About RSA problem

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About RSA problem

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About RSA problem

  1. 1. About RSA problem Cristiano Armellini,cristiano.armellini@alice.it
  2. 2. 1 < k< 2 n np= ,q = k ; q = kp k kn = pqs = p+qx 2 − sx + n = 0, x1 = p; x2 = q s ± s 2 − 4nx= 2s≥2 ns numero pari
  3. 3. k >= 2p+q≥2 nq = kp; k ≥ 2; q > p;2 ≤ p ≤ ns = p + q = p(1 + k ) ≥ 2 np ≥ 2 n /(1 + k )2 n n ≤ p≤ ; p dispari1+ k k n n ≤ p≤ k +1 kk = 2,3,4,5,6,7,8,9,...100,...,1000=> parallel computation
  4. 4. K>=2n = pq; q = kp; k > 2; k = 2,3,4,5,6,7,8,9,10Log (n) = Log ( pq) = Log ( p) + Log (q) == 2 Log ( p ) + Log (k ) Log ( n ) − Log ( k )p = 10 2 Log ( n ) − Log ( k +1) Log ( n ) − Log ( k )10 2 < p < 10 2
  5. 5. m>=2n = pqx 2 − sx + n = 0 s ± s 2 − 4nx= 2s ≥ 2 n , s ≥ 3 n ; s ≥ 4 n ;.....; s ≥ m n

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