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Illustrating the power of algorithms, Algorithmic Cryptanalysis describes algorithmic methods with cryptographically relevant examples. Focusing on both private- and public-key cryptographic algorithms, it presents each algorithm either as a textual description, in pseudo-code, or in a C code program.

Divided into three parts, the book begins with a short introduction to cryptography and a background chapter on elementary number theory and algebra. It then moves on to algorithms, with each chapter in this section dedicated to a single topic and often illustrated with simple cryptographic applications. The final part addresses more sophisticated cryptographic applications, including LFSR-based stream ciphers and index calculus methods.

Accounting for the impact of current computer architectures, this book explores the algorithmic and implementation aspects of cryptanalysis methods. It can serve as a handbook of algorithmic methods for cryptographers as well as a textbook for undergraduate and graduate courses on cryptanalysis and cryptography.

BACKGROUND A Bird's-Eye View of Modern Cryptography Preliminaries Defining security in cryptography Elementary Number Theory and Algebra Background Integers and rational numbers Greatest common divisors in Z Modular arithmetic Univariate polynomials and rational fractions Finite fields Vectors spaces and linear maps The RSA and Diffie-Hellman cryptosystems ALGORITHMS Linear Algebra Introductory example: multiplication of small matrices over F2 Dense matrix multiplication Gaussian elimination algorithms Sparse linear algebra Sieve Algorithms Introductory example: Eratosthenes's sieve Sieving for smooth composites Brute Force Cryptanalysis Introductory example: dictionary attacks Brute force and the DES algorithm Brute force as a security mechanism Brute force steps in advanced cryptanalysis Brute force and parallel computers The Birthday Paradox: Sorting or Not? Introductory example: birthday attacks on modes of operation Analysis of birthday paradox bounds Finding collisions Application to discrete logarithms in generic groups Birthday-Based Algorithms for Functions Algorithmic aspects Analysis of random functions Number theoretic applications A direct cryptographic application in the context of blockwise security Collisions in hash functions Hellman's time memory tradeoff Birthday Attacks through Quadrisection Introductory example: subset sum problems General setting for reduced memory birthday attacks Extensions of the technique Some direct applications Fourier and Hadamard-Walsh Transforms Introductory example: studying S-boxes Algebraic normal forms of boolean functions Goldreich-Levin theorem Generalization of the Walsh transform to Fp Fast Fourier transforms Lattice Reduction Definitions Introductory example: Gauss reduction Higher dimensions Shortest vectors and improved lattice reduction Dual and orthogonal lattices Polynomial Systems and Groebner Bases Computations General framework Bivariate systems of equations Definitions: multivariate ideals, monomial orderings, and Groebner bases Buchberger algorithm Macaulay's matrices Faugere's algorithms Algebraic attacks on multivariate cryptography On the complexity of Groebner bases computation APPLICATIONS Attacks on Stream Ciphers LFSR-based keystream generators Correlation attacks Algebraic attacks Extension to some nonlinear shift registers The cube attack Time memory data tradeoffs Lattice-Based Cryptanalysis Direct attacks using lattice reduction Coppersmith's small roots attacks Elliptic Curves and Pairings Introduction to elliptic curves The Weil pairing The elliptic curve factoring method Index Calculus Algorithms Introduction to index calculus A simple finite field example Generalization to finite fields with small enough characteristics Introduction to the number field sieve Smoothness probabilities References

Antoine Joux is associate professor at Universite de Versailles Saint-Quentin-en-Yvelines.

! very nice to see the connection between cryptography and the different algorithms. ! A convenient extra of the book are the good references. ! Algorithmic Cryptanalysis is a high level book that covers many interesting topics. I would recommend this book for graduate students with a strong mathematical background, a cryptographic background, knowledge in C-programming and an interest in implementing cryptanalytic attacks. As mentioned before, the book covers interesting topics when it comes to implementing an attack which I haven't seen in any other book before in this combination. ! --IACR Book Reviews, October 2010 ! The aim of the book is to survey work on cryptanalysis (both for symmetric and public key cryptography) and to present background on all major cryptanalytic tools. The author is a leading authority who has made major research contributions in most aspects of the subject. To have such a wide-ranging survey of the area written by someone with such depth of experience will be extremely valuable to students and researchers. ! Chapters 3, 4 and 15 give an excellent survey of index calculus algorithms for the discrete logarithm problem in finite fields ! the book will certainly be useful to postgraduates and researchers in cryptography and cryptanalysis. --Mathematical Reviews, Issue 2010h The book under review presents a complete panoramic of the different methods and techniques used in modern cryptanalysis ! emphasis is in the algorithms, in fact one of the main attractions of the book is the great quantity of algorithms that it presents: some described in pseudocode (listed as algorithms) and others as programs in C language (listed as programs). Additional C implementations can be downloaded from the website www.joux.biz/algcrypt ! --Zentralblatt MATH 1172 ! This book takes an algorithmic approach to the topic and covers a number of algorithms that might be used in the cryptanalysis of different systems. ! There is quite a bit of interesting material in the book ! The material is very well presented most of the time ! This book could be a very good introduction to cryptanalysis for graduate students who have already been introduced to cryptography and have a fair amount of mathematical background. The book could be used in an advanced undergraduate course as well ! It would also be quite an interesting read for those studying algorithms, as some of the algorithms presented are quite intriguing ! --Jeffrey Putnam, Computing Reviews, May 2010 This is a work suitable for first-year graduate students or advanced undergraduates. ! the addition of the online materials makes this book usable by independent readers or industry algorithm implementers in need of a reference work. ! Combining practical algorithms and supported by explanation of the relevant theory, this is a good introduction to cryptanalysis that improves on that good recipe by including key details on current computer architecture. This makes this work succeed as both handbook and textbook. --Tom Schulte, MAA Reviews, April 2010