journal-of-discrete-mathematical-sciences-and-cryptography Journal of Discrete Mathematical Sciences and Cryptography 2169-0065 0972-0529 Taru Publications 10.47974/JDMSC-1573 A new public key cryptosystem based on the non-commutative ring R Selikh Bilel Department of Mathematics, Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University of M’sila, M’sila, P. O. Box 166 Ichbilia, 28000, Algeria Chillali Abdelhakim Department of Mathematics, Physics & Computer Science, Polydisciplinary Faculty, Laboratory of Engineering Sciences, Sidi Mohamed Ben Abdellah University, Taza, Morocco Mihoubi Douadi Department of Mathematics, Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University of M’sila, M’sila, P. O. Box 166 Ichbilia, 28000, Algeria Ghadbane Nacer Department of Mathematics, Laboratory of Pure and Applied Mathematics, Mohamed Boudiaf University of M’sila, M’sila, P. O. Box 166 Ichbilia, 28000, Algeria 27 1 75 93 24 01 2024

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.

 Elliptic curve Non commutative ring Matrix Cryptography Conjugal problem Fully homomorphic cryptosystem access open retracted no