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| A New Method for Evaluation of Hamming Weight and Nonlinearity of Rotation-symmetric Boolean Functions |
| Zhang Xi-yong①②④ Qi Ying-hong① Gao Guang-pu③ Li Yu-juan④ |
①(Information Engineering University, Zhengzhou 450002, China)
②(State Key Laboratory of Mathematical Engineering and Advanced Computing, Wuxi 214215, China)
③(Luoyang University of Foreign Languages, Luoyang 471003, China)
④(Science and Technology on Information Assurance Laboratory, Beijing 100072, China) |
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Abstract Rotation-symmetric Boolean function is a class of Boolean functions with good cryptographic properties, and researches on its weight and nonlinearity cryptographic properties have good theoretical value. Different from the conventional calculation method, in this paper, these problems are converted to the evaluation of exponential sum on finite fields with a specific normal basis. Some new results about the weight and nonlinearity of some rotation-symmetric Boolean functions of degree 2 with 4 ?? n and n=2s are obtained. Using the proposed method, the weight and nonlinearity of almost all Rotation-symmetric Boolean functions of degree 2 can be evaluated. This new method is also interesting for studies on the other Boolean functions.
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Received: 29 January 2015
Published: 27 July 2015
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| Fund: The National Natural Science Foundation of China (61402522, 60803154, 61572027); Project of State Key Lab of Mathematical Engineering and Advanced Computing; Open Foundation of Science and Technology on Information Assurance?Laboratory (KJ-13-108) |
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Corresponding Authors:
Qi Ying-hong
E-mail: yinghong_qi@163.com
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