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Focusing on both private- and public-key cryptographic algorithms, this book describes algorithmic methods with cryptographically relevant examples. After introducing modern cryptography and elementary number theory and algebra, it covers linear algebra, sieving, brute force, algorithms based on the birthday paradox, Hadamard-Fourier-Walsh transforms, lattice reduction, and Gröbner bases. The author also presents advanced applications, such as LFSR-based stream ciphers, lattice methods for cryptanalysis, elliptic curves, and index calculus methods. He includes some hints and solutions to the exercises as well as C code on http://www.joux.biz/algcrypt