Paper 2025/1559
A New Generalized Lattice Attack Against a Family of RSA-Like Cryptosystems
, LTISI, CRISIN'2D, Ecole Polytechnique de Thies, Senegal, LTISI, CRISIN'2D, Ecole Polytechnique de Thies, SenegalAbstract
Recently, Cotan and Teseleanu (NordSec 2023) published an RSA-like cryptosystem. While in RSA, the public exponent $e$ and the private exponent $d$ are related by the equation $ed - k(p-1)(q-1) = 1$, in their scheme, $e$ and $d$ are related to the equation $ed - k(p^n-1)(q^n-1) = 1$ for some positive integer $n$. Teseleanu (CSCML 2024) showed that one can factor the modulus $N$ using a lattice attack if $d$ is small. In this paper, we extend his attack by showing that if the private exponent is either too small or too large, one can factor $N$ in polynomial time by solving the generalized equation $eu - (p^n - 1)(q^n - 1)v = \pm 1$ using lattice reduction techniques.
Metadata
- Available format(s)
-
PDF
- Category
- Attacks and cryptanalysis
- Publication info
- Published elsewhere. Theoretical Computer Science
- Keywords
- RSACrypanalysisCoppersmith's methodLLLLattice attack
- Contact author(s)
-
mseck @ ept edu sn
aaciss @ ept edu sn - History
- 2025-09-12: revised
- 2025-08-30: received
- See all versions
- Short URL
- https://ia.cr/2025/1559
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2025/1559,
author = {Michel Seck and Abdoul Aziz Ciss},
title = {A New Generalized Lattice Attack Against a Family of {RSA}-Like Cryptosystems},
howpublished = {Cryptology {ePrint} Archive, Paper 2025/1559},
year = {2025},
url = {https://eprint.iacr.org/2025/1559}
}
