A new block cipher algorithm that adopts the magic square of the fifth order with messages of different lengths and multi-function in GF(28)

Alattar, Ibrahim; Rahma, Abdul Monem S.

doi:10.21533/pen.v9i3.2205

Cited by 3 publications

(3 citation statements)

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“…This correspondence will be passed onto the dependent variables automatically, e. g. D+l=d+L. The matrix rank is five and its characteristic polynomial is (21). Thus, we conclude that its rank is generally five and expects that the characteristic polynomial to have the form (22):…”

Section: Magic Square 8 Bymentioning

confidence: 92%

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

Al-Ashhab

Al-qdah²

2022

IJEECS

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In this paper, we discuss and mathematically compute the eigenvalues and the characteristic polynomials of special even square matrices of orders 4x4 and 8x8. Also, we introduce two 8th order compound magic squares. The computed values are verified using Maple software. First, for the 4th order square matrix, the characteristic polynomial was derived to be: λ(λ-2s)( λ²+4Θ) with the eigenvalues: 0,2 s, and two other conjugates. In further analysis, we performed numerical classification of the squares for the matrices of order 4. Second, for the 8th order magic square, the characteristic polynomial was obtained in the form: λ3(λ-4s)(λ4+Ωλ2+θ) where Ω,Θ are constants; the eigenvalues are 0,4 s, ∓√λ1, ∓√λ2; where λ1, λ2 are the roots of the quadratic equation: λ2+Ωλ+Θ=0. Third, for the franklin square, we obtained the eigenvalues 0,4 s, and the roots of the equation: λ2+aλ+b. Finally, we suggested a hybrid image encryption technique based on Franklin magic square matrices and improved substitution technique. The proposed a grayscale image encryption/ decryption algorithm uses circular rotation of bits and Franklin magic squares’ properties in conjunction with substitution techniques to obtain a very secure algorithm against attacks.

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Section: Magic Square 8 Bymentioning

confidence: 92%

“…Alattar and Rahma [21] proposed a hybrid method to encrypt images using franklin magic square matrices and improved substitution techniques. They developed two image or text encryption algorithms based on 5 by 5 Magic Squares using GF(P) and GF (2 8 ): the first used a message length = 10 and the second used a message length = 14.…”

Section: Literature Reviewmentioning

confidence: 99%

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

Al-Ashhab

Al-qdah²

2022

IJEECS

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“…The operations of the two dynamic internal keys, the matrix multiplication and the replacement of the previous XOR make it difficult to attack the known plaintext. Alattar and Rahma [19] considered developing encryption methods using an order 5 magic square. Both GF (P) and GF (2 8 ) were used to encrypt text and images.…”

Section: Related Workmentioning

confidence: 99%

An improvement for CAST-128 encryption based on magic square and matrix inversion

Kareem,

Al-Adhami,

S. Rahma

2024

Bulletin EEI

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This paper presents two image encryption methods which aim to improve the CAST 128-bit algorithm by increasing the security level of encrypted images. The first improvement uses a magic square of order three, while the second improvement uses a 2×2 matrix over GF(P). Both modifications are used in each round of the CAST algorithm, in place of a standard algorithm which uses XOR to increase the correlation between the plaintext and ciphertext. Simulations are carried out in order to evaluate the image encryption system with regard to complexity, time consumption, histogram, information entropy, differential attacks, noise evaluation, adjacent pixels’ correlation index, National Institute of Standards and Technology (NIST) analyses, mean absolute error, and average difference. The experimental results demonstrate that the encryption and decryption time when using the proposed CAST 128-bit algorithm with magic square is less than the time required for the CAST 128-bit algorithm with the matrix. Conversely, the proposed CAST with the matrix is higher than the CAST with the magic square. Both theoretical analysis and experimental results confirm that the two proposed enhancements to CAST perform effectively with sufficient security levels.

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A Block Cipher Algorithm Based on Magic Square for Secure E-bank Systems

Hussien¹,

Rahma²,

Wahab³

2022

Computers, Materials &Amp; Continua

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A new block cipher algorithm that adopts the magic square of the fifth order with messages of different lengths and multi-function in GF(28)

Cited by 3 publications

References 0 publications

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

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

An improvement for CAST-128 encryption based on magic square and matrix inversion

A Block Cipher Algorithm Based on Magic Square for Secure E-bank Systems

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