New Cryptanalytic Attack on RSA Modulus N=pq Using Small Prime Difference Method

Abstract

This paper presents new short decryption exponent attacks on RSA, which successfully leads to the factorization of RSA modulus N = pq in polynomial time. The paper has two parts. In the first part, we report the usage of the small prime difference method of the form |b 2 p − a 2 q| < N γ where the ratio of. The second part of the paper reports four cryptanalytic attacks on t instances of RSA moduli N s = p s q s for s = 1, 2, . . . , t where we use N − a 2 +b 2 ab √ N + 1 as an approximation of φ(N) satisfying generalized key equations of the shape e s d s for unknown positive integers d, k s , d s , k s , and z s , where we establish that t RSA moduli can be simultaneously factored in polynomial time using combinations of simultaneous Diophantine approximations and lattice basis reduction methods. In all the reported attacks, we have found an improved short secret exponent bound, which is considered to be better than some bounds as reported in the literature.

Cryptoanalytic Method of Searching for the Secret Key and ITS Length on the Basis of Evolution Metaheuristics

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New Semi-Prime Factorization and Application in Large RSA Key Attacks

“…In the context of RSA cryptography applications, recent works have considered such known factorization methods to focus on security parameters such as the length of the prime factors p 1 and p 2 , of the RSA modulus n = p 1 p 2 , or other structural properties of the primes. Modifications of existing methods have become popular recently, such as using the prime sum p 1 + p 2 with sublattice reduction techniques and Coppersmith's methods [31] or using a small prime difference p 1 − p 2 method with Wiener's original method [32]. The method by Lenstra's elliptic-curve method also serves as the state-of-the-art proposal for several future studies [33].…”

Exponential increment of RSA attack range via lattice based cryptanalysis

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