On the Generalization of Butterfly Structure

  • Yongqiang Li State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences Beijing, China; School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
  • Shizhu Tian State Key Laboratory of Information Security, Institute of Information Engineering,Chinese Academy of Sciences, Beijing, China; School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
  • Yuyin Yu School of Mathematics and Information Science, Guangzhou University, Guangzhou, China
  • Mingsheng Wang State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China; School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China
Keywords: Butterfly structure, differential uniformity, nonlinearity, algebraic degree

Abstract

Butterfly structure was proposed in CRYPTO 2016 [PUB16], and it can
generate permutations over F22n from power permutations over F2n for odd n. After
that, a generalized butterfly structure was proposed in IEEE IT [CDP17], which can
generate permutations over F22n from any permutation over F2n . There is also another
generalization which was given in [FFW17]. Up to now, three constructions based on
butterfly structure and Gold type permutations are proposed. In the present paper,
we give a construction which contains the three previous constructions as special cases
and also generates new permutations with good cryptographic properties. Moreover,
we give a characterization of the number of solutions of a special system of linear
equations in a more general way, which is useful to investigate the cryptographic
properties of quadratic functions obtained with butterfly construction based on Gold
exponents.

Published
2018-03-01
How to Cite
Li, Y., Tian, S., Yu, Y., & Wang, M. (2018). On the Generalization of Butterfly Structure. IACR Transactions on Symmetric Cryptology, 2018(1), 160-179. https://doi.org/10.13154/tosc.v2018.i1.160-179
Section
Articles