## Cryptology ePrint Archive: Report 2021/1632

Cryptanalysis of RSA Variants with Primes Sharing Most Significant Bits

Meryem Cherkaoui-Semmouni and Abderrahmane Nitaj and Willy Susilo and Joseph Tonien

Abstract: We consider four variants of the RSA cryptosystem with an RSA modulus $N=pq$ where the public exponent $e$ and the private exponent $d$ satisfy an equation of the form $ed-k\left(p^2-1\right)\left(q^2-1\right)=1$. We show that, if the prime numbers $p$ and $q$ share most significant bits, that is, if the prime difference $|p-q|$ is sufficiently small, then one can solve the equation for larger values of $d$, and factor the RSA modulus, which makes the systems insecure.

Category / Keywords: public-key cryptography / RSA variants, Continued fractions, Coppersmith's method, Lattice reduction

Original Publication (in the same form): Information Security Conference ISC 2021
DOI:
10.1007/978-3-030-91356-4_3