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common.py
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common.py
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from sage.all import inverse_mod
from cryptools.env import *
def compress(mat):
s = sorted(set(mat.list()))
inv = {v: i for i, v in enumerate(s)}
return mat.apply_map(inv.__getitem__)
def colfreq(mat):
mat = mat[:,:]
for x in xrange(0, mat.ncols()):
col = mat.column(x)
cnt = Counter(col)
col = col.apply_map(cnt.__getitem__)
mat.set_column(x, col)
return mat
def rowfreq(mat):
return colfreq(mat.transpose()).transpose()
def print_latex_minicipher(T, name, extend=None):
for k in xrange(len(T)):
res = [r"$" + name + r"_{\hex{%1X}}$" % k]
for x in xrange(8):
res.append(r"$\hex{%1x}$" % T[k][x])
if extend:
res += list(extend[k])
print " & ".join(res) + r"\\"
def print_latex_func(f, name):
print name, "~&~",
res = []
for y in f:
res.append(r"$\hex{%1x}$" % y)
print " & ".join(res) + r"\\"
def print_latex_lookup(f, name):
res = []
for y in f:
res.append(r"\hex{%1x}" % y)
print r"\lookup{%s} = (%s)" % (name, ",".join(res))
def print_latex_matrix(mat, name):
print name + r" = \matb{"
for row in mat:
print " & ".join(map(str, row)), r"\\"
print "}"
S0 = SBox2([
0x00, 0x36, 0x30, 0x0d, 0x0f, 0x12, 0x35, 0x23, 0x19, 0x3f, 0x2d, 0x34, 0x03, 0x14, 0x29, 0x21,
0x3b, 0x24, 0x02, 0x22, 0x0a, 0x08, 0x39, 0x25, 0x3c, 0x13, 0x2a, 0x0e, 0x32, 0x1a, 0x3a, 0x18,
0x27, 0x1b, 0x15, 0x11, 0x10, 0x1d, 0x01, 0x3e, 0x2f, 0x28, 0x33, 0x38, 0x07, 0x2b, 0x2c, 0x26,
0x1f, 0x0b, 0x04, 0x1c, 0x3d, 0x2e, 0x05, 0x31, 0x09, 0x06, 0x17, 0x20, 0x1e, 0x0c, 0x37, 0x16,
])
etat = SBox2((0, 8, 18, 26, 1, 9, 19, 27, 2, 10, 16, 24, 3, 11, 17, 25, 4, 12, 22, 30, 5, 13, 23, 31, 6, 14, 20, 28, 7, 15, 21, 29, 32, 40, 50, 58, 33, 41, 51, 59, 34, 42, 48, 56, 35, 43, 49, 57, 36, 44, 54, 62, 37, 45, 55, 63, 38, 46, 52, 60, 39, 47, 53, 61))
eta_S0 = SBox2((0, 55, 36, 11, 25, 22, 45, 58, 14, 61, 43, 37, 26, 5, 42, 40, 60, 33, 18, 50, 16, 2, 46, 41, 39, 30, 48, 17, 54, 20, 52, 6, 59, 28, 13, 12, 4, 15, 8, 53, 57, 34, 62, 38, 27, 56, 35, 51, 29, 24, 1, 7, 47, 49, 9, 44, 10, 19, 31, 32, 21, 3, 63, 23))
T = map(SBox2, [(0, 6, 4, 7, 3, 1, 5, 2),
(7, 5, 1, 6, 4, 2, 0, 3),
(4, 3, 2, 0, 5, 6, 1, 7),
(3, 5, 2, 1, 4, 6, 7, 0),
(1, 2, 0, 6, 4, 3, 7, 5),
(6, 5, 2, 4, 7, 0, 1, 3),
(5, 2, 6, 4, 0, 3, 1, 7),
(2, 0, 1, 6, 5, 3, 4, 7)]
)
U = map(SBox2, [(0, 3, 6, 4, 2, 7, 1, 5),
(7, 4, 0, 2, 3, 6, 1, 5),
(1, 4, 2, 6, 3, 0, 5, 7),
(7, 2, 5, 1, 3, 0, 4, 6),
(7, 3, 4, 1, 0, 2, 6, 5),
(3, 7, 1, 4, 2, 0, 5, 6),
(1, 3, 7, 4, 6, 2, 5, 0),
(4, 6, 3, 0, 5, 1, 7, 2)]
)
