Hortense Boudjou Tchapgnouo, LaRI Lab, University of Maroua
Nitaj and Seck recently published an RSA variant (MJAGA 2024) based on the cubic Pell equation $\mathcal{P}_c(N): u^3+cv^3+c^2w^3-3cuvw= 1$ over $\mathbb{Z}/N\mathbb{Z}$ when $N=p^rq^s$. In their cryptosystem, the public exponent $e$ and the private exponent $d$ are related to the key equation $d\equiv e^{-1}\pmod{p^{2(r-1)}q^{2(s-1)}(p-1)^2(q-1)^2}$. In AfricaCrypt 2025, Rahmani and Nitaj published a lattice attack on their scheme in the particular case of $r=s=1$ by exploiting the key equation $ed - (p-1)^2(q-1)^2 k = 1$. In this paper, we present a new generalized partial exposure lattice attack on the scheme of Nitaj and Seck by examining the key equation $eu_0 - (p-1)^2(q-1)^2 v_0 = w_0$ when some bits of $p$ or $q$ are known.
BibTeX
@misc{cryptoeprint:2026/519,
author = {Michel Seck and Hortense Boudjou Tchapgnouo},
title = {A Generalized Partial Exposure Lattice Attack Against an {RSA} variant Based on Cubic Pell Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/519},
year = {2026},
url = {https://eprint.iacr.org/2026/519}
}
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