A generalized partial exposure lattice attack against an RSA variant based on cubic Pell curves.
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| Title: | A generalized partial exposure lattice attack against an RSA variant based on cubic Pell curves. |
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| Authors: | Seck, Michel1 (AUTHOR) mseck@ept.edu.sn, Tchapgnouo, Hortense Boudjou2 (AUTHOR) hortenseboudjou@gmail.com |
| Source: | Discrete Applied Mathematics. Jun2026, Vol. 386, p334-344. 11p. |
| Subjects: | RSA algorithm, Cryptography, Equations, Number theory |
| Abstract: | Nitaj and Seck recently published an RSA variant (MJAGA 2024) based on the cubic Pell equation P c (N) : u 3 + c v 3 + c 2 w 3 − 3 c u v w = 1 over Z / N Z when N = p r q s . In their cryptosystem, the public exponent e and the private exponent d are related to the key equation d ≡ e − 1 (mod 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 e d − (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 e u 0 − (p − 1) 2 (q − 1) 2 v 0 = w 0 when some bits of p or q are known. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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