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Add std::math::fp4::square_ext #1990

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Add std::math::fp4::square_ext #1990

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cacb5ac
Add std::math::fp4::square_ext
georgwiese Oct 30, 2024
c0860ab
Merge origin/main
georgwiese Nov 11, 2024
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25 changes: 25 additions & 0 deletions std/math/fp4.asm
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Original file line number Diff line number Diff line change
Expand Up @@ -59,6 +59,18 @@ let<T: Add + FromLiteral + Mul> mul_ext: Fp4<T>, Fp4<T> -> Fp4<T> = |a, b| match
)
};

/// Extension field squaring
/// This implementation yields a shorter expression than `mul_ext(a, a)` and should be preferred
/// when squaring expressions many times.
let<T: Add + FromLiteral + Mul> square_ext: Fp4<T> -> Fp4<T> = |a| match a {
Fp4::Fp4(a0, a1, a2, a3) => Fp4::Fp4(
a0 * a0 + 11 * (2 * a1 * a3 + a2 * a2),
2 * (a0 * a1 + 11 * a2 * a3),
2 * a0 * a2 + a1 * a1 + 11 * (a3 * a3),
2 * (a0 * a3 + a1 * a2)
)
};

/// Inversion for an Fp4 element
/// The inverse of (a0, a1, a2, a3) is a point (b0, b1, b2, b3) such that:
/// (a0 + a1 * x + a2 * x^2 + a3 * x^3) (b0 + b1 * x + b2 * x^2 + b3 * x^3) = 1 (mod x^4 - 11)
Expand Down Expand Up @@ -141,6 +153,7 @@ mod test {
use super::add_ext;
use super::sub_ext;
use super::mul_ext;
use super::square_ext;
use super::inv_ext;
use super::eq_ext;
use std::check::assert;
Expand Down Expand Up @@ -197,6 +210,18 @@ mod test {
test_mul(Fp4::Fp4(-1, -2, -3, -4), Fp4::Fp4(-3, 4, 4, 5), Fp4::Fp4(-415, -339, -223, -13));
};

let test_square = || {
// Tests consistency with mul_ext
let test_square = |a| assert(eq_ext(mul_ext(a, a), square_ext(a)), || "Wrong squaring result");

test_square(from_base(0));
test_square(from_base(1));
test_square(from_base(2));
test_square(Fp4::Fp4(1, 1, 1, 1));
test_square(Fp4::Fp4(123, 1234, 12, 12345));
test_square(Fp4::Fp4(-1, -2, -3, -4));
};

let test_inverse = || {
let test_elements = [
from_base(1),
Expand Down