Antoine Joux is associate professor at Université de Versailles Saint-Quentin-en-Yvelines.
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.
1 A bird's-eye view of modern cryptography 3
2 Elementary number theory and algebra background 23
3 Linear algebra 71
4 Sieve algorithms 123
5 Brute force cryptanalysis 155
6 The birthday paradox: Sorting or not? 185
7 Birthday-based algorithms for functions 223
8 Birthday attacks through quadrisection 251
9 Fourier and Hadamard-Walsh transforms 273
10 Lattice reduction 309
11 Polynomial systems and Grabner base computations 337
12 Attacks on stream ciphers 373
13 Lattice-based cryptanalysis 397
14 Elliptic curves and pairings 417
15 Index calculus algorithms 439