We present several new constructions of differentially 4-uniform permutations over F22 mby modifying the values of the inverse function on some subsets of F22 m. The resulted differentially 4-uniform permutations have...We present several new constructions of differentially 4-uniform permutations over F22 mby modifying the values of the inverse function on some subsets of F22 m. The resulted differentially 4-uniform permutations have high nonlinearities and algebraic degrees, which provide more choices for the design of crytographic substitution boxes.展开更多
This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic im...This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions.展开更多
基金supported by National Basic Research Programme of China(Grant No.2013CB834203)National Natural Science Foundation of China(Grant Nos.11201214 and 61472417)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA06010702)
文摘We present several new constructions of differentially 4-uniform permutations over F22 mby modifying the values of the inverse function on some subsets of F22 m. The resulted differentially 4-uniform permutations have high nonlinearities and algebraic degrees, which provide more choices for the design of crytographic substitution boxes.
基金supported by the National Key Basic Research Program of China under Grant No.2013CB834203the National Natural Science Foundation of China under Grant Nos.61472417 and 61472120the Research Council of Norway
文摘This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions.
