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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.
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]
Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 192967420
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  Data: A generalized partial exposure lattice attack against an RSA variant based on cubic Pell curves.
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  Data: <searchLink fieldCode="AR" term="%22Seck%2C+Michel%22">Seck, Michel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mseck@ept.edu.sn</i><br /><searchLink fieldCode="AR" term="%22Tchapgnouo%2C+Hortense+Boudjou%22">Tchapgnouo, Hortense Boudjou</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> hortenseboudjou@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Discrete+Applied+Mathematics%22">Discrete Applied Mathematics</searchLink>. Jun2026, Vol. 386, p334-344. 11p.
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  Data: <searchLink fieldCode="DE" term="%22RSA+algorithm%22">RSA algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22Cryptography%22">Cryptography</searchLink><br /><searchLink fieldCode="DE" term="%22Equations%22">Equations</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink>
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  Label: Abstract
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  Data: 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]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Discrete Applied Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.dam.2026.03.012
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      – Code: eng
        Text: English
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        PageCount: 11
        StartPage: 334
    Subjects:
      – SubjectFull: RSA algorithm
        Type: general
      – SubjectFull: Cryptography
        Type: general
      – SubjectFull: Equations
        Type: general
      – SubjectFull: Number theory
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      – TitleFull: A generalized partial exposure lattice attack against an RSA variant based on cubic Pell curves.
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              Text: Jun2026
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              Y: 2026
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              Value: 386
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