Abstract
We study the Multi-Power variant of the RSA cryptosystem where the modulus is of the form \(N=p^rq^s\) with \(\gcd (r,s)=1\). We present a method to solve the linear equation \(a_1x_1+a_2x_2\equiv 0\pmod {p^uq^v}\) where \(u<r\), \(v<s\), and \(a_1\), \(a_2\) are two integers satisfying \(\gcd (a_1a_2,N)=1\). We apply the new method to the cryptanalysis of two instances of the Multi-Power RSA. We define a generalization of the CRT-RSA variant of the standard RSA to the Multi-Power RSA, and apply the new method to study its security. The new method is based on Coppersmith’s method and lattice reduction techniques.
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Alquié, D., Chassé, G., Nitaj, A. (2022). Cryptanalysis of the Multi-Power RSA Cryptosystem Variant. In: Beresford, A.R., Patra, A., Bellini, E. (eds) Cryptology and Network Security. CANS 2022. Lecture Notes in Computer Science, vol 13641. Springer, Cham. https://doi.org/10.1007/978-3-031-20974-1_12
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