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 ...

• Type: Journal
• Year: 2016
• Where: IACR
• Authors: Faruk Göloglu, Vincent Rijmen, Qingju Wang
• Keywords: Biometrics, IACR 2016