Bing Shen
ABSTRACT
The diffusion function with large branch number is a fundamental building block in the construction of many block ciphers to achieve provable bounds against differential and linear cryptanalysis. Conventional diffusion functions, which are constructed based on linear error-correction code, has the undesirable side effect that a linear diffusion function by itself is “transparent” (i.e., has transition probability of 1) to differential and linear cryptanalysis. Nonlinear diffusion functions are less studied in cryptographic literature, up to now. In this paper, we propose a practical criterion for nonlinear optimal diffusion functions. Using this criterion we construct generally a class of nonlinear optimal diffusion functions over finite field. Unlike the previous constructions, our functions are non-linear, and thus they can provide enhanced protection against differential and linear cryptanalysis.
- Joan Daemen.1995.Cipher and hash function design strategies based on linear and differential cryptanalysis. PhD Thesis, KU Leuven.Google Scholar
- Youssef A M, Mister S, Tavares S E.1997. On the design of linear transformations for substitution permutation encryption networks .Workshop on Selected Areas of Cryptography (SAC'96): Workshop Record. 1997: 40-48.Google Scholar
- Wu S, Wang M, Wu W. 2012. Recursive diffusion layers for (lightweight) block ciphers and hash functions . Lecture Notes in Computer Science, Vol. 7707. Springer-Verlag, New York, NY.Google Scholar
- Sajadieh M, Dakhilalian M, Mala H, 2015. Efficient recursive diffusion layers for block ciphers and hash functions. Journal of Cryptology, 28, 2(2015), 240-256.Google ScholarDigital Library
- Li, S., Sun, S., Shi, D., Li, C., Hu, L. 2019. Lightweight Iterative MDS Matrices: How Small Can We Go? . IACR Transactions on Symmetric Cryptology, 4(2019), 147-170.Google Scholar
- W. You, D. Xin-feng, W. Jin-bo and Z. Wen-zheng, 2021,Construction of MDS Matrices Based on the Primitive Elements of the Finite Field, 2021 International Conference on Networking and Network Applications (NaNA), 2021,485-488 .Google Scholar
- Kamil O. A Generalization of the Subfield Construction,2021. International Journal of Information Security Science, 11,2(2021): 1-11.Google Scholar
- Kesarwani A, Pandey S K, Sarkar S, Recursive MDS matrices over finite commutative rings,2021. Discrete Applied Mathematics, 304,15(2021), 384-396.Google ScholarDigital Library
- Cui T, Chen S, Jin C, Construction of higher-level MDS matrices in nested SPNs,2021. Information Sciences,554,4(2021),297-312.Google ScholarCross Ref
- Zhou X, Cong T. Construction of generalized-involutory MDS matrices,2022. Cryptology ePrint Archive, 2022.Google Scholar
- Gu Dawu, Xu Shengbo. 2003. Advanced encryption Standard (AES) algorithm: design of Rijndael (in Chinese). Tsinghua University Press.Google Scholar
- Shimoyama T, Yanami H, Yokoyama K, 2001.The block cipher SC2000. Lecture Notes in Computer Science, Vol. 2355. Springer-Verlag, New York, NY.Google Scholar
- State Cryptography Administration. GM / T0002-2012.2012. SM4 block cipher algorithm. Beijing: China Standards Press.Google Scholar
- Alexander Klimov and Adi Shamir, 2005. New Applications of T-Functions in Block Ciphers and Hash Functions, Lecture Notes in Computer Science, Vol. 3557. Springer-Verlag, New York, NY.Google Scholar
- H. Han, X. X. Xu and S. Zhu. 2013. The Properties of Orthomorphisms on the Galois Field. Research Journal of Applied Sciences, Engineering and Technology 5, 5(2013), 1853-1858.Google ScholarCross Ref
- Qu Chengqin, Zhou Xuan Bai Shujun, 2018. A note on MDS transformation(in Chinese),Communication Technology 50, 05(2017),1041-1044.Google Scholar
- Liu, Y., Rijmen, V. & Leander, G. 2018. Nonlinear diffusion layers. Des. Codes Cryptogr. 86(2018), 2469 - 2484.Google ScholarDigital Library
- Shamsabad, M. R., Dehnavi, S. M. 2022. Nonlinear 4×4 MDS diffusion layers. Journal of Information and Optimization Sciences,43,4(2022), 1-14.Google Scholar
- Mann H B. The construction of orthogonal latin squares. 1942. The Annals of Mathematical Statistics, 13, 4(1942), 418-423.Google ScholarCross Ref
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