Secure Authentication Protocol Based on the Generated Magic Square

Abstract

Magic square is a rich source of mathematical properties that related with a great deal of branches of mathematics and its applications. An arrangement of n distinct integer numbers in a square of n by n represents an n order magic square such that, each of its row, column and diagonals is summed to the same constant. The constructions of magic squares are discussed by many research using different approaches. In this paper, a new method for constructing semi-magic squares depends on the proposition of the arithmetic modular together with the operations of addition, subtraction, multiplication, rotation, and reflection is introduced. Based on an example on a magic square of order 3 and the inverse of modular magic square some results are obtained. Due to the importance of the magic squares and the existence of many applications in practical life, the link between the magic squares and cryptography was found. The method is formulated based on a set of semi magic square that is computed recently using the proposed method. After that the plaintext is written in the form of a linear combination of the elements in this set to be encrypted. This accomplished by finding the ASCII code for each character in the plaintext to get the cipher text. An algorithm for generating the semi-magic squares and its application is designed and implemented to demonstrate this relationship.