On the division property of S-boxes

5 years 6 months ago
On the division property of S-boxes
Todo introduced [20] a property of multisets of a finite field called the division property. It is then used [19] in an attack against the S7 S-box of the MISTY1 cipher. This paper provides a complete mathematical analysis of the division property. The tool we use is the discrete Fourier transform. We relate the division property to the natural concept of the degree of a subset of a finite field. This indeed provides a characterization of multisets satisfying the division property. In [18], the authors gave some properties related to the division property. In this paper we give a complete characterization and reprove many of their results. We show that the division property is actually the dual of the degree of t-products of the inverse S-box and show these two characteristics are affine invariants. We then propose a very efficient way to check vulnerability of a given Sbox against attacks of this type. We also reprove some recent interesting results using the method based on the ...
Faruk Göloglu, Vincent Rijmen, Qingju Wang
Added 03 Apr 2016
Updated 03 Apr 2016
Type Journal
Year 2016
Where IACR
Authors Faruk Göloglu, Vincent Rijmen, Qingju Wang
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