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.
Highlights
The term magic square is very old, as it was over 2000 years ago
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
In the early uses of the magic squares, they were used in magic and witchcraft; they were used in several fields, the most important are astronomy, mathematics, number theory, and cryptography [2]
Summary
The term magic square is very old, as it was over 2000 years ago. Magic squares appeared first in China, moved to Japan, to India, and to the Arabs, and to Europe [1].In the early uses of the magic squares, they were used in magic and witchcraft; they were used in several fields, the most important are astronomy, mathematics, number theory, and cryptography [2].It was used in some entertaining games like chess, as the movement of the horse in the game of chess is based on the concepts of the magic squares, and most of the entertainment and intelligence games were based on the idea of magic squares such as Sudoku and others[3].Mathematicians and cryptologists have developed algorithms and methods based on the magic squares of order three (MS3) where it takes numbers between 1 and 9, the magic square of order four (MS4) takes numbers between 1 and 16. The term magic square is very old, as it was over 2000 years ago. In the early uses of the magic squares, they were used in magic and witchcraft; they were used in several fields, the most important are astronomy, mathematics, number theory, and cryptography [2]. It was used in some entertaining games like chess, as the movement of the horse in the game of chess is based on the concepts of the magic squares, and most of the entertainment and intelligence games were based on the idea of magic squares such as Sudoku and others[3]. The magic square of order five (MS5) takes numbers between 1 and 25 and so on[4]
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