Optimal S-boxes based on 3-quasigroups of order 4
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DOI: 10.23977/icamcs.2017.1016
Author(s)
Yu Zhengping, Xu Yunqing
Corresponding Author
Xu Yunqing
ABSTRACT
In this paper, we give a method for generating cryptographically strong 44-bit S-boxes with the pure non-linear representatives of 3-quasigroup of order 4. S-boxes are widely used in block ciphers and hash functions and they are usually the only non-linear part in the systems and they have to be chosen carefully. 44-bit S-boxes are very suitable in the design of lightweight cryptographies, while the constructing of 44-bit S-boxes are usually by exhaustive computer search of permutations of degree 16. Our methodology is based on 3-quasigroup operations and it enables someone to get S-boxes optimal in linearity and differential uniformity, and all the component functions (algebraic normal form) of the generated S-boxes have maximal algebraic degrees.
KEYWORDS
S-Box, 3-Quasigroup, Latin Cube, Algebraic Normal Form