Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA
Several attacks on the well-known RSA cryptosystem that can be extended to a multi-prime version of RSA reveal that it is preferable to use the modulus having more prime factors. On the contrary, the larger the number of prime factors of the modulus, the greater the risk of its factorization, due to...
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MDPI AG
2025-05-01
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| author | Jay Mehta Hitarth Rana |
| author_facet | Jay Mehta Hitarth Rana |
| author_sort | Jay Mehta |
| collection | DOAJ |
| description | Several attacks on the well-known RSA cryptosystem that can be extended to a multi-prime version of RSA reveal that it is preferable to use the modulus having more prime factors. On the contrary, the larger the number of prime factors of the modulus, the greater the risk of its factorization, due to the reduced size of its prime factors. In this paper, we derive an optimal value of the number of prime factors in a multi-prime RSA modulus and introduce the notion of the “safest-value” and determine such safest-values for moduli of different sizes. By utilizing this concept, we propose an enhanced version of our Generalized Multi-Moduli RSA (GMMRSA), which is now secure against even more attacks than its previous version. |
| format | Article |
| id | doaj-art-eecbcab47950402fbda50d9c23a26a6c |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-eecbcab47950402fbda50d9c23a26a6c2025-08-20T03:14:31ZengMDPI AGMathematics2227-73902025-05-011310169010.3390/math13101690Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSAJay Mehta0Hitarth Rana1Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, IndiaDepartment of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, IndiaSeveral attacks on the well-known RSA cryptosystem that can be extended to a multi-prime version of RSA reveal that it is preferable to use the modulus having more prime factors. On the contrary, the larger the number of prime factors of the modulus, the greater the risk of its factorization, due to the reduced size of its prime factors. In this paper, we derive an optimal value of the number of prime factors in a multi-prime RSA modulus and introduce the notion of the “safest-value” and determine such safest-values for moduli of different sizes. By utilizing this concept, we propose an enhanced version of our Generalized Multi-Moduli RSA (GMMRSA), which is now secure against even more attacks than its previous version.https://www.mdpi.com/2227-7390/13/10/1690RSA cryptosystemmulti-prime RSAmulti-moduli RSAsafest-valuesecurityGMMRSA |
| spellingShingle | Jay Mehta Hitarth Rana Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA Mathematics RSA cryptosystem multi-prime RSA multi-moduli RSA safest-value security GMMRSA |
| title | Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA |
| title_full | Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA |
| title_fullStr | Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA |
| title_full_unstemmed | Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA |
| title_short | Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA |
| title_sort | safest value of the number of primes in rsa modulus and an improvised generalized multi moduli rsa |
| topic | RSA cryptosystem multi-prime RSA multi-moduli RSA safest-value security GMMRSA |
| url | https://www.mdpi.com/2227-7390/13/10/1690 |
| work_keys_str_mv | AT jaymehta safestvalueofthenumberofprimesinrsamodulusandanimprovisedgeneralizedmultimodulirsa AT hitarthrana safestvalueofthenumberofprimesinrsamodulusandanimprovisedgeneralizedmultimodulirsa |