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Mathematical Foundations of Public Key Cryptography [Kõva köide]

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, , (University of Wisconsin-Milwaukee, USA),
  • Formaat: Hardback, 236 pages, kõrgus x laius: 234x156 mm, kaal: 476 g
  • Ilmumisaeg: 21-Oct-2015
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1498702236
  • ISBN-13: 9781498702232
Teised raamatud teemal:
Mathematical Foundations of Public Key CryptographySuurem pilt
  • Formaat: Hardback, 236 pages, kõrgus x laius: 234x156 mm, kaal: 476 g
  • Ilmumisaeg: 21-Oct-2015
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1498702236
  • ISBN-13: 9781498702232
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781498702232.html
Märksõnad:
In Mathematical Foundations of Public Key Cryptography, the authors integrate the results of more than 20 years of research and teaching experience to help students bridge the gap between math theory and crypto practice. The book provides a theoretical structure of fundamental number theory and algebra knowledge supporting public-key cryptography.

Rather than simply combining number theory and modern algebra, this textbook features the interdisciplinary characteristics of cryptographyrevealing the integrations of mathematical theories and public-key cryptographic applications. Incorporating the complexity theory of algorithms throughout, it introduces the basic number theoretic and algebraic algorithms and their complexities to provide a preliminary understanding of the applications of mathematical theories in cryptographic algorithms.

Supplying a seamless integration of cryptography and mathematics, the book includes coverage of elementary number theory; algebraic structure and attributes of group, ring, and field; cryptography-related computing complexity and basic algorithms, as well as lattice and fundamental methods of lattice cryptanalysis.

The text consists of 11 chapters. Basic theory and tools of elementary number theory, such as congruences, primitive roots, residue classes, and continued fractions, are covered in Chapters 1-6. The basic concepts of abstract algebra are introduced in Chapters 7-9, where three basic algebraic structures of groups, rings, and fields and their properties are explained.

Chapter 10 is about computational complexities of several related mathematical algorithms, and hard problems such as integer factorization and discrete logarithm. Chapter 11 presents the basics of lattice theory and the lattice basis reduction algorithmthe LLL algorithm and its application in the cryptanalysis of the RSA algorithm.

Containing a number of exercises on key algorithms, the book is suitable for use as a textbook for undergraduate students and first-year graduate students in information security programs. It is also an ideal reference book for cryptography professionals looking to master public-key cryptography.
Foreword ix
Preface xi
Acknowledgments xv
Chapter 1 Divisibility of Integers
1(26)
1.1 The Concept Of Divisibility
1(5)
1.2 The Greatest Common Divisor And The Least Common Multiple
6(6)
1.3 The Euclidean Algorithm
12(4)
1.4 Solving Linear Diophantine Equations
16(2)
1.5 Prime Factorization Of Integers
18(9)
Chapter 2 Congruences
27(20)
2.1 Congruences
27(4)
2.2 Residue Classes And Systems Of Residues
31(6)
2.3 Euler's Theorem
37(3)
2.4 Wilson's Theorem
40(7)
Chapter 3 Congruence Equations
47(24)
3.1 Basic Concepts Of Congruences Of High Degrees
47(3)
3.2 Linear Congruences
50(2)
3.3 Systems Of Linear Congruence Equations And The Chinese Remainder Theorem
52(3)
3.4 General Congruence Equations
55(2)
3.5 Quadratic Residues
57(4)
3.6 The Legendre Symbol And The Jacobi Symbol
61(10)
Chapter 4 Exponents and Primitive Roots
71(20)
4.1 Exponents And Their Properties
71(5)
4.2 Primitive Roots And Their Properties
76(3)
4.3 Indices, Construction Of Reduced System Of Residues
79(6)
4.4 Nth Power Residues
85(6)
Chapter 5 Some Elementary Results for Prime Distribution
91(18)
5.1 Introduction To The Basic Properties Of Primes And The Main Results Of Prime Number Distribution
91(4)
5.2 Proof Of The Euler Product Formula
95(2)
5.3 Proof Of A Weaker Version Of The Prime Number Theorem
97(8)
5.4 Equivalent Statements Of The Prime Number Theorem
105(4)
Chapter 6 Simple Continued Fractions
109(12)
6.1 Simple Continued Fractions And Their Basic Properties
109(4)
6.2 Simple Continued Fraction Representations Of Real Numbers
113(5)
6.3 Application Of Continued Fraction In Cryptography---Attack To RSA With Small Decryption Exponents
118(3)
Chapter 7 Basic Concepts
121(12)
7.1 MAPS
121(4)
7.2 Algebraic Operations
125(3)
7.3 Homomorphisms And Isomorphisms Between Sets With Operations
128(1)
7.4 Equivalence Relations And Partitions
129(4)
Chapter 8 Group Theory
133(18)
8.1 Definitions
133(2)
8.2 Cyclic Groups
135(2)
8.3 Subgroups And Cosets
137(4)
8.4 Fundamental Homomorphism Theorem
141(5)
8.5 Concrete Examples Of Finite Groups
146(5)
Chapter 9 Rings and Fields
151(26)
9.1 Definition Of A Ring
151(3)
9.2 Integral Domains, Fields, And Division Rings
154(5)
9.3 Subrings, Ideals, And Ring Homomorphisms
159(6)
9.4 Chinese Remainder Theorem
165(3)
9.5 Euclidean Rings
168(2)
9.6 Finite Fields
170(2)
9.7 Field Of Fractions
172(5)
Chapter 10 Some Mathematical Problems in Public Key Cryptography
177(18)
10.1 Time Estimation And Complexity Of Algorithms
177(7)
10.2 Integer Factorization Problem
184(1)
10.3 Primality Tests
185(3)
10.4 The RSA Problem And The Strong RSA Problem
188(1)
10.5 Quadratic Residues
189(3)
10.6 The Discrete Logarithm Problem
192(3)
Chapter 11 Basics of Lattices
195(12)
11.1 Basic Concepts
195(1)
11.2 Shortest Vector Problem
196(1)
11.3 Lattice Basis Reduction Algorithm
197(3)
11.4 Applications Of LLL Algorithm
200(7)
References 207(2)
Further Reading 209(2)
Index 211
Dr. Xiaoyun Wang is a professor at the Institute of Advanced Study, Tsinghua University, China. She is also the director of the Center for Cryptology Study at Tsinghua University and an adjunct professor in the Key Lab of Cryptographic Technology and Information Security at Shandong University, China.

Dr. Guangwu Xu is an associate professor in the Department of Electrical Engineering and Computer Science, University of Wisconsin-Milwaukee. Dr. Xus research concerns the efficiency, security, and reliability of information processing. He is interested in the fundamental problems of these aspects.







Dr. Mingqiang Wang

earned his PhD degree in 2004 from Shandong University, China where he serves as a professor now. Dr. Wang is a member of the Chinese Association for Cryptologic Research, his research focuses on number theory and analysis and design of public key algorithms. Dr. Xianmeng Meng

earned her bachelor's and master's degrees from Jilin University in 1993 and 1996 respectively, then graduated with a PhD degree from Shandong University, China. She is a member of the Chinese Association for Cryptologic Research and is currently a professor in Shandong University of Finance and Economics, her main research interest is number theory and cryptography.