break; + } + if(!ecPrecomp) break; + } + if(!ecPrecomp) break; + } + } + } + return ret; +} + +#include +#include +int main(int argc, char const **argv) +{ + static char const *help = + "Args: safe precomp precompa bignprecomp divp w test bench reps all help\n" + "\n" + "\tsafe : enable safe (regular) windowed method, or fast (irregular) naf otherwise\n" + "\tprecomp : enable precomputations (new algorithm), or base-line original algorithm otherwise\n" + "\tprecompa : enable precomputations in affine coordinates, or in jacobian otherwise (doesn't work ATM)\n" + "\tbignprecomp: enable precomputation tables for bign/bake algorithms, or no tables otherwise\n" + "\tdivp : enable small mult computations via division polynomials, or using 'add 2p' method otherwise\n" + "\tw : set window size for windowed/naf methods, usually 3<=W<=6\n" + "\ttest : enable tests\n" + "\tbench : enable benchmarks\n" + "\treps : set number of reps for benchmarks, usually 2<=R<=1000\n" + "\tall : enable all configurations and run tests and benchmarks\n" + "\thelp : show this help\n" + "\n" + "Example: safe precomp precompa bignprecomp divp w 3 test bench reps \n" + " Enable safe (regular) windowed method with full precomputation in affine coordinates\n" + " using division polynomials with window size 3 and run tests and benchmarks\n" + "\n" + "Example: precomp precompa bignprecomp divp w 4 bench\n" + " Enable fast (irregular) naf method with full precomputation in affine coordinates\n" + " using division polynomials with window size 4 and run benchmarks only\n" + "\n" + "Example: safe w 4 bench\n" + " Enable the original (baseline) safe (regular) windowed method without precomputations\n" + " with window size 4 and run benchmarks only\n" + "\n" + "Example: w 5 reps 10 bench\n" + " Enable the original (baseline) fast (irregular) naf method without precomputations\n" + " with window size 5 and run benchmarks only\n" + "\n" + "Example: w 4 reps 10 all\n" + " Run all possible configurations of tests and benchmarks\n" + "\n" + ; + fTest = FALSE; + fBench = FALSE; + ecSafe = FALSE; + ecPrecomp = FALSE; + ecPrecompA = FALSE; + bignPrecomp = FALSE; + ecpDivp = FALSE; + ecW = 3; + + if(argc < 2) + { + printf("Try 'help' for help. Running all configurations now\n"); + return all(); + } + + for(; --argc;) + { + ++argv; + if(!strcmp("safe", *argv)) + ecSafe = TRUE; + else if(!strcmp("precomp", *argv)) + ecPrecomp = TRUE; + else if(!strcmp("precompa", *argv)) + ecPrecompA = TRUE; + else if(!strcmp("bignprecomp", *argv)) + bignPrecomp = TRUE; + else if(!strcmp("divp", *argv)) + ecpDivp = TRUE; + else if(!strcmp("w", *argv)) + { + if(--argc) + ecW = (size_t)atoi(*++argv); + } + else if(!strcmp("reps", *argv)) + { + if(--argc) + testReps = (size_t)atoi(*++argv); + } + else if(!strcmp("test", *argv)) + fTest = TRUE; + else if(!strcmp("bench", *argv)) + fBench = TRUE; + else if(!strcmp("all", *argv)) + return all(); + else if(!strcmp("help", *argv)) + { + printf("ecsafe\n\n%s", help); + return 0; + } + else + { + printf("Unknown option [%s].", *argv); + return 1; + } + } + + if(!fTest && !fBench) + { + fTest = TRUE; + fBench = TRUE; + } + return run(); +} diff --git a/win/vs09/test.vcproj b/win/vs09/test.vcproj index c54e428a..aa22ee05 100644 --- a/win/vs09/test.vcproj +++ b/win/vs09/test.vcproj @@ -413,6 +413,10 @@ RelativePath="..\..\test\math\word_test.c" > + +