Paper 2023/1356
Small Private Key Attack Against a Family of RSA-like Cryptosystems
Abstract
Let $N=pq$ be the product of two balanced prime numbers $p$ and $q$. Elkamchouchi, Elshenawy and Shaban presented in 2002 an interesting RSA-like cryptosystem that uses the key equation $ed - k (p^2-1)(q^2-1) = 1$, instead of the classical RSA key equation $ed - k (p-1)(q-1) = 1$. The authors claimed that their scheme is more secure than RSA. Unfortunately, the common attacks developed against RSA can be adapted for Elkamchouchi \emph{et al.}'s scheme. In this paper, we introduce a family of RSA-like encryption schemes that uses the key equation $ed - k (p^n-1)(q^n-1) = 1$, where $n>0$ is an integer. Then, we show that regardless of the choice of $n$, there exists an attack based on continued fractions that recovers the secret exponent.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. NordSec 2023
- Keywords
- RSAPublic key cryptographyContinued fractions attacks
- Contact author(s)
-
george teseleanu @ yahoo com
paulcotan @ gmail com - History
- 2023-09-13: approved
- 2023-09-11: received
- See all versions
- Short URL
- https://ia.cr/2023/1356
- License
-
CC BY-NC-SA
BibTeX
@misc{cryptoeprint:2023/1356,
author = {George Teseleanu and Paul Cotan},
title = {Small Private Key Attack Against a Family of RSA-like Cryptosystems},
howpublished = {Cryptology ePrint Archive, Paper 2023/1356},
year = {2023},
note = {\url{https://eprint.iacr.org/2023/1356}},
url = {https://eprint.iacr.org/2023/1356}
}
