dc.contributor.author Schilling, Thorsten Ernst eng dc.contributor.author Zajac, Pavol eng dc.date.accessioned 2012-11-19T11:53:46Z dc.date.available 2012-11-19T11:53:46Z dc.date.issued 2012 eng dc.Published Tatra Mountains Mathematical Publications 45: 93–105 eng dc.identifier.uri https://hdl.handle.net/1956/6193 dc.description.abstract Many problems, including algebraic cryptanalysis, can be transformed to a problem of solving a (large) system of sparse Boolean equations. In this article we study 2 algorithms that can be used to remove some redundancy from such a system: Agreeing, and Syllogism method. Combined with appropriate guessing strategies, these methods can be used to solve the whole system of equations. We show that a phase transition occurs in the initial reduction of the randomly generated system of equations. When the number of (partial) solutions in each equation of the system is binomially distributed with probability of partial solution p, the number of partial solutions remaining after the initial reduction is very low for p’s below some threshold pt, on the other hand for p > pt the reduction only occurs with a quickly diminishing probability. en_US dc.language.iso eng eng dc.publisher Versita Open en_US dc.rights Attribution-NonCommercial-NoDerivs CC BY-NC-ND eng dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/ eng dc.subject Algebraic cryptanalysis eng dc.subject Agreeing eng dc.subject Boolean equations eng dc.subject SAT problem eng dc.title Phase Transition in a System of Random Sparse Boolean Equations en_US dc.type Chapter dc.type Peer reviewed dc.description.version acceptedVersion en_US dc.rights.holder Creative Commons Public License. en_US dc.identifier.doi https://doi.org/10.2478/v10127-010-0008-7
﻿

### This item appears in the following Collection(s)

Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivs CC BY-NC-ND