Extending the ElGamal Cryptosystem to the Third Group of Units of \Z_n

2025/04/21 by Hamza, Jana, Hindi, Mohammad EL, Kadri, Seifeddine +2
#20D45 #68W30 #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #Information Theory (cs.IT) #Probability (math.PR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2504.15202

Abstract

In this paper, we extend the ElGamal cryptosystem to the third group of units of the ring \Z_n, which we prove to be more secure than the previous extensions. We describe the arithmetic needed in the new setting. We also provide some numerical simulations that shows the security and efficiency of our proposed cryptosystem.

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