《计算数论与现代密码学(英文版)(精)》（作者颜松远）：数论和密码学是两个不同的学科，且分属于不同的研究领域，而现代公钥密码体制的创立和应用则将这两个不同的学科紧密地联系在一起。这是因为这些密码体制的安全性几乎完全基于某些数论问题的难解性。比如极负盛誉的RSA密码体制之所以难以破译，就是因为整数分解问题难以快速解决。《计算数论与现代密码学》可作为高等学校计算机、信息安全、电子与通信工程、数学等专业高年级本科生和研究生的教材，也可作为相关领域研究人员的参考书。

《计算数论与现代密码学(英文版)(精)》（作者颜松远）首先从计算理论的观点介绍数论中一些难解性问题，如整数分解问题和离散对数问题（包括椭圆曲线离散对数问题），然后讨论基于这些难解性问题的现代公钥密码体制，最后讨论这些难解性问题的量子计算方法以及这些密码体制的量子攻击方法：由于量子计算仅适合于快速解决某些难解性数论问题（并非所有难解性的数论及数学问题），因此还讨论了某些量子计算鞭长莫及的数学问题以及基于这些问题的抗量子密码体制。此外，《计算数论与现代密码学(英文版)(精)》还配有大量实例和练习，便于读者学习和掌握。

PartⅠpreliminaries

1 introduction

1.1 what is number theory?

1.2 what is computation theory?

1.3 what is computational number theory?

1.4 what is modern cryptography?

1.5 bibliographic notes and further reading

References

2 fundamentals

2.1 basic algebraic structures

2.2 divisibility theory

2.3 arithmetic functions

2.4 congruence theory

2.5 primitive roots

2.6 elliptic curves

2.7 bibliographic notes and further reading

References

Part Ⅱ computational number theory

3 primality testing

3.1 basic tests

3.2 miller-rabin test

3.3 elliptic curve tests

3.4 aks test

3.5 bibliographic notes and further reading

References

4 integer factorization

4.1 basic concepts

4.2 trial divisions factoring

4.3 p and p - 1 methods

4.4 elliptic curve method

4.5 continued fraction method

4.6 quadratic sieve

4.7 number field sieve

4.8 bibliographic notes and further reading

References

5 discrete logarithms

5.1 basic concepts

5.2 baby-step giant-step method

5.3 pohlig-hellman method

5.4 index calculus

5.5 elliptic curve discrete logarithms

5.6 bibliographic notes and further reading

References

Part Ⅲ modern cryptography

6secret-key cryptography

6.1 cryptography and cryptanalysis

6.2 Classic secret-key cryptography

6.3 Modern secret-key cryptography

6.4 bibliographic notes and further reading

References

7 integer factorization based cryptography

7.1 RSA cryptography

7.2 Cryptanalysis of RSA

7.3 Rabin cryptography

7.4 Residuosity based cryptography

7.5 zero-knowledge proof

7.6 bibliographic notes and further reading

References

8 discrete logarithm based cryptography

8.1 Diffie-Hellman-Merkle key-exchange protocol

8.2 e1gamal cryptography

8.3 Massey-Omura cryptography

8.4 DLP-based digital signatures

8.5 bibliographic notes and further reading

References

Elliptic Curve Discrete Logarithm Based Cryptography

9.1 Basic Ideas

9.2 Elliptic Curve Diffie-Hellman-Merkle Key Exchange Scheme

9.3 Elliptic Curve Massey-Omura Cryptography

9.4 Elliptic Curve EIGamal Cryptography

9.5 Elliptic Curve RSA Cryptosystem

9.6 Menezes-Vanstone Elliptic Curve Cryptography

9.7 Elliptic Curve DSA

9.8 Bibliographic Notes and Further Reading

References

Part Ⅳ Quantum Resistant Cryptography

10 Quantum Computational Number Theory

10.1 Quantum Algorithms for Order Finding

10.2 Quantum Algorithms for Integer Factorization

10.3 Quantum Algorithms for Discrete Logarithms

10.4 Quantum Algorithms for Elliptic Curve Discrete Logarithms

10.5 Bibliographic Notes and Further Reading

References

11 Quantum Resistant Cryptography

11.1 Coding-Based Cryptography

11.2 Lattice-Based Cryptography

11.3 Quantum Cryptography

11.4 DNA Biological Cryptography

11.5 Bibliographic Notes and Further Reading

References

Index