A Cryptographic Application of the M-Injectivity of 𝑀𝑛(𝑍𝑝) Over Itself
Wannarisuk Nongbsap1, Madan Mohan Singh2
1Wannarisuk Nongbsap*, Assistant Professor, Department of Mathematics, St. Anthony’s College, Shillong, Meghalaya, India.
2Dr. Madan Mohan Singh, Associate Professor, Department of Basic Sciences and Social Sciences, School of Technology, North Eastern Hill University, Shillong, Meghalaya, India.
Manuscript received on September 09, 2021. | Revised Manuscript received on September 16, 2021. | Manuscript published on September 30, 2021. | PP: 7-14 | Volume-10 Issue-4, November 2021. | Retrieval Number: 100.1/ijrte.D65151110421 | DOI: 10.35940/ijrte.D6515.1110421
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© The Authors. Published By: Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: In this paper, we present a public key scheme using Discrete Logarithm problem, proposed by Diffie and Hellman (DLP), particularly known as the Computational Diffie-Hellman Problem (CDH). This paper uses the Elgamal encryption scheme  and extends it so that more than one message can be sent. The combination of Hill Cipher[14 ] and the property of the matrix ring 𝑴𝒏(𝒁𝒑), of being left m-injective over itself, where 𝒑 is a very large prime, are major contributions towards the proposal of this scheme.
Keywords: m-injective, 𝑹-monomorphisms, 𝑴𝒏(𝒁𝒑), public key cryptography, Discrete Logarithm Problem, Computational Diffie-Hellman Problem, Hill Cipher.