Wienner Covert Channel.sagews

def Wiener (n, s):
    M = 10101
    E = M.powermod(s,n)#&^(M, s) % n
    cf = continued_fraction(n/s)# convert(n / s, confrac)
    m = len(cf)
    for i in range(0, m ):
        conv = cf.convergent(i)
        t = conv.numerator()
        #t = cf.quotient(i)#numtheory:-nthnumer(cf, i)
        d = E.powermod(t,n)#&^(E, t) % n
        #print d
        if d == M:
            print("k:= {0}".format(cf.convergent(i).denominator()))
            print("The totient of the modulus is {0}".format((s*t-1)/(cf.convergent(i).denominator())))
            print("The private key is {0}".format(t))
            return [t, (s*t-1)/(cf.convergent(i).denominator())]
    print("Private key not found")

def WienerCovert (P):
    p = next_prime(ZZ.random_element(P^2))
    q = next_prime(ZZ.random_element(P^2))
    while(not((q<p) and (p<2*q))):
        p = next_prime(ZZ.random_element(P^2))
        q = next_prime(ZZ.random_element(P^2))
    n = p*q
    phin = (p-1)*(q-1)
    l = ZZ(floor((n^(1/4))/3))
    for i in range(1000):
        d1 = l-i
        g = gcd(d1,phin)
        if (g == 1):
            s1 = 1/d1 % phin
            s2 = s1*P % n
            g1 = gcd(s2,phin)
            if(g1 == 1):
                d2 = 1/s2 % phin
                print "The modulus is: ", n
                print "The exponent is: ", s2
                print "The key is: ", d2
                return([n,s2,d2])

P = next_prime(983724836482)
R = WienerCovert(P)
print "end of creatiom of covert channel"
S = R[1]/P % R[0]
wienerAttackOutput = Wiener(R[0],S)
print "after wieners attack"
d = 1/R[1] % wienerAttackOutput[1]
d
if (R[2] == d):
    print "correct private key computed"

The modulus is: 162996458187706035673135889099890482856112226697 The exponent is: 94344369869984932236004780866259533022210541589 The key is: 56419832253583618233458429492162599992204825621 end of creatiom of covert channel k:= 22430205604 The totient of the modulus is 162996458187706035673135081204137668474884176916 The private key is 211798698559 after wieners attack 56419832253583618233458429492162599992204825621 correct private key computed