本书是一部讲述数论的密码学应用的研究生教材。该书是《数论与密码学教程》的第2版，它是在第一版的基础上修订而成的。书中增加了零知识的证明和不经意传输，平方筛因子分解方法，椭圆曲线在素性检验中的应用，概率加密术，hash 函数等一些新内容。全书共分6个章节，具体内容包括基础数论浅述，有限域和二次剩余，密码学，公共密钥，素性和因式分解和椭圆曲线密码学。该书可供各大专院校作为教材使用，也可供从事相关工作的人员作为参考用书使用。

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