Security issues of Novel RSA variant
The RSA is one of the current default cryptosystems that provides security with applications such as encryptions and digital signatures. It is important to further study the weak characteristics of the RSA to ensure correct utilisation in order not to be susceptible to adversaries. In this paper, we...
| Main Authors: | , , , , |
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| Format: | Article |
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Institute of Electrical and Electronics Engineers
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/103149/ |
| _version_ | 1848863946221551616 |
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| author | Nitaj, Abderrahmane Kamel Ariffin, Muhammad Rezal Adenan, Nurul Nur Hanisah Lau, Terry Shue Chien Che, Jiahui |
| author_facet | Nitaj, Abderrahmane Kamel Ariffin, Muhammad Rezal Adenan, Nurul Nur Hanisah Lau, Terry Shue Chien Che, Jiahui |
| author_sort | Nitaj, Abderrahmane |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The RSA is one of the current default cryptosystems that provides security with applications such as encryptions and digital signatures. It is important to further study the weak characteristics of the RSA to ensure correct utilisation in order not to be susceptible to adversaries. In this paper, we give detailed analysis on security of the Murru-Saettone variant of the RSA cryptosystem that utilised a cubic Pell ed−k(p2+p+1)(q2+q+1)=1 as key equation and N=pq as RSA modulus. We propose some attacks on this variant when the prime difference |p−q| is small. Our first approach is to utilise the continued fractions algorithm to determine the parameter d which enables us to determine the secret p and q . Our second approach considers the Coppersmith's method and lattice basis reduction to factor the modulus N . Our attacks improve recent cryptanalyses on the cubic Pell equation variant of RSA. Furthermore, our attacks prove that under small prime difference scenario, the number of susceptible private exponents for the cubic Pell equation variant of RSA is much larger than the standard RSA. |
| first_indexed | 2025-11-15T13:40:59Z |
| format | Article |
| id | upm-103149 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:40:59Z |
| publishDate | 2022 |
| publisher | Institute of Electrical and Electronics Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1031492023-12-05T04:11:57Z http://psasir.upm.edu.my/id/eprint/103149/ Security issues of Novel RSA variant Nitaj, Abderrahmane Kamel Ariffin, Muhammad Rezal Adenan, Nurul Nur Hanisah Lau, Terry Shue Chien Che, Jiahui The RSA is one of the current default cryptosystems that provides security with applications such as encryptions and digital signatures. It is important to further study the weak characteristics of the RSA to ensure correct utilisation in order not to be susceptible to adversaries. In this paper, we give detailed analysis on security of the Murru-Saettone variant of the RSA cryptosystem that utilised a cubic Pell ed−k(p2+p+1)(q2+q+1)=1 as key equation and N=pq as RSA modulus. We propose some attacks on this variant when the prime difference |p−q| is small. Our first approach is to utilise the continued fractions algorithm to determine the parameter d which enables us to determine the secret p and q . Our second approach considers the Coppersmith's method and lattice basis reduction to factor the modulus N . Our attacks improve recent cryptanalyses on the cubic Pell equation variant of RSA. Furthermore, our attacks prove that under small prime difference scenario, the number of susceptible private exponents for the cubic Pell equation variant of RSA is much larger than the standard RSA. Institute of Electrical and Electronics Engineers 2022 Article PeerReviewed Nitaj, Abderrahmane and Kamel Ariffin, Muhammad Rezal and Adenan, Nurul Nur Hanisah and Lau, Terry Shue Chien and Che, Jiahui (2022) Security issues of Novel RSA variant. IEEE Access, 10. 53788 - 53796. ISSN 2169-3536 https://ieeexplore.ieee.org/document/9775686 10.1109/ACCESS.2022.3175519 |
| spellingShingle | Nitaj, Abderrahmane Kamel Ariffin, Muhammad Rezal Adenan, Nurul Nur Hanisah Lau, Terry Shue Chien Che, Jiahui Security issues of Novel RSA variant |
| title | Security issues of Novel RSA variant |
| title_full | Security issues of Novel RSA variant |
| title_fullStr | Security issues of Novel RSA variant |
| title_full_unstemmed | Security issues of Novel RSA variant |
| title_short | Security issues of Novel RSA variant |
| title_sort | security issues of novel rsa variant |
| url | http://psasir.upm.edu.my/id/eprint/103149/ http://psasir.upm.edu.my/id/eprint/103149/ http://psasir.upm.edu.my/id/eprint/103149/ |