《計算數論與現代密碼學(英文版)(精)》（作者顏松遠）：數論和密碼學是兩個不同的學科，且分屬於不同的研究領域，而現代公鑰密碼體制的創立和應用則將這兩個不同的學科緊密地聯繫在一起。這是因為這些密碼體制的安全性幾乎**基於某些數論問題的難解性。比如極負盛譽的RSA密碼體制之所以難以破譯，就是因為整數分解問題難以快速解決。《計算數論與現代密碼學》可作為高等學校計算機、信息安全、電子與通信工程、數學等專業高年級本科生和研究生的教材，也可作為相關領域研究人員的參考書。

《計算數論與現代密碼學(英文版)(精)》（作者 顏松遠）首先從計算理論的觀點介紹數論中一些難解 性問題，如整數分解問題和離散對數問題（包括橢圓 曲線離散對數問題），然後討論基於這些難解性問題 的現代公鑰密碼體制，最後討論這些難解性問題的量 子計算方法以及這些密碼體制的量子攻擊方法：由於 量子計算僅適合於快速解決某些難解性數論問題（並 非所有難解性的數論及數學問題），因此還討論了某 些量子計算鞭長莫及的數學問題以及基於這些問題的 抗量子密碼體制。此外，《計算數論與現代密碼學( 英文版)(精)》還配有大量實例和練習，便於讀者學 習和掌握。

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