Question 1.sagews

Here is Alice's public key:

n = 0x462bf18da08a5a066e8c129d37c1689ffaa447b5fad69e3468f9554d44b0a8cda67fed9a6bd59214ec4fc391947c47e85a5954fd6bf18b8a920b6310b81a5b81a50cb1f2c0382543bc775aa89b6f93303d2c6389c2e46c8dcf487a5108de7bccade0793c65987c79d710eede96d277dde294c764e121e6150ba46e68f29eb559

e = 0x155a8fb411be3490bc23fda5ea2ec569af806faf811147610bb7ccfecbe6ea2af37cf07c25a8494644ac5ace694fca04929ab30da8e7b7a67f81ca9f643c1212786ed897f5dde3ee658fcd3da3ed0e1d5c42007ac44b0021731b150a35ae385576ae50d6f416cf46a69d0dce5ca2b0f20ade842b379e19174810c70cd9692d5f

And here is a sample ciphertext produced with it:

c = 0x42fb52a80869aa6ad4a55102a983fdf2d82a36361f6ef35b5927eb226fe1b01f3d046b3d84b34f493e4b23cd4ed6178bff497ff08081218771c98e2360ae5e9862ce60529edf64bcbbac99d8db30e8b66372b565f7d8d6ebbd52bc60b5c054b8b3530f24cf84f6d6d32d07f4c5cd961e3d2029e7ba51622a057959272beaf6e9

def fermat(n):
    a = isqrt(n) # int(ceil(n**0.5))
    b2 = a*a - n
    b = isqrt(n) # int(b2**0.5)
    while b*b != b2:
        a = a + 1
        b2 = a*a - n
        b = isqrt(b2) # int(b2**0.5)
    p=a+b
    q=a-b
    return p, q

tab = fermat(n)
p = tab[0]
q = tab[1]
phi = p-1 * q-1
d = xgcd(e,phi)[1];
print "d is equal to %s." % d
if d < 0:
    d = (1/e) % phi;
    print "But as a positive integer, d can be equal to %s." % d

#while j>iseqrt:
    #print "passage"
    #i=1
    #while i < iseqrt:
        #if (i*j) == n:
         #   p=i
         #   q=j
         #   j = isqrt(n) -10
         #   i = iseqrt +10
        #i+=1
            
    #j-=1

print "end"