Key exchange over particular algebraic closure ring

Abstract

In this paper, we propose a new method from Difie-Hellman key exchange based on a non-commutative integral closure ring. The key idea of our proposal is that for a given non-commutative ring, we can define the secret key and take it as a common key to encrypt and decrypt the transmitted messages. By doing, we define a new non-commutative structure over the integral closure O_L of sextic extension  L, namely L is an extension of Q of degree 6 in the form Q(\alpha,\beta), which is a rational quadratic and monogenic extension over a non-pure and monogenic cubic subfield K=Q(\beta).