On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions Method
Let N = pq be an RSA modulus where p and q are primes not necessarily of the same bit size. Previous cryptanalysis results on the difficulty of factoring the public modulus N = pq deployed on variants of RSA cryptosystem are revisited. Each of these variants share a common key relation utilizing the...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2020-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/9079788/ |
| _version_ | 1831679346615517184 |
|---|---|
| author | Wan Nur Aqlili Ruzai Muhammad Rezal Kamel Ariffin Muhammad Asyraf Asbullah Zahari Mahad Athirah Nawawi |
| author_facet | Wan Nur Aqlili Ruzai Muhammad Rezal Kamel Ariffin Muhammad Asyraf Asbullah Zahari Mahad Athirah Nawawi |
| author_sort | Wan Nur Aqlili Ruzai |
| collection | DOAJ |
| description | Let N = pq be an RSA modulus where p and q are primes not necessarily of the same bit size. Previous cryptanalysis results on the difficulty of factoring the public modulus N = pq deployed on variants of RSA cryptosystem are revisited. Each of these variants share a common key relation utilizing the modified Euler quotient (p<sup>2</sup> - 1)(q<sup>2</sup> - 1), given by the key relation ed - k(p<sup>2</sup> - 1)(q<sup>2</sup> - 1) = 1 where e and d are the public and private keys respectively. By conducting continuous midpoint subdivision analysis upon an interval containing (p<sup>2</sup> - 1)(q<sup>2</sup> - 1) together with continued fractions on the key relation, we increase the security bound for d exponentially. |
| first_indexed | 2024-12-20T05:18:01Z |
| format | Article |
| id | doaj.art-787ffefdca444b3aa2de92dbc9f01ec8 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-20T05:18:01Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-787ffefdca444b3aa2de92dbc9f01ec82022-12-21T19:52:06ZengIEEEIEEE Access2169-35362020-01-018809978100610.1109/ACCESS.2020.29910489079788On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions MethodWan Nur Aqlili Ruzai0https://orcid.org/0000-0002-0359-5690Muhammad Rezal Kamel Ariffin1https://orcid.org/0000-0001-5000-354XMuhammad Asyraf Asbullah2https://orcid.org/0000-0002-0778-4456Zahari Mahad3https://orcid.org/0000-0001-6954-8494Athirah Nawawi4https://orcid.org/0000-0002-4102-7889Institute for Mathematical Research, Universiti Putra Malaysia, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, Selangor, MalaysiaLet N = pq be an RSA modulus where p and q are primes not necessarily of the same bit size. Previous cryptanalysis results on the difficulty of factoring the public modulus N = pq deployed on variants of RSA cryptosystem are revisited. Each of these variants share a common key relation utilizing the modified Euler quotient (p<sup>2</sup> - 1)(q<sup>2</sup> - 1), given by the key relation ed - k(p<sup>2</sup> - 1)(q<sup>2</sup> - 1) = 1 where e and d are the public and private keys respectively. By conducting continuous midpoint subdivision analysis upon an interval containing (p<sup>2</sup> - 1)(q<sup>2</sup> - 1) together with continued fractions on the key relation, we increase the security bound for d exponentially.https://ieeexplore.ieee.org/document/9079788/Algebraic cryptanalysiscontinued fractions methodinteger factorization problemRSA-variants |
| spellingShingle | Wan Nur Aqlili Ruzai Muhammad Rezal Kamel Ariffin Muhammad Asyraf Asbullah Zahari Mahad Athirah Nawawi On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions Method IEEE Access Algebraic cryptanalysis continued fractions method integer factorization problem RSA-variants |
| title | On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions Method |
| title_full | On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions Method |
| title_fullStr | On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions Method |
| title_full_unstemmed | On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions Method |
| title_short | On the Improvement Attack Upon Some Variants of RSA Cryptosystem via the Continued Fractions Method |
| title_sort | on the improvement attack upon some variants of rsa cryptosystem via the continued fractions method |
| topic | Algebraic cryptanalysis continued fractions method integer factorization problem RSA-variants |
| url | https://ieeexplore.ieee.org/document/9079788/ |
| work_keys_str_mv | AT wannuraqliliruzai ontheimprovementattackuponsomevariantsofrsacryptosystemviathecontinuedfractionsmethod AT muhammadrezalkamelariffin ontheimprovementattackuponsomevariantsofrsacryptosystemviathecontinuedfractionsmethod AT muhammadasyrafasbullah ontheimprovementattackuponsomevariantsofrsacryptosystemviathecontinuedfractionsmethod AT zaharimahad ontheimprovementattackuponsomevariantsofrsacryptosystemviathecontinuedfractionsmethod AT athirahnawawi ontheimprovementattackuponsomevariantsofrsacryptosystemviathecontinuedfractionsmethod |