def hack_RSA(e, n):
'''
Finds d knowing (e,n)
applying the Wiener continued fraction attack
'''
frac = ContinuedFractions.rational_to_contfrac(
e, n) # Создаём list частных непрерывных дрообей [a0, ..., an]
convergents = ContinuedFractions.convergents_from_contfrac(
frac) # вычисление подходящих дробей
for (k, d) in convergents:
# print('k, d: ', k, d)
#check if d is actually the key
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d - 1) // k
s = n - phi + 1
# check if the equation x^2 - s*x + n = 0
# has integer roots
discr = s * s - 4 * n
# print(phi, s, discr)
if (discr >= 0):
t = Arithmetic.is_perfect_square(discr)
# print('sqrt: ', t)
if t != -1 and (s + t) % 2 == 0:
print("Hacked!")
return d
def hack_RSA(e, n):
'''
Finds d knowing (e,n)
applying the Wiener continued fraction attack
'''
# n = input("Enter e number: ")
# e = input("Enter n number: ")
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k, d) in convergents:
#check if d is actually the key
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d + 1) // k
s = n - phi + 1
# check if the equation x^2 - s*x + n = 0
# has integer roots
discr = s * s - 4 * n
if (discr >= 0):
t = Arithmetic.is_perfect_square(discr)
if t != -1 and (s + t) % 2 == 0:
print("Hacked!")
print("-------------------------")
print("d = ", d)
print("-------------------------")
def hack_RSA(e, n):
'''
Finds d knowing (e,n)
applying the Wiener continued fraction attack
'''
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k, d) in convergents:
#check if d is actually the key
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d - 1) // k
s = n - phi + 1
# check if the equation x^2 - s*x + n = 0
# has integer roots
'''discr = s * s - 4 * n
if(discr >= 0):
t = Arithmetic.is_perfect_square(discr)
if t != -1 and (s + t) % 2 == 0:
print("Hacked!")
return d'''
flag = 0
for i in range(40):
a = random.randint(2, n)
if pow(a, phi, n) != 1:
flag = 1
break
if flag == 0:
print("Hacked!")
return d
def wiener(e, n):
time.sleep(1)
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k, d) in convergents:
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d - 1) // k
s = n - phi + 1
discr = s * s - 4 * n
if (discr >= 0):
t = Arithmetic.is_perfect_square(discr)
if t != -1 and (s + t) % 2 == 0:
return d
def wiener(e,n):
time.sleep(1)
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k,d) in convergents:
if k!=0 and (e*d-1)%k == 0:
phi = (e*d-1)//k
s = n - phi + 1
discr = s*s - 4*n
if(discr>=0):
t = Arithmetic.is_perfect_square(discr)
if t!=-1 and (s+t)%2==0:
return d
def wiener(e, n):
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k,d) in convergents:
if k!=0 and (e*d-1)%k == 0:
phi = (e*d-1)//k
s = n - phi + 1
# check if the equation x^2 - s*x + n = 0
# has integer roots
discr = s*s - 4*n
if(discr>=0):
t = Arithmetic.is_perfect_square(discr)
if t!=-1 and (s+t)%2==0:
return d
def hack_RSA(e, n):
print "Hacking"
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k, d) in convergents:
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d - 1) // k
s = n - phi + 1
discr = s * s - 4 * n
if(discr >= 0):
t = Arithmetic.is_perfect_square(discr)
if t != -1 and (s + t) % 2 == 0:
print "done"
print d
return d
def wiener_hack(e, n):
# https://github.com/pablocelayes/rsa-wiener-attack
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k, d) in convergents:
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d - 1) // k
s = n - phi + 1
discr = s * s - 4 * n
if (discr >= 0):
t = Arithmetic.is_perfect_square(discr)
if t != -1 and (s + t) % 2 == 0:
print("Hacked!")
return d
return False
def hack_RSA(e, n):
print "Hacking"
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k, d) in convergents:
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d - 1) // k
s = n - phi + 1
discr = s * s - 4 * n
if (discr >= 0):
t = Arithmetic.is_perfect_square(discr)
if t != -1 and (s + t) % 2 == 0:
print "done"
print d
return d
def hack_RSA(e,n):
print "[+] Wiener attack in progress..."
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k,d) in convergents:
#check if d is actually the key
if k!=0 and (e*d-1)%k == 0:
phi = (e*d-1)//k
s = n - phi + 1
# check if the equation x^2 - s*x + n = 0
# has integer roots
discr = s*s - 4*n
if(discr>=0):
t = Arithmetic.is_perfect_square(discr)
if t!=-1 and (s+t)%2==0:
return d
def hack_RSA(e, n):
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k, d) in convergents:
#check if d is actually the key
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d - 1) // k
s = n - phi + 1
# check if the equation x^2 - s*x + n = 0
discr = s * s - 4 * n
if (discr >= 0):
t = Arithmetic.is_perfect_square(discr)
if t != -1 and (s + t) % 2 == 0:
print("Xong!")
return d
def wiener_attack(n, e):
'''
Finds d knowing (e,n)
applying the Wiener continued fraction attack
'''
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k,d) in convergents:
#check if d is actually the key
if k!=0 and (e*d-1)%k == 0:
phi = (e*d-1)//k
s = n - phi + 1
# check if the equation x^2 - s*x + n = 0
# has integer roots
discr = s*s - 4*n
if(discr>=0):
t = helper.is_perfect_square(discr)
if t!=-1 and (s+t)%2==0:
print("Hacked!")
return d
def hack_RSA(e, n):
"""
Finds d knowing (e, n) applying the Wiener continued fraction attack
"""
frac = ContinuedFractions.rational_to_contfrac(e, n)
convergents = ContinuedFractions.convergents_from_contfrac(frac)
for (k, d) in convergents:
# Check if d is actually the key
if k != 0 and (e * d - 1) % k == 0:
phi = (e * d - 1) // k
s = n - phi + 1
# Check if the equation x^2 - s*x + n = 0 has integer roots
discr = s * s - 4 * n
if(discr >= 0):
t = Arithmetic.is_perfect_square(discr)
if t != -1 and (s + t) % 2 == 0:
return d
return None
import RSA
import ContinuedFractions as CF
from Functions import *
keySet = RSA.RSA(
1024, True
) #Generates a 1024-bits weak key, verifying the conditions to apply Wiener's theorem
print('RSA key set generated')
N, e = keySet.getPublicKey()
fraction = CF.ContinuedFraction(
e, N) #Generates the continued fraction expantion of e/n
convergents = fraction.getConvergents()
crack_d = 0
for k, d in convergents:
if k != 0 and (e * d) % k == 1:
#We still need to check wether d is the right key
phiN = (e * d -
1) // k #If d is the right key, this should be equal to Phi(N)
s = N - phiN + 1 #... and this should be equal to p+q
# We solve the equation x²-sx+N = 0, the solutions should be p and q
disc = s * s - 4 * N
p = (s + Sqrt(disc) +
1) // 2 #Sqrt computes the rounded down square root
q = (s - Sqrt(disc)) // 2
if (p * q == N):
crack_d = d
break
