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· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 조합론
· ISBN : 9781466570269
· 쪽수 : 603쪽
· 출판일 : 2014-11-01
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Preface
I. Introduction and Classical Cryptography
Introduction
Cryptography and Modern Cryptography
The Setting of Private-Key Encryption
Historical Ciphers and Their Cryptanalysis
Principles of Modern Cryptography
Principle 1 ? Formal Definitions
Principle 2 ? Precise Assumptions
Principle 3 ? Proofs of Security
Provable Security and Real-World Security
References and Additional Reading
Exercises
Perfectly Secret Encryption
Definitions
The One-Time Pad
Limitations of Perfect Secrecy
Shannon’s Theorem
References and Additional Reading
Exercises
II. Private-Key (Symmetric) Cryptography
Private-Key Encryption
Computational Security
The Concrete Approach
The Asymptotic Approach
Defining Computationally Secure Encryption
The Basic Definition of Security
Semantic Security
Constructing Secure Encryption Schemes
Pseudorandom Generators and Stream Ciphers
Proofs by Reduction
A Secure Fixed-Length Encryption Scheme
Stronger Security Notions
Security for Multiple Encryptions
Chosen-Plaintext Attacks and CPA-Security
Constructing CPA-Secure Encryption Schemes
Pseudorandom Functions and Block Ciphers
CPA-Secure Encryption from Pseudorandom Functions
Modes of Operation
Stream-Cipher Modes of Operation
Block-Cipher Modes of Operation
Chosen-Ciphertext Attacks
Defining CCA-Security
Padding-Oracle Attacks
References and Additional Reading
Exercises
Message Authentication Codes
Message Integrity
Secrecy vs. Integrity
Encryption vs. Message Authentication
Message Authentication Codes ? Definitions
Constructing Secure Message Authentication Codes
A Fixed-Length MAC
Domain Extension for MACs
CBC-MAC
The Basic Construction
Proof of Security
Authenticated Encryption
Definitions
Generic Constructions
Secure Communication Sessions
CCA-Secure Encryption
Information-Theoretic MACs
Constructing Information-Theoretic MACs
Limitations on Information-Theoretic MACs
References and Additional Reading
Exercises
Hash Functions and Applications
Definitions
Collision Resistance
Weaker Notions of Security
Domain Extension: The Merkle?Damgard Transform
Message Authentication Using Hash Functions
Hash-and-MAC
HMAC
Generic Attacks on Hash Functions
Birthday Attacks for Finding Collisions
Small-Space Birthday Attacks
Time/Space Tradeoffs for Inverting Functions
The Random-Oracle Model
The Random-Oracle Model in Detail
Is the Random-Oracle Methodology Sound?
Additional Applications of Hash Functions
Fingerprinting and Deduplication
Merkle Trees
Password Hashing
Key Derivation
Commitment Schemes
References and Additional Reading
Exercises
Practical Constructions of Symmetric-Key Primitives
Stream Ciphers
Linear-Feedback Shift Registers
Adding Nonlinearity
Trivium
RC4
Block Ciphers
Substitution-Permutation Networks
Feistel Networks
DES ? The Data Encryption Standard
3DES: Increasing the Key Length of a Block Cipher
AES ? The Advanced Encryption Standard
Differential and Linear Cryptanalysis
Hash Functions
Hash Functions from Block Ciphers
MD5
SHA-0, SHA-1, and SHA-2
SHA-3 (Keccak)
References and Additional Reading
Exercises
Theoretical Constructions of Symmetric-Key Primitives
One-Way Functions
Definitions
Candidate One-Way Functions
Hard-Core Predicates
From One-Way Functions to Pseudorandomness
Hard-Core Predicates from One-Way Functions
A Simple Case
A More Involved Case
The Full Proof
Constructing Pseudorandom Generators
Pseudorandom Generators with Minimal Expansion
Increasing the Expansion Factor
Constructing Pseudorandom Functions
Constructing (Strong) Pseudorandom Permutations
Assumptions for Private-Key Cryptography
Computational Indistinguishability
References and Additional Reading
