ZHAO Qinglan, HAN Gang, ZHENG Dong, LI Xiangxue. Constructing Odd-Variable Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity and High Nonlinearity[J]. Chinese Journal of Electronics, 2019, 28(1): 45-51. doi: 10.1049/cje.2018.01.009
Citation: ZHAO Qinglan, HAN Gang, ZHENG Dong, LI Xiangxue. Constructing Odd-Variable Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity and High Nonlinearity[J]. Chinese Journal of Electronics, 2019, 28(1): 45-51. doi: 10.1049/cje.2018.01.009

Constructing Odd-Variable Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity and High Nonlinearity

doi: 10.1049/cje.2018.01.009
Funds:  This work is supported by the National Key Research and Development Program of China (No.2017YFB0802002), the National Natural Science Foundation of China (No.61472472, No.61402366), and the Natural Science Basic Research Plan in Shaanxi Province of China(No.2016JM6033). ZHAO QingLan is supported by New Star Team of Xi'an University of Posts and Telecommunications (No.2016-02).
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  • Corresponding author: ZHENG Dong (corresponding author) was born in 1964. He received Ph.D. degree from Xidian University in 1999. He then joined the School of Information Security Engineering, Shanghai JiaoTong University. He is currently a professor in Xi'an University of Post and Telecommunications, China. His research interests include information theory, cryptography and information security. (Email:zhengdong_xupt@sina.com)
  • Received Date: 2017-03-10
  • Rev Recd Date: 2017-07-07
  • Publish Date: 2019-01-10
  • Rotation symmetric Boolean functions (RSBFs) have attracted widespread attention due to their good cryptographic properties. We present a new construction of RSBFs with optimal algebraic immunity on odd number of variables. The nonlinearity of the new function is much higher than other best known RSBFs with optimal algebraic immunity. The algebraic degree of the constructed n-variable RSBF can achieve the upper bound n-1 when n/2 is odd or when n/2 is a power of 2 for n ≥ 11. In addition, the constructed function can possess almost perfect immunity to fast algebraic attacks for n=11, 13, 15.
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