Abstract
The global avalanche characteristics (the sum-of-squares indicator and the absolute indicator) measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. (1999) gave the lower bound on the sum-of-squares indicator for a balanced Boolean function satisfying the propagation criterion with respect to some vectors. In this paper, if balanced Boolean functions satisfy the propagation criterion with respect to some vectors, we give three necessary and sufficient conditions on the auto-correlation distribution of these functions reaching the minimum the bound on the sum-of-squares indicator. And we also find all Boolean functions with 3-variable, 4-variable, and 5-variable reaching the minimum the bound on the sum-of-squares indicator.
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References
Adams C, Tavares S. Generating and counting binary bent sequences. IEEE Transactions on Information Theory, 1990, 36(5): 1170–1173
Webster A F. Plaintext/ciphertext bit dependencies in cryptographic system. Master thesis, Department of Electrical Engineering, Queen’s University, Ontario, Cannada, 1985
Preneel B, Van Leekwijck W, Van Linden L, Govaerts R, Vandewalle J. Propagation characteristics of boolean functions. In: Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques on Advances in Cryptology. 1991, 161–173
Zhang K, Zheng Y. GAC-the criterion for global avalance characteristics of cryptographic functions. Journal of Universal Computer Science, 1995, 1(5): 320–337
Son J, Lim J, Chee S, Sung S. Global avalanche characteristics and nonlinearity of balanced boolean functions. Information Processing Letters, 1998, 65(3): 139–144
Sung S, Chee S, Park C. Global avalanche characteristics and propagation criterion of balanced boolean functions. Information Processing Letters, 1999, 69(1): 21–24
Charpin P, Pasalic E. On propagation characteristics of resilient functions. In: Proceedings of the 9th Annual International Workshop on Selected Areas in Cryptography. 2002, 175–195
Zhou Y, Xie M, Xiao G. On the global avalanche characteristics between two boolean functions and the higher order nonlinearity. Information Sciences, 2010, 180(2): 256–265
Zhang X, Zheng Y. Characterizing the structures of cryptographic functions satisfying the propagation criterion for almost all vectors. Designs, Codes and Cryptography, 1996, 7(1): 111–134
Carlet C. Partially-bent functions. In: Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology. 1992, 280–291
Meier W, Pasalic E, Carlet C. Algebraic attacks and decomposition of boolean functions. In: Proceedings of Advances in Cryptology-EUROCRYPT 2004: International Conference on the Theory and Applications of Cryptographic Techniques. 2004, 474–491
Zhou Y, Xiao G. On the equal-weight symmetric boolean functions. Frontiers of Computer Science in China, 2009, 3(4): 485–493
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Yu Zhou, Senior Engineer, received the BS, MS in Mathematics from Lanzhou University and PhD in Communication from Xidian University, China, in 2003, 2006 and 2009 respectively. In 2010, he joined the Science and Technology on Communication Security Laboratory, China. His research interests include sequence design, coding theory and Boolean functions.
Weiguo Zhang, associate professor, received the BS and PhD from Xidian University, China, in 2001 and 2007, respectively. In 2007, he joined State Key Laboratory of Integrated Service Networks at Xidian University. His research interests include cryptography and sequence design.
Juan Li, Engineer, received the BS and MS from Sichuan International Studies University, Sichuan International Studies University and University of Electronic Science and Technology of China, in 2004, 2010 respectively. In 2011, she joined Southwest Jiaotong University. Her research interests include communication.
Xinfeng Dong, Engineer, received the BS and MS, Sichuan University, China, in 2006, 20009 respectively. In 2010, he joined the Science and Technology on Communication Security Laboratory. His research interests include Boolean functions.
Guozhen Xiao, professor, received the BS in Mathematics from Northeast Normal University, Changchun, China, in 1954, and the MS in Mathematics from the East China Normal University, Shanghai, China, in 1956. From 1956 to 1960, he was an associate instructor in Northeast Normal University. He joined Xidian University, China, in 1960, and became a full professor in 1981. His research interests include cryptography, coding, and information theory.
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Zhou, Y., Zhang, W., Li, J. et al. The autocorrelation distribution of balanced Boolean function. Front. Comput. Sci. 7, 272–278 (2013). https://doi.org/10.1007/s11704-013-2013-x
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DOI: https://doi.org/10.1007/s11704-013-2013-x