1 Introduction.- 2 Basic cryptosystems.- A Classical cryptology.- 3 The RSA cryptosystem.- B Key addition and modular arithmetic.- 4 Group cryptography and discrete logarithms.- 5 Elliptic curves.- C Breaking the unbreakable.- 6 Differential and linear cryptanalysis.- 7 Hash functions.- D Codebooks.- 8 Signatures.- 9 Security and reductions.- E Steganography.- 10 Identification and authentication.- F Transposition ciphers.- 11 Random generation.- G Some cryptographers.- 12 Proof systems and zero knowledge.- H People using cryptography.- 13 Integral lattices.- I The Zimmermann telegram.- 14 Quantum computation.- J Enigma, Turing, and Colossus.- 15 The computer algebra toolbox.- List of notation and sources of quotations, images, and ornaments.- Bibliography.- Index.