Quadratic Relations for S-Boxes: Their Minimum Representations and Bounds

Authors:
Routo Terada;Paulo G. Pinheiro
Affiliations:
-;-
Venue:
ISC '01 Proceedings of the 4th International Conference on Information Security
Year:
2001

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Abstract

We introduce polynomial approximations and consider the particular case of quadratic approximations. We establish an isomorphism between the set of quadratic Boolean functions and graphs. As its consequence, we can reduce problems involvingquadratic Boolean functions into problems with graphs and vice-versa. We present the problem of findinga minimum representation of quadratic functions, and prove bounds on the number of terms and variables. With these bounds, we were able to find quadratic relations with the highest probabilities for SERPENT and CRYPTON, former AES candidates.