matesS3R2(CryptoX_solve.sage)

CryptoX_solve.sage

from sage.all import *
from Crypto.Util.number import *

#Common Modulus attack
def common_modulus_attack(c1,c2,e1,e2,n):
    print '-----------------------------------Starting Common modulus attack ...----------------------------'
    g,a,b = xgcd(e1,e2)
    print a,b
    c1 = pow(c1,a,n)
    c2 = pow(c2,b,n)
    m = int(c1*c2)
    m = pow(m,1/g)
    print 'Found plaintext: '
    print long_to_bytes(m)


n = 16551607791513310143367718420160496017716438900159843171951158812834625404025819000006450794387195406345952438600612732574009790172009017187068132583686325525604998698900736192681010644918133643334867213766651610742025315226553357161124371160165728228238808856850234798660237966304139110197982306465482087141

e1 = 65537
e2 = 65539
c1 = 1129577506068504469345887363147787486017374614115334845659793955402788290276839150314266230618914458454490822134129029320196215857189604704858201914703171395094716563126451957806227382204438629408146257354346918995020514101912710194471044390206478595928893069122774855951576832331537914647316369902972676419
c2 = 2312267001662149847216610383002454962845172172590149633659040319002856658500558236678068991511310275065117853509318224378486528518801367253730813242027077527555556802869225370500266724893566221191787616000347525781413708804332132838890466815970966346122371108786541601825960204632255691107425283995717582890

common_modulus_attack(c1,c2,e1,e2,n)