| Foreword Preface to the Second Edition Chapter Ⅰ. Some Topics in Elementary Number Theory 1. Time estimates for doing arithmetic 2. Divisibility and the Euclidean algorithm 3. Congruences 4. Some applications to factoring Chapter Ⅱ. Finite Fields and Quadratic Residues 1. Finite fields 2. Quadratic residues and reciprocity Chapter Ⅲ. Cryptography 1. Some simple cryptosystems 2. Enciphering matrices Chapter Ⅳ. Public Key 1. The idea of public key cryptography 2. RSA 3. Discrete log 4. Knapsack 5. Zero-knowledge protocols and oblivious transfer Chapter Ⅴ. Primality and Factoring 1. Pseudoprimes 2. The rho method 3. Fermat factorization and factor hases 4. The continued fraction method 5. The quadratic sieve method Chapter Ⅵ. Elliptic Curves 1. Basic facts 2. Elliptic curve cryptosystems 3. Elliptic curve primality test 4. Elliptic curve factorization Answers to Exercises Index |
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