A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Modern Computer Algebra
Revisiting Wiener's Attack --- New Weak Keys in RSA
ISC '08 Proceedings of the 11th international conference on Information Security
Generalization of Some Attacks on RSA with Small Prime Combination and Small Private Exponent
APCIP '09 Proceedings of the 2009 Asia-Pacific Conference on Information Processing - Volume 01
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Let N = pq be RSA modulus where primes p and q are of the same bit-length. If |ρq - p| = N1/4+γwhere ρ is a known constant satisfying 1 ≤ ρ ≤ 2 and the constant γ satisfies 0 N and weak key attack against RSA modulus N. We present algorithms to find the factorization of N in time O(Nγ+ε) by some square root attacks, such as the baby-step giant-step method and a more sophisticated square root attack. Using similar techniques of Blömer and May (PKC 2004), we present a weak key attack and find new weak keys over the work of Maitra and Sarkar (ISC 2008).