Mutant Gröbner Basis Algorithm
نویسندگان
چکیده
This paper explores how to use the concept of mutants in the computation of a Gröbner basis for polynomial equations. We compare our approach to the algorithm F4 of Faugère, and we perform experiments on polynomials system coming from multivariate public key cryptosystems in comparison with the experimental results from Magma implementation of F4. The experimental results demonstrate that the mutant strategy could indeed work better in the case of polynomial systems with underlying structures that could be fully exploited by the mutant strategy.
منابع مشابه
Gröbner-shirshov Basis for the Braid Semigroup
We found Gröbner-Shirshov basis for the braid semigroup B n+1. It gives a new algorithm for the solution of the word problem for the braid semigroup and so for the braid group.
متن کاملInvolutive Algorithms for Computing Gröbner Bases
In this paper we describe an efficient involutive algorithm for constructing Gröbner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain way. In the presented algorithm a reduced Gröbner basis is the internally fixed subset of an involutive basis, and having computed the later, the former can be...
متن کاملGröbner Basis and Indecomposable Modules over a like Dedekind Ring
Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.
متن کاملGröbner Bases Algorithm
Gröbner Bases is a technique that provides algorithmic solutions to a variety of problems in Commutative Algebra and Algebraic Geometry. In this introductory tutorial the basic algorithms as well as their generalization for computing Gröbner basis of a set of multivariate polynomials are presented. The Gröbner basis technique is applied to solve systems of polynomial equations in several variab...
متن کاملEfficient decoding of (binary) cyclic codes above the correction capacity of the code using Gröbner bases
This paper revisits the topic of decoding cyclic codes with Gröbner bases. We introduce new algebraic systems, for which the Gröbner basis computation is easier. We show that formal decoding formulas are too huge to be useful, and that the most efficient technique seems to be to recompute a Gröbner basis for each word (online decoding). We use new Gröbner basis algorithms and “trace preprocessi...
متن کامل