AuthorsB. Greve, Ø. Ytrehus, H. Raddum and G. Fløystad
TitleSolving non-linear Boolean equation systems by variable elimination
AfilliationCryptography
StatusPublished
Publication TypeJournal Article
Year of Publication2019
JournalApplicable Algebra in Engineering, Communication and Computing
Date PublishedAug
Publisher Springer
ISSN1432-0622
Abstract

In this paper we study Boolean equation systems, and how to eliminate variables from them while bounding the degree of polynomials produced. A procedure for variable elimination is introduced, and we relate the techniques to Gröbner bases and XL methods. We prove that by increasing the degree of the polynomials in the system by one for each variable eliminated, we preserve the solution space, provided that the system satisfies a particular condition. We then estimate how many variables we need to eliminate in order to solve the resulting system by re-linearization, and show that we get complexities lower than the trivial brute-force {\$}{\$}{\backslash}mathcal {\O{\}(2^n){\$}{\$}O(2n)when the system is overdetermined.

URLhttps://doi.org/10.1007/s00200-019-00399-7
DOI10.1007/s00200-019-00399-7
Citation KeyGreve2019