Open AccessOn the Generalization of Butterfly Structure
Author(s) -
Yongqiang Li,
Shizhu Tian,
Yuyin Yu,
Mingsheng Wang
Publication year - 2018
Publication title -
iacr transaction on symmetric cryptology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.715
H-Index - 10
ISSN - 2519-173X
DOI - 10.46586/tosc.v2018.i1.160-179
Subject(s) - generalization , permutation (music) , butterfly , quadratic equation , type (biology) , benchmark (surveying) , mathematics , computer science , cryptography , combinatorics , discrete mathematics , pure mathematics , algorithm , physics , biology , geometry , geography , mathematical analysis , ecology , geodesy , acoustics
Butterfly structure was proposed in CRYPTO 2016 [PUB16], and it cangenerate permutations over F22n from power permutations over F2n for odd n. Afterthat, a generalized butterfly structure was proposed in IEEE IT [CDP17], which cangenerate permutations over F22n from any permutation over F2n . There is also anothergeneralization which was given in [FFW17]. Up to now, three constructions based onbutterfly structure and Gold type permutations are proposed. In the present paper,we give a construction which contains the three previous constructions as special casesand also generates new permutations with good cryptographic properties. Moreover,we give a characterization of the number of solutions of a special system of linearequations in a more general way, which is useful to investigate the cryptographicproperties of quadratic functions obtained with butterfly construction based on Goldexponents.