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Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA

Author

Listed:
  • Jay Mehta

    (Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, India
    These authors contributed equally to this work.)

  • Hitarth Rana

    (Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, India
    These authors contributed equally to this work.)

Abstract

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.

Suggested Citation

  • Jay Mehta & Hitarth Rana, 2025. "Safest-Value of the Number of Primes in RSA Modulus and an Improvised Generalized Multi-Moduli RSA," Mathematics, MDPI, vol. 13(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1690-:d:1661183
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    References listed on IDEAS

    as
    1. Luis V. Dieulefait & Jorge Urroz, 2020. "Factorization and Malleability of RSA Moduli, and Counting Points on Elliptic Curves Modulo N," Mathematics, MDPI, vol. 8(12), pages 1-10, November.
    2. Shixiong Wang & Minghao Sun, 2024. "New Cryptanalysis of Prime Power RSA with Two Private Exponents," Mathematics, MDPI, vol. 12(21), pages 1-12, October.
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