Computational number theory and modern cryptography
副标题：无
作 者：Song Y. Yan[编著]
分类号：
ISBN：9787040344714
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简介
《计算数论与现代密码学》：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。
目录
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
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
Computational number theory and modern cryptography
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