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Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
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Open Access Research Article

A new public key cryptosystem based on the non-commutative ring R

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pp. 75–93Vol. 27Issue 1January 2024DOI: 10.47974/JDMSC-1573 Crossmark XML
Received:
10 Aug 2021
Published Online:
24 Jan 2024
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1573
Pages:
75–93

Abstract

In this paper, we present a new public cryptosystem based on one of the most problems  (word problem, solving a non-linear system problem, integer factorization problem and discrete logarithm problem,...) is the conjugal classical problem (CCP) over a non commutative ring. In generally this cryptosystem is very difficult to solve for decipher. Firstly, by using the elliptic curve over the finite ring Fq[e],  where e4 = e3,  with  q = pd and p is prime number greater than or equal to 5, d ϵ ℕ*  [12] we define the non-commutative ring R. Secondly, by using the protocol of Diffie-Hellman [4] we have proposed a novel encryption scheme on R and we study the problem CCP over it. Precisely, we will make a new fully homomorphic encryption scheme over the ring R based on the two difficult problems; conjugal classical problem and discrete logarithm problem.

Keywords

Subject Classifications

[2010] 14H5216S5011T5594A6011T71

References

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