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linisynth.py
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#!/usr/bin/env python
from __future__ import print_function
# imports
from pysmt.shortcuts import *
from pysmt.typing import BOOL, INT
import string
import itertools
import copy
import tqdm
import sys
import argparse
import time
import re
from warnings import warn
from functools import reduce
################################################################################
# shortcuts {{{
def shortcuts():
d = {}
d['privacy-free-and-gate'] = \
{ "gate" : and_gate
, "size" : 1
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 2
, "h_calls_ev" : 1
, "privacy_free" : 1
, "adaptive" : 0
}
d['mux4in'] = \
{ "gate" : mux2_gate
, "size" : 4
, "input_bits" : 5
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['mux4in-2'] = \
{ "gate" : mux2_gate
, "size" : 4
, "input_bits" : 5
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 6
, "h_calls_ev" : 4
, "helper_bits" : 0
}
d['size3-in3-out2'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 3
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['size3-in3-out2-2'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 3
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 6
, "h_calls_ev" : 4
, "helper_bits" : 0
}
d['size3-in3-out2-3'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 3
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 8
, "h_calls_ev" : 6
, "helper_bits" : 0
}
d['size3-in2-out2'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 2
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['size3-in2-out2-2'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 2
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 5
, "h_calls_ev" : 3
, "helper_bits" : 0
}
d['size3-in2-out2-3'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 2
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 6
, "h_calls_ev" : 4
, "helper_bits" : 0
}
d['any-size-3-in2'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['any-size-3-in2-2'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 5
, "h_calls_ev" : 3
, "helper_bits" : 0
}
d['any-size-3-in2-3'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 2
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['any-size-3-in2-4'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 2
, "h_calls_gb" : 4
, "h_calls_ev" : 1
, "helper_bits" : 0
}
d['any-size-3-in3'] = \
{ "gate" : None
, "size" : 3
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['1-out-of-2-mux'] = \
{ "gate" : mux_gate
, "size" : 2
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['mux2'] = \
{ "gate" : mux_gate
, "size" : 2
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
, "adaptive" : 0
}
d['privacy-free-mux'] = \
{ "gate" : mux_gate
, "size" : 1
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 2
, "h_calls_ev" : 1
, "helper_bits" : 0
, "adaptive" : 0
, "privacy_free" : True
}
d['privacy-free-mux2'] = \
{ "gate" : mux2_gate
, "size" : 2
, "input_bits" : 5
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 6
, "h_calls_ev" : 4
, "helper_bits" : 0
, "adaptive" : 1
, "privacy_free" : True
}
d['2-bit-leq'] = \
{ "gate" : leq_gate
, "size" : 1
, "input_bits" : 4
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 2
, "h_calls_ev" : 1
, "helper_bits" : 0
}
d['leq2'] = \
{ "gate" : leq_gate
, "size" : 2
, "input_bits" : 4
