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A Generalized Attack on Some Variants of the RSA Cryptosystem

Abstract : Let N = pq be an RSA modulus with unknown factorization. The RSA cryptosystem can be attacked by using the key equation ed−k(p−1)(q−1) = 1. Similarly, some variants of RSA, such as RSA combined with singular elliptic curves, LUC and RSA with Gaussian primes can be attacked by using the key equation ed−k(p^2 − 1)( q^2 − 1) = 1. In this paper, we consider the more general equation eu− (p^2 − 1)( q^2 − 1) v = w and present a new attack that finds the prime factors p and q in the case that u, v and w satisfy some specific conditions. The attack is based on Coppersmith's technique and improves the former attacks.
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https://hal-normandie-univ.archives-ouvertes.fr/hal-02321006
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Submitted on : Sunday, October 20, 2019 - 10:36:19 AM
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Abderrahmane Nitaj, Yanbin Pan, Joseph Tonien. A Generalized Attack on Some Variants of the RSA Cryptosystem. 25th International Conference on Selected Areas in Cryptography SAC 2018, 2018, Calgary, Canada. ⟨10.1007/978-3-030-10970-7_19⟩. ⟨hal-02321006⟩

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