dissertacao.pdf

A Implementations of the attacks from section
3.2
A.1 Common Modulus Attack
rcm = {};
i = 3;
While[i < 13,
nbits = 2∧ nbits = 2 i; ∧ nbits = 2 i; ∧i; p = RandomPrime[{2∧ (nbits/2 − 1), 2∧ p = RandomPrime[{2 (nbits/2) − 1}];
∧ (nbits/2 − 1), 2∧ p = RandomPrime[{2 (nbits/2) − 1}];
∧ (nbits/2 − 1), 2∧ (nbits/2) − 1}];
q = RandomPrime[{2∧ (nbits/2 − 1), 2∧ q = RandomPrime[{2 (nbits/2) − 1}];
∧ (nbits/2 − 1), 2∧ q = RandomPrime[{2 (nbits/2) − 1}];
∧ (nbits/2 − 1), 2∧ (nbits/2) − 1}];
While[q == p, q = RandomPrime[{2∧ (nbits/2 − 1), 2∧ While[q == p, q = RandomPrime[{2 (nbits/2) − 1}]];
∧ (nbits/2 − 1), 2∧ While[q == p, q = RandomPrime[{2 (nbits/2) − 1}]];
∧ (nbits/2 − 1), 2∧ (nbits/2) − 1}]];
n = p ∗ q;
e1 = n;
While[e1 == n, e1 = RandomPrime[n]; ]
e2 = n;
While[e2 == ne2 ne2 ne2 == e1, e2 = RandomPrime[n]; ]
m = RandomPrime[n];
c1 = PowerMod[m, e1, n];
c2 = PowerMod[m, e2, n];
r = Append[rcm, {nbits, Timing[
l = ExtendedGCD[e1, e2];
a1 = l[[2, 1]];
a2 = l[[2, 2]];
dec = Mod[PowerMod[c1, a1, n] ∗ PowerMod[c2, a2, n], n]
][[1]]}];
Print[rcm];
i++;
]
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