Welcome to the resource topic for 2024/2065
Title:
Partial Exposure Attacks Against a Family of RSA-like Cryptosystems
Authors: George Teseleanu
Abstract:An RSA generalization using complex integers was introduced by Elkamchouchi, Elshenawy, and Shaban in 2002. This scheme was further extended by Cotan and Teșeleanu to Galois fields of order n \geq 1. In this generalized framework, the key equation is ed - k (p^n-1)(q^n-1) = 1, where p and q are prime numbers. Note that, the classical RSA, and the Elkamchouchi \emph{et al.} key equations are special cases, namely n=1 and n=2. In addition to introducing this generic family, Cotan and Teșeleanu describe a continued fractions attack capable of recovering the secret key d if d < N^{0.25n}. This bound was later improved by Teșeleanu using a lattice based method. In this paper, we explore other lattice attacks that could lead to factoring the modulus N = pq. Namely, we propose a series of partial exposure attacks that can aid an adversary in breaking this family of cryptosystems if certain conditions hold.
ePrint: https://eprint.iacr.org/2024/2065
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .