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內容簡介

　　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，而現代公鑰密碼體製的創立和應用則將這兩個不同的學科緊密地聯係在一起。這是因為這些密碼體製的安全性幾乎完全基於某些數論問題的難解性。比如極負盛譽的RSA密碼體製之所以難以破譯，就是因為整數分解問題難以快速解決。《信息安全係列：計算數論與現代密碼學（英文版）》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（包括橢圓麯綫離散對數問題），然後討論基於這些難解性問題的現代公鑰密碼體製，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製的量子攻擊方法：由於量子計算僅適閤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），因此還討論瞭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製。此外，書中還配有大量實例和練習，便於讀者學習和掌握。《信息安全係列：計算數論與現代密碼學（英文版）》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。

作者簡介

　　Song Y. Yan（顔鬆遠），江西吉安人。獲中國科學院研究生院理學碩士學位，並獲英國約剋大學數學博士學位。長期在國外大學從事計算數論、計算理論和密碼學等方麵的科研與教學工作，在Springer齣版專著4部：1.《Number Theory for Computing》第1版（2000年）、第2版（2002年）、波蘭文版（2006年，華沙國傢科技齣版社）、中文版（2007年，清華大學齣版社）；2.《Primality Testing and Integer Factorization in Public-Key Cryptography》第1版（2004年）、第2版（2009年）；3.《Cryptanalytic Attacks on RSA》第1版（2007年）、俄文版（2010年，莫斯科國傢科技齣版中心）；4.《Quantum Attacks on Public-Key Cryptosystems》第1版（2012年）。

內頁插圖

目錄

Part I preliminaries
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
……
Part IV Quantum resistant cryptography
Index

前言/序言

　　The book is about number theory and modem cryptography. More specically， it is about computational number theory and modem public-key cryptography based on number theory. It consists of four parts. The first part， consisting of two chapters， provides some preliminaries. Chapter 1 provides some basic concepts of number theory， computation theory， computational number theory， and modem public-key cryptography based on number theory. In chapter 2， a complete introduction to some basic concepts and results in abstract algebra and elementary number theory is given.
　　The second part is on computational number theory. There are three chapters in this part.Chapter 3 deals with algorithms for primality testing， with an emphasis on the Miller-Rabin test， the elliptic curve test， and the AKS test. Chapter 4 treats with algorithms for integer factorization， including the currently fastest factoring algorithm NFS （Number Field Sieve），and the elliptic curve factoring algorithm ECM （Elliptic Curve Method）. Chapter 5 discusses various modem algorithms for discrete logarithms and for elliptic curve discrete logarithms.It is well-known now that primality testing can be done in polynomial-time on a digital computer， however， integer factorization and discrete logarithms still cannot be performed in polynomial-time. From a computational complexity point of view， primality testing is feasible （tractable， easy） on a digital computer， whereas integer factorization and discrete logarithms are infeasible （intractable， hard， difficult）. Of course， no-one has yet been able to prove that the integer factorization and the discrete logarithm problems must be infeasible on a digital computer.
　　Building on the results in the first two parts， the third part of the book studies the modem cryptographic schemes and protocols whose security relies exactly on the infeasibility of the integer factorization and discrete logarithm problems. There are four chapters in this part.Chapter 6 presents some basic concepts and ideas of secret-key cryptography. Chapter 7 studies the integer factoring based public-key cryptography， including， among others， the most famous and widely used RSA cryptography， the Rabin cryptosystem， the probabilistic encryption and the zero-knowledge proof protocols. Chapter 8 studies the discrete logarithm based cryptography， including the DHM key-exchange protocol （the world's first public-key system）， the E1Gamal cryptosystem， and the US Government's Digital Signature Standard （DSS）， Chapter 9 discusses various cryptographic systems and digital signature schemes based on the infeasibility of the elliptic curve discrete logarithm problem， some of them are just the elliptic curve analogues of the ordinary public-key cryptography such as elliptic curve DHM， elliptic curve E1Gamal， elliptic curve RSA， and elliptic curve DSA/DSS.
信息安全係列：計算數論與現代密碼學（英文版） [Computational Number Theory and Modern Cryptography] 下載 mobi epub pdf txt 電子書

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