Enhancing SPN ciphers: Dynamic substitution-key addition layers via binary block circulant matrices
DOI:
https://doi.org/10.54654/isj.v1i24.1100Keywords:
AES block cipher, Affine transformation, Dynamic S-box, Dynamic XOR table, Binary block circulant matrixTóm tắt
The SPN (Substitution-Permutation Network) block cipher is one of the fundamental and important structures in the field of symmetric encryption, widely used in modern encryption algorithms such as AES. Due to its ability to efficiently diffuse and obscure data, SPN plays a key role in building secure and reliable encryption systems. However, with the development of the SPN block cipher, many studies have been conducted to identify cryptanalytic attack methods to break this cipher. To enhance the security of the SPN block cipher, recent research has focused on dynamic transformations of its components and often relies on the secret component, the key. In this study, we propose a new method that combines the dynamicization of two key components: the substitution layer and the key addition layer of the SPN block cipher. This method is based on using a binary block circular shift matrix, formed by combining a binary circular shift matrix with a binary Hadamard matrix. Our algorithm only requires the use of 26 additional key bits but can generate up to 228 key-dependent S-boxes with strong cryptographic properties and 233 key-dependent XOR tables. When applying these key-dependent S-boxes and XOR tables to dynamically modify the AES block cipher, it can increase the security level of the dynamic AES block cipher by 233 compared to AES
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. Youssef, A.M., Tavares, S.E. và Heys, H.M., "A new class of substitution-permutation networks", In: Proceedings of the Workshop on Selected Areas in Cryptography (SAC), vol. 96, pp. 132–147, 1996.
. Dodis, Y., Katz, J., Steinberger, J., Thiruvengadam, A. và Zhang, Z., "Provable security of substitution-permutation networks", Cryptology ePrint Archive, 2017.
. Sajjad, M., Shah, T., Hamza, R., Almutairi, B. và Serna, R.J., "Multiple color images security by SPN over the residue classes of Gaussian integer", Scientific Reports, vol. 15, no. 1, pp. 6425, 2025.
. Daemen, J. và Rijmen, V., "AES Proposal: Rijndael (Version 2)", NIST AES Website, 1999.
. Biham, E. và Shamir, A., "Differential cryptanalysis of DES-like cryptosystems", Journal of Cryptology, vol. 4, pp. 3–72, 1991.
. Gilbert, H. và Jean, J.E., "Differential Cryptanalysis", Symmetric Cryptography, Volume 2: Cryptanalysis and Future Directions, pp. 1, 2024.
. Matsui, M., "Linear cryptanalysis method for DES cipher", In: Advances in Cryptology—EUROCRYPT’93, vol. 12, pp. 386–397, 1993.
. Das, A., "Bit-Based MILP Modelling of Non-Bit-Permutation Linear Layers for Linear Cryptanalysis", In: Proceedings of the 2024 19th Asia Joint Conference on Information Security (AsiaJCIS), pp. 1–8, IEEE, 2024.
. Schneier, B., "The Twofish encryption algorithm", Dr. Dobb’s Journal: Software Tools for the Professional Programmer, vol. 23, no. 12, pp. 30–34, 1998.
. Luong, T.T. và Linh, H.D., "Generating key-dependent involutory MDS matrices through permutations, direct exponentiation, and scalar multiplication", International Journal of Information and Computer Security, vol. 23, no. 4, pp. 410–432, 2024.
. Noura, H.N., Salman, O. và Chehab, A., "Conception of efficient key-dependent binary diffusion matrix structures for dynamic cryptographic algorithms", Journal of Information Security and Applications, vol. 76, pp. 103514, 2023.
. T. T. Luong, "Building the dynamic diffusion layer for SPN block ciphers based on direct exponent and scalar multiplication," Journal of Science and Technology on Information Security, vol. 1, no. 15, pp. 38–45, 2022.
. T. T. Luong and T. M. Phuong, "Generating efficient circulant-like MDS matrices for implementation," Journal of Science and Technology on Information Security, vol. 2, no. 22, pp. 58–68, 2024.
. Zhu, H., Tong, X., Wang, Z. và Ma, J., "A novel method of dynamic S-box design based on combined chaotic map and fitness function", Multimedia Tools and Applications, vol. 79, pp. 12329–12347, 2020.
. Waqas, U., Afzal, S., Mir, M.A. và Yousaf, M., "Generation of AES-like S-boxes by replacing affine matrix", In: Proceedings of the 2014 12th International Conference on Frontiers of Information Technology, pp. 159–164, IEEE, 2014.
