Speeding up deciphering by hypergraph ordering

Peter Horak, Zsolt Tuza

Research output: Contribution to journalArticle

3 Citations (Scopus)

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(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.

Original languageEnglish
Pages (from-to)175-185
Number of pages11
JournalDesigns, Codes, and Cryptography
Volume75
Issue number1
DOIs
Publication statusPublished - 2015

Fingerprint

Hypergraph
Gluing
Unknown
Linear equations
Exponent
Time-average
System of Linear Equations
Fast Algorithm
Galois field
Minimise

Keywords

  • Hypergraph ordering
  • Sparse systems of Boolean equations

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications

Cite this

Speeding up deciphering by hypergraph ordering. / Horak, Peter; Tuza, Zsolt.

In: Designs, Codes, and Cryptography, Vol. 75, No. 1, 2015, p. 175-185.

Research output: Contribution to journalArticle

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