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