Paper 2024/2065
Partial Exposure Attacks Against a Family of RSA-like Cryptosystems
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.
Metadata
- Available format(s)
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. MDPI Cryptography
- Keywords
- lattice attackpartial exposure attacksRSA
- Contact author(s)
- george teseleanu @ yahoo com
- History
- 2024-12-24: revised
- 2024-12-23: received
- See all versions
- Short URL
- https://ia.cr/2024/2065
- License
-
CC BY-NC-SA
BibTeX
@misc{cryptoeprint:2024/2065, author = {George Teseleanu}, title = {Partial Exposure Attacks Against a Family of {RSA}-like Cryptosystems}, howpublished = {Cryptology {ePrint} Archive, Paper 2024/2065}, year = {2024}, url = {https://eprint.iacr.org/2024/2065} }