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
We study the differential uniformity of a class of permutations over F2 n with n even. These permutations are different from the inverse function as the values x^(-1) are modified to be(γx)^(-1) on some cosets of a f...We study the differential uniformity of a class of permutations over F2 n with n even. These permutations are different from the inverse function as the values x^(-1) are modified to be(γx)^(-1) on some cosets of a fixed subgroup γ of F_(2n)~*. We obtain some sufficient conditions for this kind of permutations to be differentially 4-uniform, which enable us to construct a new family of differentially 4-uniform permutations that contains many new Carlet-Charpin-Zinoviev equivalent(CCZ-equivalent) classes as checked by Magma for small numbers n. Moreover, all of the newly constructed functions are proved to possess optimal algebraic degree and relatively high nonlinearity.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 National Natural Science Foundation of China(Grant Nos.61202463 and 61202471)Shanghai Key Laboratory of Intelligent Information Processing(Grant No.IIPL-2014-005)
文摘We study the differential uniformity of a class of permutations over F2 n with n even. These permutations are different from the inverse function as the values x^(-1) are modified to be(γx)^(-1) on some cosets of a fixed subgroup γ of F_(2n)~*. We obtain some sufficient conditions for this kind of permutations to be differentially 4-uniform, which enable us to construct a new family of differentially 4-uniform permutations that contains many new Carlet-Charpin-Zinoviev equivalent(CCZ-equivalent) classes as checked by Magma for small numbers n. Moreover, all of the newly constructed functions are proved to possess optimal algebraic degree and relatively high nonlinearity.
