A New Attack on RSA and Demytko's Elliptic Curve Cryptosystem

Abderrahmane Nitaj; Emmanuel Fouotsa

Paper 2019/1050

A New Attack on RSA and Demytko's Elliptic Curve Cryptosystem

Abderrahmane Nitaj and Emmanuel Fouotsa

Abstract

Let $N = p q$ be an RSA modulus and $e$ be a public exponent. Numerous attacks on RSA exploit the arithmetical properties of the key equation $e d - k (p - 1) (q - 1) = 1$ . In this paper, we study the more general equation $e u - (p - s) (q - r) v = w$ . We show that when the unknown integers $u$ , $v$ , $w$ , $r$ and $s$ are suitably small and $p - s$ or $q - r$ is factorable using the Elliptic Curve Method for factorization ECM, then one can break the RSA system. As an application, we propose an attack on Demytko's elliptic curve cryptosystem. Our method is based on Coppersmith's technique for solving multivariate polynomial modular equations.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Minor revision. Journal of Discrete Mathematical Sciences and Cryptography
Keywords: RSA Cryptanalysis Coppersmith's method Elliptic Curve Method Demytko's scheme.
Contact author(s): abderrahmane nitaj @ unicaen fr
History: 2019-09-18: received
Short URL: https://ia.cr/2019/1050
License: CC BY

BibTeX

@misc{cryptoeprint:2019/1050,
      author = {Abderrahmane Nitaj and Emmanuel Fouotsa},
      title = {A New Attack on {RSA} and Demytko's Elliptic Curve Cryptosystem},
      howpublished = {Cryptology {ePrint} Archive, Paper 2019/1050},
      year = {2019},
      url = {https://eprint.iacr.org/2019/1050}
}