Attacking an RSA-like Cryptosystem Using Continued Fractions and Lattices

George Teseleanu

Paper 2025/1739

Attacking an RSA-like Cryptosystem Using Continued Fractions and Lattices

George Teseleanu

Abstract

Let $N = pq$ be the product of two balanced primes. Cotan and Te\c seleanu (2023) introduced a family of RSA-like cryptosystems defined by $ed - k(p^n - 1)(q^n - 1) = 1$, where $n \geq 1$, encompassing classical RSA ($n=1$) and the Elkamchouchi–Elshenawy–Shaban variant ($n=2$). We present a new attack for $n=3$ that integrates continued fractions with lattice-based methods, naturally extending previous results for $n = 1, 2, 4, 6$.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. NordSec 2025
Keywords: continued fraction attack lattice attack small private key attack RSA
Contact author(s): george teseleanu @ yahoo com
History: 2026-02-20: revised; 2025-09-23: received; See all versions
Short URL: https://ia.cr/2025/1739
License: CC BY-NC-SA

BibTeX

@misc{cryptoeprint:2025/1739,
      author = {George Teseleanu},
      title = {Attacking an {RSA}-like Cryptosystem Using Continued Fractions and Lattices},
      howpublished = {Cryptology {ePrint} Archive, Paper 2025/1739},
      year = {2025},
      url = {https://eprint.iacr.org/2025/1739}
}