In this paper, we introduce a D-H key distribution protocol over polynomial rings. These protocols use some polynomials with two cyclomic cosets in the center of the ring as part of the private keys. We give some examples over the polynomial rings Zp, where p is a prime number. We also give a security analysis of the proposed protocols and conclude that the only possible attack is by brute force. | Journal of Science & Technology 123 (2017) 032-035 Key Distribution and Agreement Diffie – Hellman Over Polynomial Rings with Two Cyclomic Cossets Le Danh Cuong1, Nguyen Le Cuong2*, Nguyen Binh1 Posts and Telecommunications Institute of Technology, 2Electric Power University 1 Received: June 27, 2017; Accepted: November 03, 2017 Abstract In this paper, we introduce a D-H key distribution protocol over polynomial rings. These protocols use some polynomials with two cyclomic cosets in the center of the ring as part of the private keys. We give some examples over the polynomial rings Zp, where p is a prime number. We also give a security analysis of the proposed protocols and conclude that the only possible attack is by brute force. In this paper, D-H key distribution and agreement protocols are also described in PR with two cyclotomic cosets based on DLP. DLP over number rings is important problem in public-key DLP is studied in the case of polynomial rings with two cyclotomic coset. Keywords: key distribution, authentication, discrete logarithm problem, polynomial rings, cyclotomic coset a consequence of this, there exists an active field of research known as noncommutative algebraic cryptography, aiming to develop and analyze new cryptosystems and key exchange protocols based on noncommutative cryptographic platforms. 1. Introduction The ElGamal protocol [2] and all its variants are based on the Discrete Logarithm Problem (DLP) over a finite field Zp, here p is a large prime. The discrete logarithm problem (DLP) in a finite cyclic group G is an algorithmic question to find for any given pair of elements g,h ∈ G a number n ∈ N satisfying gn = h. This problem is extremely important due to its relation to cryptography. One of the most prominent and long withstanding protocols, the Diffie-Hellman key-exchange protocol, is based on the assumption that DLP is hard in certain groups. The DiffieHellman protocol proposed in [3] was the first practical
