Table of contents
About this book
Introduction
Algebraic Cryptanalysis bridges the gap between a course in cryptography, and being able to read the cryptanalytic literature. This book is divided into three parts: Part One covers the process of turning a cipher into a system of equations; Part Two covers finite field linear algebra; Part Three covers the solution of Polynomial Systems of Equations, with a survey of the methods used in practice, including SATsolvers and the methods of Nicolas Courtois.
The cipher Keeloq, used in nearly all automobiles with remote keyless entry, is described as a running example, including the manipulation of the equations to enable their solution. The stream cipher Trivium, along with its variants BiviumA and BiviumB, and the stream cipher family QUAD are also analyzed as extensive examples, including summaries of several published attacks.
Additional topics include:
Analytic Combinatorics, and its application to cryptanalysis
The equicomplexity of linear algebra operations
Graph coloring
Factoring integers via the quadratic sieve, with its applications to the cryptanalysis of RSA
Algebraic Cryptanalysis is designed for advancedlevel students in computer science and mathematics as a secondary text or reference book for selfguided study. This book is particularly suitable for researchers in Applied Abstract Algebra or Algebraic Geometry who wish to find more applied topics, practitioners working for security and communications companies, or intelligence agencies.
Keywords
Bibliographic information
 Book Title Algebraic Cryptanalysis

Authors
Gregory Bard
 DOI https://doi.org/10.1007/9780387887579
 Copyright Information SpringerVerlag US 2009
 Publisher Name Springer, Boston, MA
 eBook Packages Computer Science Computer Science (R0)
 Hardcover ISBN 9780387887562
 Softcover ISBN 9781489984500
 eBook ISBN 9780387887579
 Edition Number 1
 Number of Pages XXXIII, 356
 Number of Illustrations 0 b/w illustrations, 0 illustrations in colour

Topics
Data Structures and Information Theory
Field Theory and Polynomials
Linear and Multilinear Algebras, Matrix Theory
Cryptology
Algebraic Geometry
Systems and Data Security
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Reviews
From the reviews:
“Algebraic cryptanalysis is a welltitled book. The theme is the reduction of attacks on ciphers (cryptosystems) to systems of polynomial equations over finite fields and subsequent heuristics for efficiently solving these systems. The book is written from the standpoint of realworld computational algebra, and contains numerous gems concerning details on how various algorithms and the heuristics using them really work. The book has an overall tripartite structure.” (Bruce Litow, ACM Computing Reviews, April, 2010)
“The book contains of 3 parts, each having 5 chapters, and 5 Appendices which describe codebreaking by solving equation systems. The author explains the mathematical background of the breaking method and exemplifies it on various ciphers. … The entire work is well structured having a good mathematical background. … recommended to graduate students who want to do their dissertation in any part of cryptanalysis. It is also useful to researchers in Applied Abstract Algebra, cryptography or any other area of these domains.” (Nicolae Constantinescu, Zentralblatt MATH, Vol. 1183, 2010)
“This book gives an overview of algebraic cryptanalysis. … the book seems to be the only broad treatise on the subject available. … it can show a graduate student where to look further … .” (Safuat Hamdy, Mathematical Reviews, Issue 2012 k)