Algorithmic Cryptanalysis

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.

Table of Contents

Part I: Background
Chapter 1: A bird’s-eye view of modern cryptography
Chapter 2: Elementary number theory and algebra background

Part II: Algorithms
Chapter 3: Linear algebra
Chapter 4: Sieve algorithms
Chapter 5: Brute force cryptanalysis
Chapter 6: The birthday paradox: Sorting or not?
Chapter 7: Birthday-based algorithms for functions
Chapter 8: Birthday attacks through quadrisection
Chapter 9: Fourier and Hadamard-Walsh transforms
Chapter 10: Lattice reduction
Chapter 11: Polynomial systems and Gröbner base computations

Part III: Applications
Chapter 12: Attacks on stream ciphers
Chapter 13: Lattice-based cryptanalysis
Chapter 14: Elliptic curves and pairings
Chapter 15: Index calculus algorithms