Mu = SBox2((0, 9, 59, 50, 4, 13, 63, 54, 40, 33, 19, 26, 44, 37, 23, 30, 32, 41, 27, 18, 36, 45, 31, 22, 8, 1, 51, 58, 12, 5, 55, 62, 16, 25, 43, 34, 20, 29, 47, 38, 56, 49, 3, 10, 60, 53, 7, 14, 48, 57, 11, 2, 52, 61, 15, 6, 24, 17, 35, 42, 28, 21, 39, 46))
Mup = SBox2((0, 9, 27, 18, 12, 5, 23, 30, 8, 1, 19, 26, 4, 13, 31, 22, 48, 57, 43, 34, 60, 53, 39, 46, 56, 49, 35, 42, 52, 61, 47, 38, 40, 33, 51, 58, 36, 45, 63, 54, 32, 41, 59, 50, 44, 37, 55, 62, 24, 17, 3, 10, 20, 29, 15, 6, 16, 25, 11, 2, 28, 21, 7, 14))
X = GF(2).polynomial_ring().gen()
F3 = GF(2**3, name='w', modulus=X**3 + X + 1)
fromF = lambda x: x.integer_representation()
toF = F3.fetch_int
F6 = GF(2**6, name='v')
x = PolynomialRing(F3, names='x').gen()
inv = SBox2.gen.from_poly(x**6)
w = F3.gen()
assert w**3 + w + 1 == 0
fexp = SBox2([0] + [(w**i).integer_representation() for i in xrange(1, 8)])
flog = ~fexp
# fexp (0, 2, 4, 3, 6, 7, 5, 1)
# flog (0, 7, 1, 3, 2, 6, 4, 5)
texlog_list = [r"{\WZ}"] + [r"\WW^%d" % flog[i] for i in xrange(1, 8)]
def texlog(c):
if not isinstance(c, int):
c = c.integer_representation()
return texlog_list[c]
def texpoly(poly, no7=True, no0=False, linear=False):
coeffs = list(poly) + [0] * 8
res = []
for e in xrange(8):
if linear and e in (3, 5, 6):
assert coeffs[e] == 0
continue
if no0 and e == 0:
assert coeffs[e] == 0
continue
if no7 and e == 7:
assert coeffs[e] == 0
continue
if e == 0:
res.append(texlog(coeffs[0]))
elif e == 1:
res.append(texlog(coeffs[e]) + "x")
else:
res.append(texlog(coeffs[e]) + "x^%d" % e)
return "$" + " + ".join(res[::-1]) + "$"
q = SBox2((0, 7, 6, 1, 5, 2, 3, 4)) # (w + 1)*x^4 + (w^2 + w + 1)*x^2 + (w + 1)*x
z = SBox2((0, 3, 7, 4, 2, 1, 5, 6)) # x^4 + w^2*x^2 + (w^2 + w)*x
def openButterfly(e, alpha, n=3, sx=False, sy=False):
F = GF(2**n, name='w')
if n == 3:
assert F == F3
ei = inverse_mod(e, 2**n-1)
alpha = F.fetch_int(alpha)
s = []
for x, k in product(range(2**n), range(2**n)):
x = F.fetch_int(x)
k = F.fetch_int(k)
x += k**e
x = x**ei
if sx: x, k = k, x
x += alpha*k
x, k = k, x
x += alpha*k
if sy: x, k = k, x
x = x**e
x += k**e
x = x.integer_representation()
k = k.integer_representation()
s.append((x << n) | k)
return SBox2(s)
def closedButterfly(e, alpha, n=3):
F = GF(2**n, name='w')
if n == 3:
assert F == F3
alpha = F.fetch_int(alpha)
s = []
for x, y in product(range(2**n), range(2**n)):
x = F.fetch_int(x)
y = F.fetch_int(y)
l = (x + alpha*y)**e + y**e
r = (y + alpha*x)**e + x**e
l = l.integer_representation()
r = r.integer_representation()
s.append((l << n) | r)
return SBox2(s)
def interpolate2x2(mat):
subs = [mat[3*i:3*i+3,3*j:3*j+3] for i in xrange(2) for j in xrange(2)]
res = []
for sub in subs:
lin = SBox2.gen.from_matrix(sub)
lin.n = 3
res.append(lin.interpolation_polynomial(F3))
return res