def solve(self, target, all=False):
target = vector(self.field, target) - self.zero
x = self.matrix.solve_right(vector(self.field, target))
if not all:
return x
for z in self.kernel:
yield z + x
def __init__(self, oracle, n_in, field=F2, ntests=10):
self.oracle = oracle
self.field = field
self.n_in = int(n_in)
self.zero = vector(field, oracle([0] * n_in))
self.n_out = len(self.zero)
cols = []
for i in range(n_in):
x = [0] * n_in
x[i] = 1
y = vector(field, oracle(x)) - self.zero
cols.append(y)
self.matrix = matrix(field, cols).transpose()
self._kernel = None
self.rank = self.matrix.rank()
self.kernel_dimension = self.matrix.ncols() - self.rank
self.test_oracle(ntests)
def matrix_mult_int_rev(mat, x):
"""
LSB to MSB vector
>>> matrix_mult_int_rev( \
matrix(GF(2), [[1, 0, 1], [1, 0, 0]]), \
0b110) # read as 6 -> 0,1,1 -> 1,0 -> 1
1
"""
assert mat.base_ring() == GF(2)
n = mat.ncols()
x = vector(GF(2), Bin(x, n).tuple[::-1])
y = mat * x
return Bin(y[::-1]).int
def matrix_mult_int(mat, x):
"""
MSB to LSB vector
>>> matrix_mult_int( \
matrix(GF(2), [[1, 0, 1], [1, 0, 0]]), \
0b110) # read as 6 -> 1,1,0 -> 1,1 -> 3
3
"""
assert mat.base_ring() == GF(2)
n = mat.ncols()
x = vector(GF(2), Bin(x, n).tuple)
y = mat * x
return Bin(y).int
def oracle(x):
nonlocal m
return m * vector(fld, x)