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Cryptography for Secure Encryption 1st ed. 2022 [Kietas viršelis]

  • Formatas: Hardback, 319 pages, aukštis x plotis: 235x155 mm, weight: 739 g, 14 Tables, color; 15 Illustrations, color; 8 Illustrations, black and white; XII, 319 p. 23 illus., 15 illus. in color., 1 Hardback
  • Serija: Universitext
  • Išleidimo metai: 04-Jun-2022
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030979016
  • ISBN-13: 9783030979010
Kitos knygos pagal šią temą:
Cryptography for Secure Encryption 1st ed. 2022Didesnis paveikslėlis
  • Formatas: Hardback, 319 pages, aukštis x plotis: 235x155 mm, weight: 739 g, 14 Tables, color; 15 Illustrations, color; 8 Illustrations, black and white; XII, 319 p. 23 illus., 15 illus. in color., 1 Hardback
  • Serija: Universitext
  • Išleidimo metai: 04-Jun-2022
  • Leidėjas: Springer Nature Switzerland AG
  • ISBN-10: 3030979016
  • ISBN-13: 9783030979010
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783030979010.html
Raktažodžiai:
This text is intended for a one-semester course in cryptography at the advanced undergraduate/Master's degree level.  It is suitable for students from various STEM backgrounds, including engineering, mathematics, and computer science, and may also be attractive for researchers and professionals who want to learn the basics of cryptography. Advanced knowledge of computer science or mathematics (other than elementary programming skills) is not assumed. The book includes more material than can be covered in a single semester. The Preface provides a suggested outline for a single semester course, though instructors are encouraged to select their own topics to reflect their specific requirements and interests. Each chapter contains a set of carefully written exercises which prompts review of the material in the chapter and expands on the concepts.  Throughout the book, problems are stated mathematically, then algorithms are devised to solve the problems. Students are tasked to write computer programs (in C++ or GAP) to implement the algorithms.   The use of programming skills to solve practical problems adds extra value to the use of this text.





This book combines mathematical theory with practical applications to computer information systems. The fundamental concepts of classical and modern cryptography are discussed in relation to probability theory, complexity theory, modern algebra, and number theory.  An overarching theme is cyber security:  security of the cryptosystems and the key generation and distribution protocols, and methods of cryptanalysis (i.e., code breaking). It contains chapters on probability theory, information theory and entropy, complexity theory, and the algebraic and number theoretic foundations of cryptography.  The book then reviews symmetric key cryptosystems, and discusses one-way trap door functions and public key cryptosystems including RSA and  ElGamal.  It contains a chapter on digital signature schemes, including material on message authentication and forgeries, and chapters on key generation and distribution. It contains a chapter on elliptic curve cryptography, including new material on the relationship between singular curves, algebraic groups and Hopf algebras.  
1 Introduction to Cryptography
1(8)
1.1 Introduction to Cryptography
1(1)
1.2 The Players in the Game
2(2)
1.3 Ciphertext Only Attack: An Example
4(3)
1.4 Exercises
7(2)
2 Introduction to Probability
9(20)
2.1 Introduction to Probability
9(5)
2.1.1 Abstract Probability Spaces
11(3)
2.2 Conditional Probability
14(1)
2.3 Collision Theorems
15(4)
2.4 Random Variables
19(3)
2.5 2-Dimensional Random Variables
22(3)
2.6 Bernoulli's Theorem
25(1)
2.7 Exercises
26(3)
3 Information Theory and Entropy
29(24)
3.1 Entropy
29(6)
3.1.1 Entropy and Randomness: Jensen's Inequality
31(4)
3.2 Entropy of Plaintext English
35(5)
3.2.1 ASCII Encoding
39(1)
3.3 Joint and Conditional Entropy
40(4)
3.4 Unicity Distance
44(6)
3.5 Exercises
50(3)
4 Introduction to Complexity Theory
53(20)
4.1 Basics of Complexity Theory
53(1)
4.2 Polynomial Time Algorithms
54(4)
4.3 Non-polynomial Time Algorithms
58(3)
4.4 Complexity Classes P, PP, BPP
61(7)
4.4.1 Probabilistic Polynomial Time
62(4)
4.4.2 An Example
66(2)
4.5 Probabilistic Algorithms for Functions
68(1)
4.6 Exercises
69(4)
5 Algebraic Foundations: Groups
73(28)
5.1 Introduction to Groups
73(2)
5.2 Examples of Infinite Groups
