Awni M. Gaftan, Akram S. Mohammed, Osama H. Subhi, Implementation Diffie-Hellman by Using Standard Groups and Hosoya-Polynomial to Generate a Matrix as Key Cryptosystem, Journal of Engineering and Applied Sciences, Volume 14,Issue 11, 2019, Pages 3806-3812, ISSN 1816-949x, jeasci.2019.3806.3812, (https://makhillpublications.co/view-article.php?doi=jeasci.2019.3806.3812) Abstract: In this study we used standard groups and Hosoya polynomial to implement Diffie-Hellman method to generate matrix key cryptosystem instead of the number which is generate as a key in this method. Also, we using Dihedral group with Hosoya polynomial for group graph to encrypt plain text and to decrypt cipher text and we produce the statistical table for the ratio to any letter in plain text and every letter in cipher text. Keywords: Hosoya polynomial;dihedral group;Diffie-Hellman;encryption processes;decryption processes;cipher text