[Resource Topic] 2014/949: Simplification/complication of the basis of prime Boolean ideal

Welcome to the resource topic for 2014/949

Simplification/complication of the basis of prime Boolean ideal

Authors: Alexander Rostovtsev, Anna Shustrova


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.

ePrint: https://eprint.iacr.org/2014/949

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .