An Efficient ElGamal Cryptosystem Based on Prime Power Moduli and Modular Key Exchange
Keywords:
Cryptography, public key cryptosystem, ElGamal cryptosystem, signature scheme, prime numbers, Hash function, group of units, Diffie--Hellman key exchange.Abstract
In this paper, we give a security enhancement of ElGamal cryptosystem based on the use of the group of units U(n), where n = pt or 2pt, where p is an odd prime number and t is a positive integer dynamically determined by users using a modification of the Diffie-Hellman key exchange protocol. The paper presents in details the procedures of the key generation, encryption, decryption and digital signature for the proposed cryptosystem. As applications, we apply procedures of this cryptosystem over plaintexts and implemented its algorithms in the SageMath Software. Finally, we provide results concerning its complexity evaluation, its expansion rate, and its performance timing. The results show that this system is suitable for scalable real-time encryption applications as it is indicating the successful optimization performance and robust integration of security features.
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