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New simultaneous Diophantine attacks on generalized RSA key equations

RSA stands as a widely adopted method within asymmetric cryptography, commonly applied for digital signature validation and message encryption. The security of RSA relies on the challenge of integer factorization, a problem considered either computationally infeasible or highly intricate, especially...

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Main Authors: Ruzai, Wan Nur Aqlili, Ariffin, Muhammad Rezal Kamel, Asbullah, Muhammad Asyraf, Abd Ghafar, Amir Hamzah
Format: Article
Language:English
Published: King Saud bin Abdulaziz University 2024
Online Access:http://psasir.upm.edu.my/id/eprint/113455/1/113455.pdf
http://psasir.upm.edu.my/id/eprint/113455/
https://linkinghub.elsevier.com/retrieve/pii/S1319157824001630
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spelling my.upm.eprints.1134552024-11-25T06:18:25Z http://psasir.upm.edu.my/id/eprint/113455/ New simultaneous Diophantine attacks on generalized RSA key equations Ruzai, Wan Nur Aqlili Ariffin, Muhammad Rezal Kamel Asbullah, Muhammad Asyraf Abd Ghafar, Amir Hamzah RSA stands as a widely adopted method within asymmetric cryptography, commonly applied for digital signature validation and message encryption. The security of RSA relies on the challenge of integer factorization, a problem considered either computationally infeasible or highly intricate, especially when dealing with sufficiently large security parameters. Effective exploits of the integer factorization problem in RSA can allow an adversary to assume the identity of the key holder and decrypt such confidential messages. The keys employed in secure hardware are particularly significant due to the typically greater value of the information they safeguard, such as in the context of securing payment transactions. In general, RSA faces various attacks exploiting weaknesses in its key equations. This paper introduces a new vulnerability that enables the concurrent factorization of multiple RSA moduli. By working with pairs (Ni,ei) and a fixed value y satisfying the Diophantine equation eixi2−y2ϕ(Ni)=zi, we successfully factorized these moduli simultaneously using the lattice basis reduction technique. Notably, our research expands the scope of RSA decryption exponents considered as insecure. King Saud bin Abdulaziz University 2024 Article PeerReviewed text en cc_by_nc_nd_4 http://psasir.upm.edu.my/id/eprint/113455/1/113455.pdf Ruzai, Wan Nur Aqlili and Ariffin, Muhammad Rezal Kamel and Asbullah, Muhammad Asyraf and Abd Ghafar, Amir Hamzah (2024) New simultaneous Diophantine attacks on generalized RSA key equations. Journal of King Saud University - Computer and Information Sciences, 36 (5). art. no. 102074. pp. 1-9. ISSN 1319-1578; eISSN: 2213-1248 https://linkinghub.elsevier.com/retrieve/pii/S1319157824001630 10.1016/j.jksuci.2024.102074
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description RSA stands as a widely adopted method within asymmetric cryptography, commonly applied for digital signature validation and message encryption. The security of RSA relies on the challenge of integer factorization, a problem considered either computationally infeasible or highly intricate, especially when dealing with sufficiently large security parameters. Effective exploits of the integer factorization problem in RSA can allow an adversary to assume the identity of the key holder and decrypt such confidential messages. The keys employed in secure hardware are particularly significant due to the typically greater value of the information they safeguard, such as in the context of securing payment transactions. In general, RSA faces various attacks exploiting weaknesses in its key equations. This paper introduces a new vulnerability that enables the concurrent factorization of multiple RSA moduli. By working with pairs (Ni,ei) and a fixed value y satisfying the Diophantine equation eixi2−y2ϕ(Ni)=zi, we successfully factorized these moduli simultaneously using the lattice basis reduction technique. Notably, our research expands the scope of RSA decryption exponents considered as insecure.
format Article
author Ruzai, Wan Nur Aqlili
Ariffin, Muhammad Rezal Kamel
Asbullah, Muhammad Asyraf
Abd Ghafar, Amir Hamzah
spellingShingle Ruzai, Wan Nur Aqlili
Ariffin, Muhammad Rezal Kamel
Asbullah, Muhammad Asyraf
Abd Ghafar, Amir Hamzah
New simultaneous Diophantine attacks on generalized RSA key equations
author_facet Ruzai, Wan Nur Aqlili
Ariffin, Muhammad Rezal Kamel
Asbullah, Muhammad Asyraf
Abd Ghafar, Amir Hamzah
author_sort Ruzai, Wan Nur Aqlili
title New simultaneous Diophantine attacks on generalized RSA key equations
title_short New simultaneous Diophantine attacks on generalized RSA key equations
title_full New simultaneous Diophantine attacks on generalized RSA key equations
title_fullStr New simultaneous Diophantine attacks on generalized RSA key equations
title_full_unstemmed New simultaneous Diophantine attacks on generalized RSA key equations
title_sort new simultaneous diophantine attacks on generalized rsa key equations
publisher King Saud bin Abdulaziz University
publishDate 2024
url http://psasir.upm.edu.my/id/eprint/113455/1/113455.pdf
http://psasir.upm.edu.my/id/eprint/113455/
https://linkinghub.elsevier.com/retrieve/pii/S1319157824001630
_version_ 1817844640090423296
score 13.244413

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