International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 01 May 2015

Abderrahmane Nitaj, Tajjeeddine Rachidi
ePrint Report ePrint Report
In this paper, we study the problem of factoring an RSA modulus $N=pq$ in polynomial time, when $p$ is a weak prime, that is, $p$ can be expressed as $ap=u_0+M_1u_1+\\ldots+M_ku_k$ for some $k$ integers $M_1,\\ldots, M_k$ and $k+2$ suitably small parameters $a$, $u_0,\\ldots u_k$. We further compute a lower bound for the set of weak moduli, that is, moduli made of at least one weak prime, in the interval $[2^{2n},2^{2(n+1)}]$ and show that this number is much larger than the set of RSA prime factors satisfying Coppersmith\'s conditions, effectively extending the likelihood for factoring RSA moduli. We also prolong our findings to moduli composed of two weak primes.

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