A Comparative Study of Researches Based on Magic Square in Encryption with Proposing a New Technology

Abstract

This paper aims to develop a new cryptographic algorithm that is based on the magic square method of order five with multi message lengths to be more complex in order to increase the complexity; in addition to comparing the cipher with the use of the magic square of order five, four and three (all single message length. The proposed work has been done by using two extra rounds and depending on round statuse ( even or odd) , messages are detected to be used. The key is placed in agreed positions, then the remaining positions are filled with the message, and then certain sums are calculated to represent the encrypted text. Speed, complexity, histogram calculations for images, and NIST calculations for texts were calculated, and the results were compared, where the complexity of the algorithms was as follows ((P)15 × (256)10)2 × (P)11 × (256)14 and ((256)15 × (256)10)2 × (256)11 × (256)14 for GF(P) and GF(28) respectively , From that, it has been discovered that the proposed algorithm (Magic Square of order five with multi message length) is better than the rest of the algorithms as it has excellent complexity and a slight difference in the speed. Index Terms— Cryptography, GF(28), linear equation system, Magic Square.

An investigation of even ordered magic squares (4, 6, and 8): characteristic polynomials, eigenvalues, and encryption

“…Alattara and Rahma [23] developed an encryption algorithm using magic squares (5 by 5) with multi message lengths for added security. The algorithm used two rounds and selected a message interchangeably.…”

“…where Ω, 𝛩 are constants. Also, when we perform thesubstitution 𝑥 = λ², we obtain the roots of this equation (the eigenvalues): 0, 4s, ∓√λ 1 , ∓√ λ 2 , where λ 1 , λ 2 are the roots of the quadratic in (23).…”