Cryptology ePrint Archive: Report 2020/354

A Generalization of the ElGamal public-key cryptosystem

Rajitha Ranasinghe and Pabasara Athukorala

Abstract: The ElGamal cryptosystem is one of the most widely used public-key cryptosystems that depends on the difficulty of computing the discrete logarithms over finite fields. Over the years, the original system has been modified and altered in order to achieve a higher security and efficiency. In this paper, a generalization for the original ElGamal system is proposed which also relies on the discrete logarithm problem. The encryption process of the scheme is improved such that it depends on the prime factorization of the plaintext. Modular exponentiation is taken twice during the encryption; once with the number of distinct prime factors of the plaintext and then with the secret encryption key. If the plaintext consists of only one distinct prime factor, then the new method is similar to that of the basic ElGamal algorithm. The proposed system preserves the immunity against the Chosen Plaintext Attack (CPA).

Category / Keywords: public-key cryptography / Public-key cryptography, ElGamal encryption, discrete logarithm problem, Prime factorization, Chosen plaintext attack

Date: received 25 Mar 2020, last revised 26 Mar 2020

Contact author: rajithapera18 at gmail com,athukorala madushani@gmail com

Available format(s): PDF | BibTeX Citation

Note: According to the suggestions, We modified our system to address the issue with the distribution of secrets in such a way to select the secret key y such that (iy) is coprime to (p-1).

Version: 20200326:165453 (All versions of this report)

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