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['2-bit-eq'] = \
{ "gate" : eq_gate
, "size" : 2
, "input_bits" : 4
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['eq3'] = \
{ "gate" : eq3_gate
, "size" : 2
, "input_bits" : 4
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['2-bit-eq-small'] = \
{ "gate" : eq_gate
, "size" : 1
, "input_bits" : 4
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['eq-smaller2'] = \
{ "gate" : eq_gate
, "size" : 2
, "input_bits" : 4
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 3
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['privacy-free-lt'] = \
{ "gate" : lt_gate
, "size" : 1
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 2
, "h_calls_ev" : 1
, "helper_bits" : 0
, "adaptive" : 0
, "privacy_free" : 1
}
d['2-bit-lt'] = \
{ "gate" : lt2_gate
, "size" : 2
, "input_bits" : 4
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['lt2'] = \
{ "gate" : lt2_gate
, "size" : 3
, "input_bits" : 4
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 8
, "h_calls_ev" : 4
, "helper_bits" : 0
}
d['free-xor'] = \
{ "gate" : xor_gate
, "size" : 0
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 0
, "h_calls_ev" : 0
}
d['nested-xor'] = \
{ "gate" : nested_xor_gate
, "size" : 0
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 0
, "h_calls_ev" : 0
, "helper_bits" : 0
}
d['and-xor'] = \
{ "gate" : andxor_gate
, "size" : 2
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
}
d['cheaper-and'] = \
{ "gate" : and_gate
, "size" : 3
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 2
, "h_calls_gb" : 4
, "h_calls_ev" : 1
}
d['half-gate-h2'] = \
{ "gate" : and_gate
, "size" : 2
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 2
, "h_calls_gb" : 4
, "h_calls_ev" : 1
, "adaptive" : 0
}
d['cheaper-and2'] = \
{ "gate" : and_gate
, "size" : 2
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 2
, "h_calls_gb" : 4
, "h_calls_ev" : 1
}
d['half-gate'] = \
{ "gate" : and_gate
, "size" : 2
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "adaptive" : 0
}
d['half-gate-adaptive'] = \
{ "gate" : and_gate
, "size" : 2
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "adaptive" : 1
}
d['half-gate-cheaper'] = \
{ "gate" : and_gate
, "size" : 2
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 1
}
d['one-third-gate'] = \
{ "gate" : and_gate
, "size" : 1
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 1
}
d['one-third-gate-big'] = \
{ "gate" : and_gate
, "size" : 2
, "input_bits" : 2
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 1
}
d['and3'] = \
{ "gate" : and3_gate
, "size" : 4
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 8
, "h_calls_ev" : 4
, "helper_bits" : 1
, "helper_gate" : and3_helper_gate
}
d['and3-smaller'] = \
{ "gate" : and3_gate
, "size" : 3
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 8
, "h_calls_ev" : 4
, "helper_bits" : 1
, "helper_gate" : and3_helper_gate
}
d['and3-nohelper'] = \
{ "gate" : and3_gate
, "size" : 4
, "input_bits" : 3
, "output_bits" : 1
, "h_arity" : 1
, "h_calls_gb" : 8
, "h_calls_ev" : 4
, "helper_bits" : 0
}
d['adder-nohelper'] = \
{ "gate" : adder_gate
, "size" : 2
, "input_bits" : 3
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 0
}
d['adder'] = \
{ "gate" : adder_gate
, "size" : 2
, "input_bits" : 3
, "output_bits" : 2
, "h_arity" : 1
, "h_calls_gb" : 4
