论文信息 - Some Binomial and Trinomial Differentially 4-Uniform Permutation Polynomials

Some Binomial and Trinomial Differentially 4-Uniform Permutation Polynomials

Permutation polynomials with low differential uniformity are important candidate functions to design substitution boxes of block ciphers. In this paper, we investigate several classes of differential 4-uniform binomial and trinomial permutation polynomials over the finite field 𝔽2n of 2n elements.

[1] Hans Dobbertin,et al. Almost Perfect Nonlinear Power Functions on GF(2n): The Welch Case , 1999, IEEE Trans. Inf. Theory.

[2] Tadao Kasami,et al. The Weight Enumerators for Several Clauses of Subcodes of the 2nd Order Binary Reed-Muller Codes , 1971, Inf. Control..

[3] Yin Tan,et al. Binomial differentially 4 uniform permutations with high nonlinearity , 2012, Finite Fields Their Appl..

[4] Yongqiang Li,et al. Constructing differentially 4-uniform permutations over GF(22m) from quadratic APN permutations over GF(22m+1) , 2014, Des. Codes Cryptogr..

[5] Hans Dobbertin,et al. One-to-One Highly Nonlinear Power Functions on GF(2n) , 1998, Applicable Algebra in Engineering, Communication and Computing.

[6] Robert Gold,et al. Maximal recursive sequences with 3-valued recursive cross-correlation functions (Corresp.) , 1968, IEEE Trans. Inf. Theory.

[7] Lei Hu,et al. Constructing new differentially 4-uniform permutations from the inverse function , 2014, Finite Fields Their Appl..

[8] Carl Bracken,et al. A highly nonlinear differentially 4 uniform power mapping that permutes fields of even degree , 2009, Finite Fields Their Appl..