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

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.