The “ Gluing Algorithm” of Semaev (Des. Codes Cryptogr. 49:47–60, 2008)-that finds all solutions of a sparse system of linear equations over the Galois field GF(q)-has average running time O(mqmaxǀUk1Xjǀ-k) where m is the total number of equations, and Uk 1Xj is the set of all unknowns actively occurring in the first k equations. In order to make the implementation of the algorithm faster, our goal here is to minimize the exponent of q in the case where every equation contains at most three unknowns. The main result states that if the total number ǀUm 1Xjǀ of unknowns is equal to m, then the best achievable exponent is between c1m and c2m for some positive constants c1 and c2.
- Hypergraph ordering
- Sparse systems of Boolean equations
ASJC Scopus subject areas
- Computer Science Applications
- Applied Mathematics