On the Generalization of Butterfly Structure

Butterfly structure was proposed in CRYPTO 2016 [PUB16], and it can generate permutations over

[1]  Kaisa Nyberg,et al.  Differentially Uniform Mappings for Cryptography , 1994, EUROCRYPT.

[2]  Gohar M. M. Kyureghyan,et al.  On inverses of APN exponents , 2012, 2012 IEEE International Symposium on Information Theory Proceedings.

[3]  Antonia W. Bluher,et al.  On xq+1+ax+b , 2004, Finite Fields Their Appl..

[4]  Anne Canteaut,et al.  On a generalisation of Dillon’s APN permutation , 2017 .

[5]  Yongqiang Li,et al.  A matrix approach for constructing quadratic APN functions , 2014, Des. Codes Cryptogr..

[6]  Xiang-dong Hou,et al.  Affinity of permutations of P2n , 2006, Discret. Appl. Math..

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

[8]  Shihui Fu,et al.  Differentially 4-Uniform Permutations with the Best Known Nonlinearity from Butterflies , 2017, IACR Trans. Symmetric Cryptol..

[9]  Yongqiang Li,et al.  Constructing S-boxes for Lightweight Cryptography with Feistel Structure , 2014, CHES.

[10]  Claude Carlet,et al.  Codes, Bent Functions and Permutations Suitable For DES-like Cryptosystems , 1998, Des. Codes Cryptogr..

[11]  Alex Biryukov,et al.  Cryptanalysis of a Theorem: Decomposing the Only Known Solution to the Big APN Problem , 2016, CRYPTO.

[12]  Jakub Töpfer.  Links Between Differential and Linear Cryptanalysis , 2015 .