Abstract
The autocorrelation of a Boolean function possesses the capability to reflect such characteristics as linear structure, Strict Avalanche Criterion(SAC) and Propagation Criterion(PC) of degree k. But it can do nothing in determining the order of SAC or PC. A calculating table for the autocorrelation is constructed in this paper so as to show what is beyond the autocorrelation and how the three cryptographic characteristics are exhibited. A deeper study on the calculating table in a similar way has helped us to develop a new concept, named as the general autocorrelation, to address efficiently the problem how to determine the orders of SAC and PC. The application on the Advanced Encryption Standard(AES) shows the SAC and PC characteristics of Boolean functions of AES S-box.
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References
Jenniefer Seberry, Zhang Xianmo, Zheng Yuliang, Nonlinearity and propagation characteristics of balanced Boolean functions, Information and Computation, 119(1995)1, 1–13.
Kaoru Kurosawa, Takashi Satoh, Design of SAC/PC(1) of order k Boolean functions and three other cryptographic criteria, Advances in Cryptology-EUROCRYPT’97, Konstanz, Germany, May 11–15, 1997, 435–449.
J. Seberry, Zhang Xianmo, Highly nonlinear 0–1 balanced Boolean functions satisfying strict avalanche criterion, Advances in Cryptology-AUSCRYPT’92, Queensland, Australia, December 13, 1992, 145–155.
Zhang Xianmo, Zheng Yuliang, Auto-correlations and new bounds on the nonlinearity of Boolean functions, Advances in Cryptology—EUROCRYPT’96, Zaragaza, Spain, May 12–16, 1996, 294–306.
Subhamoy Maitra, Highly nonlinear balanced Boolean functions with very good autocorrelation property, International Workshop on Coding and Cryptography January 8–12, 2001, Paris, France, 355–364.
Feng Dengguo, Spectrum Theory and its Applications in Cryptology, Beijing, Science Press, 48–62, (in Chinese).
Wen Qiaoyan, Niu Xinxin, Yang Yixian, Boolean Functions in Modern Cryptology, Beijing, Science Press, 13–19, (in Chinese).
Joan Daemen, Vincent Rijmen, AES proposal: Rijndael, First Advanced Encryption Standard Candidate Conference, Ventura, California, August 20–22, 1998, 1–45.
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Partially supported by the National 973 Project (G1999035803), National 863 Project (2002AA143021) and the National Cryptography Development Funds for the Tenth Five-year Project
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Wei, B., Liu, D., Ma, W. et al. New concept for determining the orders of SAC and PC. J. of Electron.(China) 21, 191–197 (2004). https://doi.org/10.1007/BF02687871
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DOI: https://doi.org/10.1007/BF02687871