Bivium as a Mixed Integer Programming Problem

Publication: Research - peer-reviewArticle in proceedings – Annual report year: 2009

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Trivium is a stream cipher proposed for the eSTREAM project. Raddum introduced some reduced versions of Trivium, named Bivium A and Bivium B. In this article we present a numerical attack on the Biviums. The main idea is to transform the problem of solving a sparse system of quadratic equations over $GF(2)$ into a combinatorial optimization problem. We convert the Boolean equation system into an equation system over $\mathbb{R}$ and formulate the problem of finding a $0$-$1$-valued solution for the system as a mixed-integer programming problem. This enables us to make use of several algorithms in the field of combinatorial optimization in order to find a solution for the problem and recover the initial state of Bivium. In particular this gives us an attack on Bivium B in estimated time complexity of $2^{63.7}$ seconds. But this kind of attack is also applicable to other cryptographic algorithms.
Original languageEnglish
Title of host publicationCryptography and Coding : 12th IMA International Conference, Cryptography and Coding 2009 Cirencester, UK, DEcenber 2009
EditorsMatthew G. Parker
PublisherSpringer
Publication date2009
Pages133-152
ISBN (print)978-3-642-10867-9
StatePublished

Conference

Conference12th IMA International Conference on Cryptography and Coding
Period01/01/09 → …
NameLecture Notes of Computer Science
Number5921
ISSN (Print)0302-9743
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