. Agarwal, P., Singh, A. và Kilicman, A., "Development of key-dependent dynamic S-boxes with dynamic irreducible polynomial and affine constant", Advances in Mechanical Engineering, vol. 10, no. 7, pp. 1687814018781638, 2018.
. Alhadawi, H.S., Majid, M.A., Lambić, D. và Ahmad, M., "A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm", Multimedia Tools and Applications, vol. 80, pp. 7333–7350, 2021.
. Hussain, I., Anees, A., Al-Maadeed, T.A. và Mustafa, M.T., "Construction of S-box based on chaotic map and algebraic structures", Symmetry, vol. 11, no. 3, pp. 351, 2019.
]Artuğer, F., "A novel algorithm based on DNA coding for substitution box generation problem", Neural Computing and Applications, vol. 36, no. 3, pp. 1283–1294, 2024.
. Maolood, A.T. et al., "Fast Novel Efficient S-Boxes with Expanded DNA Codes", Security and Communication Networks, vol. 2023, no. 1, pp. 5767102, 2023.
. Salih, A.I., Alabaichi, A.M. và Tuama, A.Y., "Enhancing advance encryption standard security based on dual dynamic XOR table and mixcolumns transformation", Indonesian Journal of Electrical Engineering and Computer Science, vol. 19, no. 3, pp. 1574–1581, 2020.
. Luong, T.T., Cuong, N.N. và Vo, B., "AES Security Improvement by Utilizing New Key-Dependent XOR Tables", IEEE Access, 2024.
. Luong, T.T. và Linh, H.D., "On generating new key dependent XOR tables to improve AES security and evaluating the randomness of the output of block ciphers", International Journal of Information and Computer Security, vol. 23, no. 1, pp. 16–39, 2024.
. Hoang, D.L. và Luong, T.T., "Enhancing block cipher security with key-dependent random XOR tables generated via hadamard matrices and Sudoku game", Journal of Intelligent & Fuzzy Systems, vol. 46, no. 4, pp. 7805–7821, 2024.
. Kim, S.H. và Han, G.T., "Enhanced hybrid encryption method using the half-key exchange and the dynamic S-box and shift-row in AES", Information, vol. 19, no. 2, pp. 683, 2016.
. Prasetiyo, B. và Ardian, M.N., "Enhancement security AES algorithm using a modification of transformation ShiftRows and dynamic S-box", In: Journal of Physics: Conference Series, vol. 1567, no. 3, pp. 032025, IOP Publishing, 2020.
. Navneet, J.R. et al., "AES algorithm with dynamic shift rows and bit permuted mix column", In: Proceedings of the 2023 International Conference on Next Generation Electronics (NEleX), pp. 1–6, IEEE, 2023.
. Artuğer, F. và Özkaynak, F., "A method for generation of substitution box based on random selection", Egyptian Informatics Journal, vol. 23, no. 1, pp. 127–135, 2022.
. Nyberg, K., "Perfect nonlinear S-boxes", In: Workshop on the Theory and Application of Cryptographic Techniques, pp. 378–386, Springer, 1991.
. Burnett, L.D., "Heuristic optimization of Boolean functions and substitution boxes for cryptography", PhD Thesis, Queensland University of Technology, 2005.
. Gupta, K.C. và Ray, I.G., "Cryptographically significant MDS matrices based on circulant and circulant-like matrices for lightweight applications", Cryptography and Communications, vol. 7, pp. 257–287, 2015.
. Han, H., Tang, C., Lou, Y. và Xu, M., "Construction of efficient MDS matrices based on block circulant matrices for lightweight application", Fundamenta Informaticae, vol. 145, no. 2, pp. 111–124, 2016.
. Elumalai, R. và Reddy, A.R., "Improving diffusion power of AES Rijndael with 8x8 MDS matrix", International Journal of Scientific & Engineering Research, vol. 2, no. 3, 2011.
. Sajadieh, M. et al., "On construction of involutory MDS matrices from Vandermonde Matrices in GF(2^q)", Designs, Codes and Cryptography, vol. 64, pp. 287–308, 2012.
. Knudsen, L.R., "Truncated and higher order differentials", In: Fast Software Encryption: Second International Workshop, pp. 196–211, Springer, 1995.
. Kocher, P., Jaffe, J. và Jun, B., "Differential power analysis", In: Advances in Cryptology - CRYPTO’99, vol. 19, pp. 388–397, Springer, 1999.
. Bassham III, L.E. et al., "SP 800-22 Rev. 1a. A statistical test suite for random and pseudorandom number generators for cryptographic applications", NIST Special Publication, 2010.
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