def mat_field_mul_const(field, c):
assert field.base_ring() == GF(2)
d = field.degree()
m = matrix(GF(2), d, d)
for i, e in enumerate(reversed(range(d))):
x = 1 << e
res = field.fetch_int(x) * field.fetch_int(c)
res = tobin(res.integer_representation(), d)
m.set_column(i, res)
return m
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), tobin(x, n))
y = mat * x
return frombin(y)
def cmul_xor_ddt(self, F=None):
if F is None:
F = GF(self.insize, name='a')
cxddt = matrix(ZZ, self.insize, self.outsize)
for x in xrange(1, self.insize):
for dx in xrange(2, self.insize):
x2 = (F.fetch_int(x) *
F.fetch_int(dx)).integer_representation()
y = self[x]
y2 = self[x2]
dy = y2 ^ y
cxddt[dx, dy] += 1
return cxddt
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), tobin(x, n)[::-1])
y = mat * x
return frombin(y[::-1])
def xor_cmul_ddt(self, F=None):
if F is None:
F = GF(self.insize, name='a')
xcddt = matrix(ZZ, self.insize, self.outsize)
for x in xrange(self.insize):
for dx in xrange(1, self.insize):
x2 = x ^ dx
y = self[x]
y2 = self[x2]
dy = (F.fetch_int(y2) * F.fetch_int(y)
**(self.outsize - 2)).integer_representation()
xcddt[dx, dy] += 1
return xcddt
def mat_from_linear_func(m, n, func):
mat = matrix(GF(2), n, m)
for i, e in enumerate(reversed(range(m))):
x = 1 << e
res = tobin(func(x), n)
mat.set_column(i, res)
return mat
def as_matrix(self):
assert self.is_linear()
m = matrix(GF(2), self.n, self.m)
for e in range(self.m):
x = 1 << e
m.set_column(self.m - 1 - e, tobin(self[x], self.n))
return m
def idup(mat):
"""
I mat
0 I
"""
assert mat.nrows() == mat.ncols()
n = mat.nrows()
res = identity_matrix(GF(2), 2 * n)
res[:n, n:] = mat
return res
def idlo(mat):
"""
I 0
mat I
"""
assert mat.nrows() == mat.ncols()
n = mat.nrows()
res = identity_matrix(GF(2), 2 * n)
res[n:, :n] = mat
return res
def diag(a, b):
"""
a 0
0 b
"""
assert a.nrows() == a.ncols() == b.nrows() == b.ncols()
n = a.nrows()
res = identity_matrix(GF(2), 2 * n)
res[:n, :n] = a
res[n:, n:] = b
return res
def hdim(self, right_to_left=False):
"""
hdim[i,j] = i-th output bit contains monomial x1...xn/xj
"""
res = matrix(GF(2), self.in_bits, self.out_bits)
anf = mobius(tuple(self))
for j in xrange(self.in_bits):
mask = (1 << self.in_bits) - 1
mask ^= 1 << (self.in_bits - 1 - j)
res.set_column(j, tobin(anf[mask], self.out_bits))
if right_to_left:
res = res[::-1, ::-1]
return res
def random_matrix(*args):
return sage_random_matrix(GF(2), *args)
def minilat_binary(self, mod=4):
"""minilat % mod and then mod/2 -> 1, 0 -> 0"""
mat = self.minilat() % 4
for x in mat.list():
assert x in (0, mod / 2), "invalid mod for given function"
return (mat.lift() / (mod / 2)).change_ring(GF(2))
def exponent(n, e, fld=None):
fld = fld or GF(2**n, name='a')
x = PolynomialRing(fld, names='x').gen()
return from_poly(x**e)