75(2)
5.3 Examples of Finite Groups
77(7)
5.3.1 The Symmetric Group on n Letters
77(4)
5.3.2 The Group of Residues Modulo n
81(3)
5.4 Direct Product of Groups
84(1)
5.5 Subgroups
85(2)
5.6 Homomorphisms of Groups
87(1)
5.7 Group Structure
88(9)
5.7.1 Some Number Theory
92(5)
5.8 Exercises
97(4)
6 Algebraic Foundations: Rings and Fields
101(16)
6.1 Introduction to Rings and Fields
101(5)
6.1.1 Polynomials in F[ x]
104(2)
6.2 The Group of Units of Zn
106(4)
6.2.1 A Formula for Euler's Function
109(1)
6.3 U(ZP) Is Cyclic
110(1)
6.4 Exponentiation in Zn
111(5)
6.4.1 Quadratic Residues
112(4)
6.5 Exercises
116(1)
7 Advanced Topics in Algebra
117(22)
7.1 Quotient Rings and Ring Homomorphisms
117(9)
7.1.1 Quotient Rings
117(6)
7.1.2 Ring Homomorphisms
123(3)
7.2 Simple Algebraic Extensions
126(2)
7.2.1 Algebraic Closure
128(1)
7.3 Finite Fields
128(6)
7.4 Invertible Matrices over Zpq
134(2)
7.5 Exercises
136(3)
8 Symmetric Key Cryptography
139(34)
8.1 Simple Substitution Cryptosystems
140(3)
8.1.1 Unicity Distance of the Simple Substitution Cryptosy stem
142(1)
8.2 The Affine Cipher
143(2)
8.2.1 Unicity Distance of the Affine Cipher
145(1)
8.3 The Hill 2 × 2 Cipher
145(4)
8.3.1 Unicity Distance of the Hill 2 × 2 Cipher
148(1)
8.4 Cryptanalysis of the Simple Substitution Cryptosystem
149(6)
8.5 Polyalphabetic Cryptosystems
155(8)
8.5.1 The Vigenere Cipher
156(1)
8.5.2 Unicity Distance of the Vigenere Cipher
157(1)
8.5.3 Cryptanalysis of the Vigenere Cipher
157(3)
8.5.4 The Vernam Cipher
160(2)
8.5.5 Unicity Distance of the Vernam Cipher
162(1)
8.6 Stream Ciphers
163(1)
8.7 Block Ciphers
164(4)
8.7.1 Iterated Block Ciphers
165(3)
8.8 Exercises
168(5)
9 Public Key Cryptography
173(30)
9.1 Introduction to Public Key Cryptography
173(4)
9.1.1 Negligible Functions
174(1)
9.1.2 One-Way Trapdoor Functions
175(2)
9.2 The RSA Public Key Cryptosystem
177(3)
9.3 Security of RSA
180(13)
9.3.1 Pollard p --- 1
181(2)
9.3.2 Pollard ρ
183(4)
9.3.3 Difference of Two Squares
187(6)
9.4 The ElGamal Public Key Cryptosystem
193(3)
9.5 Hybrid Ciphers
196(1)
9.6 Symmetric vs. Public Key Cryptography
197(2)
9.7 Exercises
199(4)
10 Digital Signature Schemes
203(14)
10.1 Introduction to Digital Signature Schemes
203(2)
10.2 The RSA Digital Signature Scheme
205(2)
10.3 Signature with Privacy
207(1)
10.4 Security of Digital Signature Schemes
208(1)
10.5 Hash Functions and DSS
209(6)
10.5.1 The Discrete Log Family
210(2)
10.5.2 The MD-4 Family
212(2)
10.5.3 Hash-Then-Sign DSS
214(1)
10.6 Exercises
215(2)
11 Key Generation
217(38)
11.1 Linearly Recursive Sequences
217(9)
11.2 The Shrinking Generator Sequence
226(5)
11.3 Linear Complexity
231(4)
11.4 Pseudorandom Bit Generators
235(16)
11.4.1 Hard-Core Predicates
237(1)
11.4.2 Hard-Core Predicates and the DLA
238(4)
11.4.3 The Blum--Micali Bit Generator
242(3)
11.4.4 The Quadratic Residue Assumption
245(2)
11.4.5 The Blum--Blum--Shub Bit Generator
247(4)
11.5 Exercises
251(4)
12 Key Distribution
255(16)
12.1 The Diffie--Hellman Key Exchange Protocol
255(1)
12.2 The Discrete Logarithm Problem
256(12)
12.2.1 The General DLP
258(4)
12.2.2 Index Calculus
262(3)
12.2.3 Efficiency of Index Calculus
265(2)
12.2.4 The Man-in-the-Middle Attack
267(1)
12.3 Exercises
268(3)
13 Elliptic Curves in Cryptography
271(26)
13.1 The Equation y1 = x3 + ax + b
271(5)
13.2 Elliptic Curves
276(2)
13.3 Singular Curves
278(1)
13.4 The Elliptic Curve Group
279(8)
13.4.1 Structure of E(K)
285(2)
13.5 The Elliptic Curve Key Exchange Protocol
287(9)
13.5.1 Comparing ECKEP and DHKEP
289(1)
13.5.2 What Elliptic Curves to Avoid
290(2)
13.5.3 Examples of Good Curves
292(4)
13.6 Exercises
296(1)
14 Singular Curves
297(14)
14.1 The Group Ens(K)
297(4)
14.2 The DLP in EnS(K)
301(2)
14.3 The Group Gc(K)
303(3)
14.4 Ens(K) Gc(K)
306(3)
14.5 Exercises
309(2)
References 311(4)
Index 315
Robert G. Underwood is a Professor in both the Department of Mathematics and the Department of Computer Science in the College of Sciences at Auburn University at Montgomery.   His research in mathematics involves the classification of Hopf orders in group rings and the application of Hopf orders to Galois module theory.  His interests in Computer Science include cryptography and automata theory, specifically, algebraic generalizations of the Myhill-Nerode theorem.  Professor Underwood is the author of Fundamentals of Hopf Algebras and An Introduction to Hopf Algebras."