def c_s_k_ske(self,x2):
self.x121=gmpy2.powmod(x2,self.k11,self.p)
if(gmpy2.is_even(self.x121)):
self.e2=gmpy2.sub(self.x121,1)
else:
self.e2=self.x121
self.d2=gmpy2.divm(1,self.e2,gmpy2.sub(self.p,1))
def c_s_k_sbox(self,x2):
self.x21=gmpy2.powmod(x2,self.k1,self.p)
if(gmpy2.is_even(self.x21)):
self.e1=gmpy2.sub(self.x21,1)
self.x(self.e1)
else:
self.e1=self.x21
self.x(self.e1)
self.d1=gmpy2.divm(1,self.e1,gmpy2.sub(self.p,1))
def weiner(N,e):
for c in cf2cvg(f2cf(e,N)):
k = c.numerator
if k == 0:
continue
d = c.denominator
phi = (e*d - 1) / k
b = N - phi + 1
det = b*b - 4*N
if det < 0:
continue
root = g.mpz(g.sqrt(det))
if g.is_square(det) and g.is_even(b + root):
p = (b + root) / 2
q = (b - root) / 2
if checkFactors(p,q,N):
return (p,q,d)
raise Exception("Invalid result generated")
def wiener_attack(N, e):
"""Perform Wiener's attack.
:param N: RSA public key N.
:param e: RSA public key e.
"""
convergents = cf_convergents(cf(e, N))
for k,d in convergents:
if k == 0 or (e * d - 1) % k != 0:
continue
phi = (e * d - 1) / k
c = N - phi + 1
# now p,q can be the root of x**2 - s*x + n = 0
det = c * c - 4 * N
if not det >= 0:
continue
s, r = gmpy2.isqrt_rem(det)
if r == 0 and gmpy2.is_even(c + s):
return (d, (c + s) / 2,(c - s) / 2)
# Failed
return None
def wiener_attack(N, e):
"""Perform Wiener's attack.
:param N: RSA public key N.
:param e: RSA public key e.
"""
convergents = cf_convergents(cf(e, N))
for k, d in convergents:
if k == 0 or (e * d - 1) % k != 0:
continue
phi = (e * d - 1) // k
c = N - phi + 1
# now p,q can be the root of x**2 - s*x + n = 0
det = c * c - 4 * N
if not det >= 0:
continue
s, r = gmpy2.isqrt_rem(det)
if r == 0 and gmpy2.is_even(c + s):
return (d, (c + s) // 2, (c - s) // 2)
# Failed
return None
