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'''
Created on Dec 14, 2011
@author: pablocelayes
'''
import ContinuedFractions, Arithmetic, RSAvulnerableKeyGenerator
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
# TEST functions
def test_hack_RSA():
print("Testing Wiener Attack")
times = 5
while(times>0):
e,n,d = RSAvulnerableKeyGenerator.generateKeys(1024)
print("(e,n) is (", e, ", ", n, ")")
print("d = ", d)
hacked_d = hack_RSA(e, n)
if d == hacked_d:
print("Hack WORKED!")
else:
print("Hack FAILED")
print("d = ", d, ", hacked_d = ", hacked_d)
print("-------------------------")
times -= 1
if __name__ == "__main__":
#test_is_perfect_square()
#print("-------------------------")
test_hack_RSA()