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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| Format: | Article |
| Language: | English |
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King Saud bin Abdulaziz University
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/113455/ http://psasir.upm.edu.my/id/eprint/113455/1/113455.pdf |
| _version_ | 1848866228745011200 |
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| author | Ruzai, Wan Nur Aqlili Ariffin, Muhammad Rezal Kamel Asbullah, Muhammad Asyraf Abd Ghafar, Amir Hamzah |
| author_facet | Ruzai, Wan Nur Aqlili Ariffin, Muhammad Rezal Kamel Asbullah, Muhammad Asyraf Abd Ghafar, Amir Hamzah |
| author_sort | Ruzai, Wan Nur Aqlili |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T14:17:16Z |
| format | Article |
| id | upm-113455 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:17:16Z |
| publishDate | 2024 |
| publisher | King Saud bin Abdulaziz University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| 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 |
| title | 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_short | New simultaneous Diophantine attacks on generalized RSA key equations |
| title_sort | new simultaneous diophantine attacks on generalized rsa key equations |
| url | http://psasir.upm.edu.my/id/eprint/113455/ http://psasir.upm.edu.my/id/eprint/113455/ http://psasir.upm.edu.my/id/eprint/113455/ http://psasir.upm.edu.my/id/eprint/113455/1/113455.pdf |