Cryptology ePrint Archive: Report 2014/949

Simplification/complication of the basis of prime Boolean ideal

Alexander Rostovtsev and Anna Shustrova

Abstract: Prime Boolean ideal has the basis of the form (x1 + e1, ..., xn + en) that consists of linear binomials. Its variety consists of the point (e1, ..., en). Complication of the basis is changing the simple linear binomials by non-linear polynomials in such a way, that the variety of ideal stays fixed. Simplification of the basis is obtaining the basis that consists of linear binomials from the complicated one that keeps its variety. Since any ideal is a module over the ring of Boolean polynomials, the change of the basis is uniquely determined by invertible matrix over the ring. Algorithms for invertible simplifying and complicating the basis of Boolean ideal that fixes the size of basis are proposed. Algorithm of simplification optimizes the choose of pairs of polynomials during the Groebner basis computation, and eliminates variables without using resultants.

Category / Keywords: secret-key cryptography / block ciphers, Boolean functions, cryptanalysis, characteristic set, Groebner basis, hash functions, varieties

Date: received 19 Nov 2014

Contact author: alexander rostovtsev at ibks ftk spbstu ru

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Version: 20141119:111810 (All versions of this report)

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