Cryptography

5.

Cryptographic Hash Functions

5.1.

Hash Function Properties

5.1.1.

Deterministic Output

5.1.2.

Fixed Output Length

5.1.3.

Efficient Computation

5.1.4.

Pre-image Resistance

5.1.4.1.

One-way Property

5.1.4.2.

Computational Requirements

5.1.5.

Second Pre-image Resistance

5.1.5.1.

Weak Collision Resistance

5.1.5.2.

Target Collision Resistance

5.1.6.

Collision Resistance

5.1.6.1.

Strong Collision Resistance

5.1.6.2.

Birthday Paradox

5.1.6.3.

Security Implications

5.1.7.

Avalanche Effect

5.1.7.1.

Sensitivity to Input Changes

5.1.7.2.

Output Distribution

5.1.8.

Pseudorandomness

5.1.8.1.

Statistical Properties

5.1.8.2.

Distinguishability

5.2.

Hash Function Constructions

5.2.1.

Merkle-Damgård Construction

5.2.1.1.

Compression Function

5.2.1.2.

Message Padding

5.2.1.3.

Length Encoding

5.2.1.4.

Iteration Process

5.2.1.5.

Length Extension Attacks

5.2.1.6.

Strengthening Techniques

5.2.2.

Sponge Construction

5.2.2.1.

Absorbing Phase

5.2.2.2.

Squeezing Phase

5.2.2.3.

Rate and Capacity

5.2.2.4.

Security Analysis

5.2.2.5.

Resistance to Generic Attacks

5.2.3.

Wide Pipe Construction

5.2.3.1.

Internal State Size

5.2.3.2.

Security Benefits

5.2.4.

HAIFA Construction

5.2.4.1.

Salt and Counter Integration

5.2.4.2.

Length Extension Prevention

5.3.

Hash Function Families

5.3.1.

5.3.1.1.

5.3.1.1.1.

Design Principles

5.3.1.1.2.

Security Weaknesses

5.3.1.2.

5.3.1.2.1.

Algorithm Description

5.3.1.2.2.

Collision Attacks

5.3.1.2.3.

5.3.2.

5.3.2.1.

5.3.2.1.1.

Original Design

5.3.2.1.2.

Withdrawal Reasons

5.3.2.2.

5.3.2.2.1.

Algorithm Structure

5.3.2.2.2.

Security Analysis

5.3.2.2.3.

Collision Attacks

5.3.2.2.4.

Deprecation Timeline

5.3.2.3.

5.3.2.3.1.

5.3.2.3.2.

5.3.2.3.3.

5.3.2.3.4.

5.3.2.3.5.

5.3.2.3.6.

5.3.2.3.7.

Algorithm Differences

5.3.2.3.8.

Security Status

5.3.2.4.

5.3.2.4.1.

Keccak Algorithm

5.3.2.4.2.

Sponge Construction

5.3.2.4.3.

5.3.2.4.4.

5.3.2.4.5.

5.3.2.4.6.

5.3.2.4.7.

5.3.2.4.8.

5.3.3.

Other Hash Functions

5.3.3.1.

5.3.3.2.

5.3.3.3.

5.3.3.4.

5.4.

Specialized Hash Functions

5.4.1.

Password Hashing Functions

5.4.1.1.

5.4.1.1.1.

Iteration Count

5.4.1.1.2.

5.4.1.1.3.

5.4.1.2.

5.4.1.2.1.

Blowfish Integration

5.4.1.2.2.

5.4.1.2.3.

Salt Generation

5.4.1.3.

5.4.1.3.1.

Memory-Hard Function

5.4.1.3.2.

5.4.1.3.3.

ASIC Resistance

5.4.1.4.

5.4.1.4.1.

5.4.1.4.2.

5.4.1.4.3.

5.4.1.4.4.

Parameter Selection

5.4.2.

Key Derivation Functions

5.4.2.1.

5.4.2.1.1.

Extract and Expand

5.4.2.1.2.

Salt and Info Parameters

5.4.2.2.

PBKDF2 Applications

5.4.2.3.

Concatenation KDF

5.4.3.

Message Authentication Codes

5.4.3.1.

HMAC Construction

5.4.3.1.1.

Inner and Outer Padding

5.4.3.1.2.

Security Analysis

5.4.3.1.3.

Key Length Considerations

5.4.3.2.

CMAC Construction

5.4.3.2.1.

Block Cipher Integration

5.4.3.2.2.

Subkey Generation

5.4.3.3.

5.4.3.3.1.

GCM Integration

5.4.3.3.2.

Galois Field Operations

5.5.

Hash Function Applications

5.5.1.

Data Integrity Verification

5.5.1.1.

5.5.1.2.

Digital Forensics

5.5.1.3.

Software Distribution

5.5.2.

Password Storage

5.5.2.1.

Salting Techniques

5.5.2.2.

Rainbow Table Prevention

5.5.2.3.

5.5.3.

Digital Signatures

5.5.3.1.

Hash-and-Sign Paradigm

5.5.3.2.

Message Digest Creation

5.5.4.

5.5.4.1.

Blockchain Applications

5.5.4.2.

Mining Difficulty

5.5.5.

Random Oracle Model

5.5.5.1.

Theoretical Framework

5.5.5.2.

Security Proofs

5.5.6.

Commitment Schemes

5.5.6.1.

Hiding Property

5.5.6.2.

Binding Property

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6. Message Authentication and Integrity