Quadratic Equations from a Kind of S-boxes

Authors:
Jia Xie;Weiwei Cao;Tianze Wang
Affiliations:
The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, China 100790 and The state key laboratory of information securtity, Graduate School o ...;The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, China 100790 and The state key laboratory of information securtity, Graduate School o ...;The state key laboratory of information securtity, Institute of software, Chinese Academy of Science, Beijing, China 100790 and The state key laboratory of information securtity, Graduate School o ...
Venue:
Information Security Applications
Year:
2009

Citing 6
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Abstract

Algebraic attack studies ciphers from the point of view of solving equations. It is important to measure the security of block ciphers how many linearly independent bi-affine or quadratic equations they satisfy. As the S-box is the main nonlinear part of block ciphers, it really makes sense to get the number of linearly independent bi-affine and quadratic equations that an S-box satisfies to analyse the security of block ciphers. The article answers this question for two S-boxes based on APN power functions, and shows how to find out the equations by two toy examples. The techniques can be generalized to other S-boxes constructed by power functions. According to these conclusions, we can estimate the safety of such kind of block ciphers.