### Abstract

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(mq^{maxǀUk1Xjǀ-k}) where m is the total number of equations, and U^{k} _{1}X_{j} 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 ǀU^{m} _{1}X_{j}ǀ of unknowns is equal to m, then the best achievable exponent is between c_{1}m and c_{2}m for some positive constants c_{1} and c_{2}.

Original language | English |
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Pages (from-to) | 175-185 |

Number of pages | 11 |

Journal | Designs, Codes, and Cryptography |

Volume | 75 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2015 |

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### Keywords

- Hypergraph ordering
- Sparse systems of Boolean equations

### ASJC Scopus subject areas

- Computer Science Applications
- Applied Mathematics

### Cite this

*Designs, Codes, and Cryptography*,

*75*(1), 175-185. https://doi.org/10.1007/s10623-013-9899-z