In this introductory textbook the author explains the key topics in cryptography. He takes a modern approach, where defining what is meant by "secure" is as important as creating something that achieves that goal, and security definitions are central to the discussion throughout.
The chapters in Part 1 offer a brief introduction to the mathematical foundations: modular arithmetic, groups, finite fields, and probability; primality testing and factoring; discrete logarithms; elliptic curves; and lattices. Part 2 of the book shows how historical ciphers were broken, thus motivating the design of modern cryptosystems since the 1960s; this part also includes a chapter on information-theoretic security. Part 3 covers the core aspects of modern cryptography: the definition of security; modern stream ciphers; block ciphers and modes of operation; hash functions, message authentication codes, and key derivation functions; the "naive" RSA algorithm; public key encryption and signature algorithms; cryptography based on computational complexity; and certificates, key transport and key agreement. Finally, Part 4 addresses advanced prot ocols, where the parties may have different or even conflicting security goals: secret sharing schemes; commitments and oblivious transfer; zero-knowledge proofs; and secure multi-party computation.
β¦ Table of Contents
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Modular Arithmetic, Groups, Finite Fields and Probability....Pages 3-25
Primality Testing and Factoring....Pages 27-50
Discrete Logarithms....Pages 51-66
Elliptic Curves....Pages 67-78
Lattices....Pages 79-93
Implementation Issues....Pages 95-115
Front Matter....Pages 117-117
Historical Ciphers....Pages 119-132
The Enigma Machine....Pages 133-161
Information-Theoretic Security....Pages 163-177
Historical Stream Ciphers....Pages 179-194
Front Matter....Pages 195-195
Defining Security....Pages 197-223
Modern Stream Ciphers....Pages 225-240
Block Ciphers and Modes of Operation....Pages 241-269
Hash Functions, Message Authentication Codes and Key Derivation Functions....Pages 271-294
The βNaiveβ RSA Algorithm....Pages 295-311
Public Key Encryption and Signature Algorithms....Pages 313-347
Cryptography Based on Really Hard Problems....Pages 349-367
Certificates, Key Transport and Key Agreement....Pages 369-399
Front Matter....Pages 401-401
Secret Sharing Schemes....Pages 403-416
Commitments and Oblivious Transfer....Pages 417-424
Front Matter....Pages 401-401
Zero-Knowledge Proofs....Pages 425-438
Secure Multi-party Computation....Pages 439-450
Back Matter....Pages 451-481
β¦ Subjects
Data Structures, Cryptology and Information Theory; Mathematics of Computing; Security Science and Technology; Discrete Mathematics