, "h_calls_ev" : 2
, "helper_bits" : 1
}
return d
# }}}
# helper functions and constants# {{{
T = TRUE()
F = FALSE()
def mapall(f, stuff):
return reduce(lambda z, x: And(z, f(x)), stuff, T)
def mapsome(f, stuff):
return reduce(lambda z, x: Or(z, f(x)), stuff, F)
def bits(x, size):
return [ (x&(2**i)>0) for i in range(size) ]
# }}}
# gates {{{
def all_gates(nins, nouts):
truth_tables = []
for i in range(nouts):
tt = list(itertools.product(*[[True,False]]*(2**nins)))
truth_tables.append(tt)
indices = itertools.product(*[list(range(len(truth_tables[0])))]*nouts)
for assn in indices:
def gate(inp, assn=assn):
outputs = []
for (out, ix) in enumerate(assn):
outputs.append(truth_tables[out][ix][inp])
return outputs
yield gate
def mux2_gate(x):
[x0, x1, y0, y1, c] = bits(x,5)
return [y0, y1] if c else [x0, x1]
def mux_gate(x):
[x0, x1, c] = bits(x,3)
return [x1 if c else x0]
def eq_gate(i):
x = (i) & 0b11
y = (i & 0b1100) >> 2
return [x == y]
def eq3_gate(i):
x = (i) & 0b111
y = (i & 0b111000) >> 3
return [x == y]
def lt_gate(i):
[x,y] = bits(i,2)
return [x < y]
def lt2_gate(i):
x = i & 0b11
y = (i & 0b1100) >> 2
return [x < y]
def leq_gate(i):
x = (i) & 0b11
y = (i & 0b1100) >> 2
return [x <= y]
def and_gate(i):
[x,y] = bits(i, 2)
return [x and y]
def and3_gate(i):
[x,y,z] = bits(i,3)
return [x and y and z]
def xor_gate(i):
[x,y] = bits(i, 2)
return [x ^ y]
def andxor_gate(i):
[x,y,z] = bits(i, 3)
return [(x & y) ^ z]
def nested_xor_gate(i):
[x,y,z] = bits(i, 3)
return [x^y^z]
def adder_gate(i):
[x, y, cin] = bits(i, 3)
z = x ^ y ^ cin
cout = (x & y) | (z & cin)
return [z, cout]
# }}}
# helper gates {{{
def and3_helper_gate(i, j, z_gb):
[a0,a1,a2] = bits(i^j, 3)
return (a0 & a1) ^ z_gb
# }}}
# symbolic matrix class {{{
class smatrix (list):
def __init__(self, nrows, ncols, premapping={}, initialize=True):
self.nrows = nrows
self.ncols = ncols
for y in range(nrows):
if initialize:
if y in premapping:
assert( ncols == len(premapping[y]) )
self.append( premapping[y] )
else:
self.append([ FreshSymbol(BOOL) for x in range(ncols) ])
else:
self.append([ None for x in range(ncols) ])
def dims(self): return (self.nrows, self.ncols)
def transpose(self):
A_t = smatrix(self.ncols, self.nrows, initialize=False)
for i in range(self.nrows):
for j in range(self.ncols):
A_t[j][i] = self[i][j]
return A_t
def mul(self, A):
assert(self.ncols == A.nrows)
A_t = A.transpose()
C = smatrix(self.nrows, A.ncols, initialize=False)
for i in range(self.nrows):
for j in range(A_t.nrows):
z = reduce( Xor, [ And(x, y) for (x, y) in zip(self[i], A_t[j]) ])
C[i][j] = z
return C
def det(self):
assert(self.nrows == self.ncols)
zs = []
for pi in itertools.permutations(list(range(self.nrows))):
xs = [ self[i][pi[i]] for i in range(self.nrows) ]
zs.append( And( *xs ) )
return reduce( Xor, zs )
def reverse_mapping(self, model):
out = []
for i in range(self.nrows):
out.append([])
for j in range(self.ncols):
if model.get_value(self[i][j]).is_true():
out[i].append( 1 )
else:
out[i].append( 0 )
return out
def concat_rows(self, rows):
if not rows: return copy.deepcopy(self)
ncols = max(*([self.ncols] + list(map(len, rows))))
out = smatrix(self.nrows + len(rows), ncols, initialize=False)
elems = copy.deepcopy(self) + copy.deepcopy(rows)
for i in range(out.nrows):
while len(elems[i]) < ncols:
elems[i].append( F )
out[i] = elems[i]
return out
# adds zero cols as necessary
def eq(self, other):
