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Paper 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.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
block ciphersBoolean functionscryptanalysischaracteristic setGroebner basishash functionsvarieties
Contact author(s)
alexander rostovtsev @ ibks ftk spbstu ru
History
2014-11-19: received
Short URL
https://ia.cr/2014/949
License
Creative Commons Attribution
CC BY
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