A New Method for Construction of Orthomorphic Permutations with the Highest Degree

DOI

10.2991/cnct-16.2017.79How to use a DOI?

Keywords

Information Security, Cryptography, orthomorphic permutation, Boolean function

Abstract

Orthomorphic permutation is proposed in 1942, which is a special permutation with many good cryptographic properties. Orthomorphic permutation has similar structure with a one-way function used in hash functions called Davies-Meyer construction. However, the algebraic degrees of previous constructions of orthomorphic permutations by Boolean functions are not the highest, which can be attacked by higher order differential attack. In this paper, we develop a new method for construction of orthomorphic permutations with the highest degree so that they are resistant to higher order differential analysis. We also generalize the construction from four aspects to generate more orthomorphic permutations with the highest degree. Moreover, we give the total number of orthomorphic permutations constructed after applying these generalizations. Our improvement on the degree of orthomorphic permutation can be used as a reference of designing S-box with great cryptographic properties in new algorithms.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Zi-dong LU
AU  - Xue-jia LAI
PY  - 2016/12
DA  - 2016/12
TI  - A New Method for Construction of Orthomorphic Permutations with the Highest Degree
BT  - Proceedings of the International Conference on Computer Networks and Communication Technology (CNCT 2016)
PB  - Atlantis Press
SP  - 579
EP  - 584
SN  - 2352-538X
UR  - https://doi.org/10.2991/cnct-16.2017.79
DO  - 10.2991/cnct-16.2017.79
ID  - LU2016/12
ER  -