assert(self.nrows == other.nrows)
return mapall(lambda t: vec_eq(t[0], t[1]), list(zip(self, other)))
def with_rows(self, rows):
out = smatrix( len(rows), self.ncols, initialize=False )
for (i, row) in zip(list(range(len(rows))), rows):
out[i] = copy.copy(self[row])
return out
def max_hamming_weight(self, n):
return mapall(lambda row: hamming_weight_leq(row, n), self)
def get_variables(self):
return sum(self, [])
# }}}
# vector ops {{{
def hamming_weight_leq(vec, n):
ints = [ FreshSymbol(INT) for x in vec ]
p = T
total = Int(0)
for (x, y) in zip(vec, ints):
q = Ite(x, Equals(y, Int(1)), Equals(y, Int(0)))
p = And(p,q)
total = Plus(total, y)
q = LE(total, Int(n))
p = And(p, q)
return p
def id_matrix(nrows, ncols):
I = smatrix(nrows, ncols)
for row in range( nrows ):
for col in range( ncols ):
if row == col:
I[row][col] = T
else:
I[row][col] = F
return I
def vec_leq(v,w):
assert(len(v) == len(w))
if len(v) == 1: return And(Not(v[0]), w[0])
return Or(And(Not(v[-1]), w[-1]), And(Not(Xor(v[-1], w[-1])), vec_leq(v[:-1], w[:-1])))
def vec_eq(v, w):
vp = copy.copy(v)
wp = copy.copy(w)
if len(v) < len(w):
for i in range(len(w) - len(v)):
vp.append(F)
elif len(w) < len(v):
for i in range(len(v) - len(w)):
wp.append(F)
assert(len(vp) == len(wp))
cs = [ Not(Xor(x,y)) for (x,y) in zip(vp,wp) ]
return And(*cs)
def right_zeros(v, num_nonzero):
return Not(Or(*v[num_nonzero:]))
# }}}
# oracle constraint class {{{
class constraint:
def __init__(self, lhs, rhs):
self.lhs = lhs
self.rhs = rhs
def __repr__(self):
return "Constraint lhs={} rhs={}".format(self.lhs, self.rhs)
def basis_change(self, B):
lhs_ = self.lhs.mul(B)
rhs_ = self.rhs.mul(B)
return constraint(lhs_, rhs_)
def reverse_mapping(self, model):
lhs_ = self.lhs.reverse_mapping(model)
rhs_ = self.rhs.reverse_mapping(model)
return constraint(lhs_, rhs_)
def eq(self, other):
return And( self.lhs.eq(other.lhs), self.rhs.eq(other.rhs) )
def get_variables(self):
return self.lhs.get_variables() + self.rhs.get_variables()
# }}}
################################################################################
## formula generation
def generate_constraints(n_constraints, arity, previous_fresh, adaptive=True):# {{{
n_fresh = n_constraints + previous_fresh
cs = []
for i in range(n_constraints):
lhs = smatrix( arity, n_fresh, initialize=False )
rhs = smatrix( 1, n_fresh, initialize=False )
for j in range( arity ):
for k in range( n_fresh ):
if k < previous_fresh:
lhs[j][k] = FreshSymbol(BOOL)
elif adaptive and previous_fresh <= k < i + previous_fresh:
lhs[j][k] = FreshSymbol(BOOL)
else:
lhs[j][k] = F
for k in range( n_fresh ):
if k == i + previous_fresh:
rhs[0][k] = T
else:
rhs[0][k] = F
cs.append( constraint( lhs, rhs ))
# ensure lexocographic ordering
lex = T
for i in range(n_constraints - 1):
v = sum(cs[i].lhs, [])
w = sum(cs[i+1].lhs, [])
p = vec_leq(v,w)
lex = And(lex,p)
return (cs, lex)
# }}}
def get_view(Gb, params, i, j, z):# {{{
width = Gb[0][0].ncols
size = Gb[0][0].nrows
alphas = bits(i ^ j, params['input_bits'])
v = smatrix(params['input_bits'], width, initialize=False)
for row in range(params['input_bits']):
for col in range(width):
if row == col or (col == params['delta'] and alphas[row]):
v[row][col] = T
else:
v[row][col] = F
return v.concat_rows( Gb[i][z][:-params['output_bits']] ) # Gb[i] without its output row
# }}}
def security(Gb, Gb_C, B, params):# {{{
