### Public Key Cipher with Signature Based on Diffie-Hellman and the Magic Square Problem

#### Abstract

In the present paper, wedeveloped a new variant of asymmetric cipher (Public Key) algorithm based on the Discrete Logarithm Problem (DLP) uses Diffie-Hellman key exchange protocol and the mathematical features of magic square. The proposed method exploits the DLP problem in the key exchange by using the final value of Diffie-Hellman key agreement, just as the dimension to the magic construction and through which determines the type of magic square construction if it is (odd, singly-even or doubly-even) magic square as well as through which determines starting number and the difference value. From the other point, it exploits the magic squares problem in encryption/decryption and signing/verifyingoperations. The developed methodextremely speed in the Encryption/Decryption process as well as in the digital signaturethat uses aSecure Hash Algorithm SHA-1, since the proposed cipher does not use logarithm and the factorization as the traditional algorithms in ciphering and deciphering operations just in the mutual exchanging, but it depends mainly upon the magic constant and magic sum as alternate that deduced from the result of multiplied fixed value, which selected randomly and imposesto keep secret, as we shall explained in the next sections.

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