preprints

2025-26

1. To Appear

   A multi-moduli approach towards enhancing the security of multi-prime RSA

   Jay Mehta, and Hitarth Rana

   Journal of Discrete Mathematical Sciences and Cryptography, To appear., 2025-26

   Abs

   The popular RSA cryptosystem, based on the problem of integer factorization can widely be seen in practice even today. Since its inception, several enhancements and generalizations of RSA are proposed including its several multi-prime variants where the RSA modulus is a product of more than two primes. In this paper, we propose a generalized multi-moduli RSA cryptosystem (GMMRSA) which is a multi-prime RSA but with more than one modulus. We show that this multi-moduli approach yields a more secure cryptosystem than a multi-prime RSA with a single modulus without compromising its computational and time efficiencies.

2. Communicated

   A new cryptosystem with enhanced RSA security and forward secrecy: A hybrid approach

   Jay Mehta, and Pushparajsinh Parmar

   Communicated, 2025-26

   Abs

   The Diffie-Hellman problem and the integer factorization problem are two major, well-known, and difficult problems in cryptography. In this paper, we propose a new cryptosystem based on these two problems, which is a hybrid of the Diffie-Hellman and RSA. We prove that the hybrid approach not only enhances the security of our proposed cryptosystem in comparison to RSA, but also provides an additional desirable attribute, namely the perfect forward secrecy.

2026-27

1. In Preparation

   A new digital signature scheme based on Elgamal and RSA: A hybrid approach

   Jay Mehta, and Pushparajsinh Parmar

   In Preparation, 2026-27

   Abs

   In this paper, we proposed a new hybrid digital signature scheme based on two well-known problems in cryptography: the integer factorization problem and the discrete logarithm problem. We will prove that, the proposed hybrid scheme is superior to both the Elgamal and RSA signature schemes.

2. In Preparation

   φ(n)-evaluation algorithm: a novel approach for an efficient retrieval of Euler’s totient of an RSA Modulus

   Jay Mehta, and Hitarth Rana

   In Preparation, 2026-27

   Abs

   In this paper, we propose an algorithm to efficiently retrieve the value of Euler’s totient function of an RSA modulus, consequently voiding the RSA encryption. Furthermore, we show that the proposed algorithm is significantly faster and more effective when the prime factors of an RSA modulus are closer to each other. We conjecture a relation between the difference of two prime factors of the RSA modulus and the required number of steps for the algorithm.