Exponential increment of RSA attack range via lattice based cryptanalysis
The RSA cryptosystem comprises of two important features that are needed for encryption process known as the public parameter e and the modulus N. In 1999, a cryptanalysis on RSA which was described by Boneh and Durfee focused on the key equation and e of the same magnitude to N. Their method was a...
| Main Authors: | , , , , |
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| Format: | Article |
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Springer
2021
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| _version_ | 1811137522691997696 |
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| author | Nitaj, Abderahmanne Ariffin, Muhammad Rezal Kamel Adenan, Nurul Nur Hanisah Ahmadian, Ali Merenda, Domenica Stefania |
| author_facet | Nitaj, Abderahmanne Ariffin, Muhammad Rezal Kamel Adenan, Nurul Nur Hanisah Ahmadian, Ali Merenda, Domenica Stefania |
| author_sort | Nitaj, Abderahmanne |
| collection | UPM |
| description | The RSA cryptosystem comprises of two important features that are needed for encryption process known as the public parameter e and the modulus N. In 1999, a cryptanalysis on RSA which was described by Boneh and Durfee focused on the key equation and e of the same magnitude to N. Their method was applicable for the case of via Coppersmith’s technique. In 2012, Kumar et al. presented an improved Boneh-Durfee attack using the same equation which is valid for any e with arbitrary size. In this paper, we present an exponential increment of the two former attacks using the variant equation . The new attack breaks the RSA system when a and |c| are suitably small integers. Moreover, the new attack shows that the Boneh-Durfee attack and the attack of Kumar et al. can be derived using a single attack. We also showed that our bound manage to improve the bounds of Ariffin et al. and Bunder and Tonien. |
| first_indexed | 2024-09-25T03:35:38Z |
| format | Article |
| id | upm.eprints-97233 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-09-25T03:35:38Z |
| publishDate | 2021 |
| publisher | Springer |
| record_format | dspace |
| spelling | upm.eprints-972332024-07-29T03:49:36Z http://psasir.upm.edu.my/id/eprint/97233/ Exponential increment of RSA attack range via lattice based cryptanalysis Nitaj, Abderahmanne Ariffin, Muhammad Rezal Kamel Adenan, Nurul Nur Hanisah Ahmadian, Ali Merenda, Domenica Stefania The RSA cryptosystem comprises of two important features that are needed for encryption process known as the public parameter e and the modulus N. In 1999, a cryptanalysis on RSA which was described by Boneh and Durfee focused on the key equation and e of the same magnitude to N. Their method was applicable for the case of via Coppersmith’s technique. In 2012, Kumar et al. presented an improved Boneh-Durfee attack using the same equation which is valid for any e with arbitrary size. In this paper, we present an exponential increment of the two former attacks using the variant equation . The new attack breaks the RSA system when a and |c| are suitably small integers. Moreover, the new attack shows that the Boneh-Durfee attack and the attack of Kumar et al. can be derived using a single attack. We also showed that our bound manage to improve the bounds of Ariffin et al. and Bunder and Tonien. Springer 2021 Article PeerReviewed Nitaj, Abderahmanne and Ariffin, Muhammad Rezal Kamel and Adenan, Nurul Nur Hanisah and Ahmadian, Ali and Merenda, Domenica Stefania (2021) Exponential increment of RSA attack range via lattice based cryptanalysis. Multimedia Tools and Applications, 81 (25). pp. 36607-36622. ISSN 1380-7501; ESSN: 1573-7721 https://link.springer.com/article/10.1007/s11042-021-11335-8?error=cookies_not_supported&code=81fcf9cb-c1e6-4b19-9ff3-ad3379d9d10b 10.1007/s11042-021-11335-8 |
| spellingShingle | Nitaj, Abderahmanne Ariffin, Muhammad Rezal Kamel Adenan, Nurul Nur Hanisah Ahmadian, Ali Merenda, Domenica Stefania Exponential increment of RSA attack range via lattice based cryptanalysis |
| title | Exponential increment of RSA attack range via lattice based cryptanalysis |
| title_full | Exponential increment of RSA attack range via lattice based cryptanalysis |
| title_fullStr | Exponential increment of RSA attack range via lattice based cryptanalysis |
| title_full_unstemmed | Exponential increment of RSA attack range via lattice based cryptanalysis |
| title_short | Exponential increment of RSA attack range via lattice based cryptanalysis |
| title_sort | exponential increment of rsa attack range via lattice based cryptanalysis |
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