Dynamic determinant matrix-based block cipher algorithm

Rijndael (AES) is a well-known block cipher algorithm with proven robustness towards countless cryptographic attacks. Somehow, the substitution box (s-box) in the AES block cipher is fixed or static for all rounds and has become the target of many attacks. The design of the s-box is the most crucial part while designing a new block cipher algorithm since it is the only non-linear element of the cipher. In this research, emphasis is given on increasing the complexity of a block cipher algorithm. We propose a new dynamic determinant block cipher (DDBC) designed based on the determinant matrix properties which shall meet the security requirements of a secure block cipher. This research will first make use of the matrix determinants properties, linear equations and its inverses, identifies the similarity elements and combines them with irreducible polynomials and affine transformation to produce new determinants-boxes to be used in the substitution layer. This research also proposes a new method namely RotateSwapDeterminant function that uses rotation and swapping of the bit based on the 4x4 determinant computations and will act as the permutation layer in the DDBC algorithm. The output from the DDBC algorithm will be tested and validated through NIST Statistical Test Suite. The s-box test will be carried out to verify the security of the new determinant s-boxes constructed. The correlation coefficient and key sensitivity of plaintext and ciphertext produced by DDBC algorithm will be tested through avalanche effect experiments. Analyses on linear, differential and short attack will be performed against the DDBC algorithm to estimate the possible success of all three attacks. The performance analysis is performed on DDBC algorithm to test for the encryption and decryption speed of the block cipher and lastly the complexity analysis is performed on the selected determinant s-boxes to examine the level of complexity contributed by tested and untested determinant sboxes. Through these extensive experiments, the proposed DDBC algorithm has successfully passed the NIST Statistical Test with all 15 tests show p-value > 0.01. The results from the s-box test indicate that the determinant s-boxes constructed provides good balanced, sufficient differential uniformity, excellent non-linearity, acceptable algebraic degree and adequate signal to noise ratio (SNR). For the avalanche effect analysis, the DDBC algorithm shows that most of the correlation values tested on the proposed determinant s-boxes and the RotateSwapDeterminant function are near to 0 which indicate a strong positive (or negative) non-linear relationship which means the DDBC algorithm has a high confusion property. The analysis on linear, differential and short attack shows required complexity to be more then 2102 attempts for linear cryptanalysis, required complexity to be more then 2104 attempts for differential cryptanalysis and (((28)10)256)5 total possibilities of attempts for short attack which provide sufficient evidence that the DDBC algorithm is resistance towards all three attacks. The performance analysis in terms of processing speed of the encryption and decryption process of the DDBC algorithm shows minimal differences in both AES and DDBC algorithm despite of the difference method of transformation used in both algorithms. Lastly, the complexity analysis shows that the determinant s-box that has go through the s-box analysis test show better avalanche criteria proving higher level of complexity compared to non-tested determinant s-box. From the result of the analysis, it has been justified that the proposed DDBC algorithm can be considered as one of the secure symmetric block cipher and can be used as an alternative to other cryptographic algorithm in computer security research area.

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