Key Exchange Over Particular Algebraic Closure Ring

In this paper, we propose a new method of Diffie-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(α, β), which is a rational quadratic and monogenic extension over a non-pure and monogenic cubic subfield K = ℚ(β).