Exercises
III. Public-Key (Asymmetric) Cryptography
Number Theory and Cryptographic Hardness Assumptions
Preliminaries and Basic Group Theory
Primes and Divisibility
Modular Arithmetic
Groups
The Group ZN
Isomorphisms and the Chinese Remainder Theorem
Primes, Factoring, and RSA
Generating Random Primes
Primality Testing
The Factoring Assumption
The RSA Assumption
Relating the RSA and Factoring Assumptions
Cryptographic Assumptions in Cyclic Groups
Cyclic Groups and Generators
The Discrete-Logarithm/Diffie?Hellman Assumptions
Working in (Subgroups of) Zp
Elliptic Curves
Cryptographic Applications
One-Way Functions and Permutations
Constructing Collision-Resistant Hash Functions
References and Additional Reading
Exercises
Algorithms for Factoring and Computing Discrete Logarithms
Algorithms for Factoring
Pollard’s p ? 1 Algorithm
Pollard’s Rho Algorithm
The Quadratic Sieve Algorithm
Algorithms for Computing Discrete Logarithms
The Pohlig?Hellman Algorithm
The Baby-Step/Giant-Step Algorithm
Discrete Logarithms from Collisions
The Index Calculus Algorithm
Recommended Key Lengths
References and Additional Reading
Exercises
Key Management and the Public-Key Revolution
Key Distribution and Key Management
A Partial Solution: Key-Distribution Centers
Key Exchange and the Diffie?Hellman Protocol
The Public-Key Revolution
References and Additional Reading
Exercises
Public-Key Encryption
Public-Key Encryption ? An Overview
Definitions
Security against Chosen-Plaintext Attacks
Multiple Encryptions
Security against Chosen-Ciphertext Attacks
Hybrid Encryption and the KEM/DEM Paradigm
CPA-Security
CCA-Security
CDH/DDH-Based Encryption
El Gamal Encryption
DDH-Based Key Encapsulation
A CDH-Based KEM in the Random-Oracle Model
Chosen-Ciphertext Security and DHIES/ECIES
RSA Encryption
Plain RSA
Padded RSA and PKCS #1 v1.5
CPA-Secure Encryption without Random Oracles
OAEP and RSA PKCS #1 v
A CCA-Secure KEM in the Random-Oracle Model
RSA Implementation Issues and Pitfalls
References and Additional Reading
Exercises
Digital Signature Schemes
Digital Signatures ? An Overview
Definitions
The Hash-and-Sign Paradigm
RSA Signatures
Plain RSA
RSA-FDH and PKCS #1 v
Signatures from the Discrete-Logarithm Problem
The Schnorr Signature Scheme
DSA and ECDSA
Signatures from Hash Functions
Lamport’s Signature Scheme
Chain-Based Signatures
Tree-Based Signatures
Certificates and Public-Key Infrastructures
Putting It All Together ? SSL/TLS
Signcryption
References and Additional Reading
Exercises
Advanced Topics in Public-Key Encryption
Public-Key Encryption from Trapdoor Permutations
Trapdoor Permutations
Public-Key Encryption from Trapdoor Permutations
The Paillier Encryption Scheme
The Structure of ZN2
The Paillier Encryption Scheme
Homomorphic Encryption
Secret Sharing and Threshold Encryption
Secret Sharing
Verifiable Secret Sharing
Threshold Encryption and Electronic Voting
The Goldwasser?Micali Encryption Scheme
Quadratic Residues Modulo a Prime
Quadratic Residues Modulo a Composite
The Quadratic Residuosity Assumption
The Goldwasser?Micali Encryption Scheme
The Rabin Encryption Scheme
Computing Modular Square Roots
A Trapdoor Permutation Based on Factoring
The Rabin Encryption Scheme
References and Additional Reading
Exercises
Index of Common Notation
Appendix A: Mathematical Background
Identities and Inequalities
Asymptotic Notation
Basic Probability
The "Birthday" Problem
Finite Fields
Appendix B: Basic Algorithmic Number Theory
Integer Arithmetic
Basic Operations
The Euclidean and Extended Euclidean Algorithms
Modular Arithmetic
Basic Operations
Computing Modular Inverses
Modular Exponentiation
Montgomery Multiplication
Choosing a Uniform Group Element
Finding a Generator of a Cyclic Group
Group-Theoretic Background
Efficient Algorithms
References and Additional Reading
Exercises
References
Index