secure = T
with tqdm.tqdm(total=2**(params['color_bits']+params['input_bits']+params['helper_bits']), desc="security") as pbar:
for i in range(2**params['color_bits']):
for j in range(2**params['input_bits']):
for z in range(2**params['helper_bits']):
view = get_view(Gb, params, i, j, z)
s = security_(view, Gb_C[i][z], B[i][j][z], params['reach'], params['delta'])
secure = And(secure, s)
pbar.update(1)
return secure
# }}}
def security_(view, Cs, B, reach, delta):# {{{
mat_const = And(*[ right_zeros(row, reach) for row in view.mul(B) ] )
con_const = T
for C in Cs:
C_ = C.basis_change(B)
p = And(*[ right_zeros(v, reach) for v in C_.lhs ])
q = And(*[ right_zeros(v, reach) for v in C_.rhs ])
con_const = And( con_const, Implies(p, q) )
basis_const = Not( right_zeros( B[delta], reach ))
return And(*[ mat_const, con_const, basis_const ])
# }}}
def helper_bit_permuted( m ):# {{{
p = And(m[0][0], m[1][1])
q = And(m[0][1], m[1][0])
return (Or(p,q), q)
# }}}
def correctness(Gb, Gb_C, B, Ev, Ev_C, params):# {{{
accum = T
zijs = {}
with tqdm.tqdm(total=2**(params['input_bits']+params['color_bits']), desc="correctness") as pbar:
for i in range(2**params['color_bits']):
for j in range(2**params['input_bits']):
z_assns = []
for z_gb in range(2**params['helper_bits']):
if 'helper_gate' in params:
z_ev = params['helper_gate'](i,j,z_gb)
p = correctness_(Gb, Gb_C, B, Ev, Ev_C, i, j, z_gb, z_ev, params)
z_assns.append([F,T] if z_ev else [T,F])
else:
qs = []
for z_ev in range(2**params['helper_bits']):
q = correctness_(Gb, Gb_C, B, Ev, Ev_C, i, j, z_gb, z_ev, params)
qs.append(q)
z_assns.append(qs)
p = Or(*qs)
accum = And(accum, p)
if params['helper_bits'] == 1: # TODO expand to general case
(q,zij) = helper_bit_permuted(z_assns)
accum = And(accum, q)
zijs[(i,j)] = zij
pbar.update(1)
return (accum, zijs)
# }}}
def correctness_(Gb, Gb_C, B, Ev, Ev_C, i, j, z_gb, z_ev, params):# {{{
# concat the output wires to the view, check that the top part is id, bottom eq to ev
view = get_view(Gb, params, i, j, z_gb)
outs = Gb[i][z_gb].with_rows(params['output_rows'])
for k in range(params['output_bits']):
if params['gate'](i^j)[k]:
outs[k][params['delta']] = Not( outs[k][params['delta']] )
checkL = view.concat_rows(outs).mul(B[i][j][z_gb])
checkR = id_matrix(view.nrows, view.ncols).concat_rows(Ev[j][z_ev])
ev_correct = checkL.eq(checkR)
# ev_correct = outs.mul(B[i][j][z_gb]).eq(Ev[j][z_ev])
# each evaluator oracle query equals one in the basis changed garble constraints
Gb_C_ = [ c.basis_change(B[i][j][z_gb]) for c in Gb_C[i][z_gb] ]
matched_oracles = T
for ev_c in Ev_C[j][z_ev]:
c = Or( *[ev_c.eq(d) for d in Gb_C_])
matched_oracles = And(matched_oracles, c)
return And(ev_correct, matched_oracles)
# }}}
def generate_gb(params, check_security=True, check_correct=True, check_inv=True):# {{{
input_bits = params['input_bits']
output_bits = params['output_bits']
h_arity = params['h_arity']
h_calls_gb = params['h_calls_gb']
h_calls_ev = params['h_calls_ev']
gate = params['gate']
size = params['size']
reach = params['reach'] = size + input_bits + h_calls_ev
gb_width = params['gb_width'] = input_bits + 1 + h_calls_gb
ev_width = params['ev_width'] = size + input_bits + h_calls_ev
delta = params['delta'] = input_bits
if not 'adaptive' in params:
params['adaptive'] = 1
adaptive = params['adaptive']
if not 'helper_bits' in params:
params['helper_bits'] = 0
if not 'privacy_free' in params:
params['privacy_free'] = False
helper_bits = params['helper_bits']
params['output_rows'] = list(range( size, size + output_bits))
if params['privacy_free']:
color_bits = params['color_bits'] = 0
else:
color_bits = params['color_bits'] = input_bits
# print "params =", params
################################################################################
## variables
# a garbling scheme for each i
gb = []
cs = []
lex_gb = T
with tqdm.tqdm(total=2**(color_bits+helper_bits), desc="gb") as pbar:
for i in range(2**color_bits):
gb.append([])
cs.append([])
for z in range(2**helper_bits):
g = smatrix( size + output_bits, gb_width )
(c,lex) = generate_constraints( h_calls_gb, h_arity, input_bits+1, adaptive)
lex_gb = And(lex_gb, lex)
gb[i].append(g)
cs[i].append(c)
pbar.update(1)
# a basis change for each (i,j)
bs = []
bi = []
with tqdm.tqdm(total=2**(color_bits+helper_bits+input_bits), desc="bs") as pbar:
for i in range(2**color_bits):
bs.append([])
bi.append([])
for j in range(2**input_bits):
bs[i].append([])
bi[i].append([])
for z in range(2**helper_bits):
b = smatrix( gb_width, gb_width, { delta:[F]*(gb_width-1)+[T] })
view = get_view(gb, params, i, j, z)
b_ = view.concat_rows(smatrix(view.ncols - view.nrows, gb_width))
bs[i][j].append(b)
bi[i][j].append(b_)
pbar.update(1)
# an evaluation scheme for each j
ev = []
ec = []
lex_ev = T
with tqdm.tqdm(total=2**(input_bits+helper_bits), desc="ev") as pbar:
for j in range(2**input_bits):
ev.append([])
ec.append([])
for z in range(2**helper_bits):
e = smatrix( output_bits, ev_width )
(c, lex) = generate_constraints( h_calls_ev, h_arity, size + input_bits )
lex_ev = And(lex_ev, lex)
ev[j].append(e)
ec[j].append(c)
pbar.update(1)
################################################################################
## constraints
# bs_invertable = And(*[ And(*[ b.det() for b in bi ]) for bi in bs ])
bs_invertable = T
if check_inv:
I = id_matrix( gb_width, gb_width )
with tqdm.tqdm(total=2**(color_bits+input_bits+helper_bits), desc="inv") as pbar:
for i in range(2**color_bits):
for j in range(2**input_bits):
for z in range(2**helper_bits):
p = I.eq( bs[i][j][z].mul(bi[i][j][z]) )
bs_invertable = And(bs_invertable, p)
pbar.update(1)
if check_security:
secure = security(gb, cs, bs, params)
else:
secure = T
if check_correct:
(correct, zijs) = correctness(gb, cs, bs, ev, ec, params)
else:
correct = T
zijs = {}
ham_gb = T
if 'hamming_weight_gb' in params:
print("max hamming weight (gb):", params['hamming_weight_gb'])
ham_gb = mapall(lambda outer: \
mapall(lambda e: e.max_hamming_weight(params['hamming_weight_gb']), outer), gb)
ham_ev = T
if 'hamming_weight_ev' in params:
print("max hamming weight (ev):", params['hamming_weight_ev'])
ham_ev = mapall(lambda outer: \
mapall(lambda e: e.max_hamming_weight(params['hamming_weight_ev']), outer), ev)
lex = And(lex_gb, lex_ev)
################################################################################
## the formula
return { 'formula' : And(*[ bs_invertable, secure, correct, ham_gb, ham_ev, lex ])
, 'params' : params
, 'bs' : bs
, 'gb' : gb
, 'cs' : cs
, 'ev' : ev
, 'ec' : ec
, 'zijs' : zijs
}
# }}}
################################################################################
## solver
def check_scheme(scheme, solver='z3'):# {{{
s = Solver(name=solver)
s.add_assertion(scheme['formula'])
ok = s.solve()