Cryptography

10.

Advanced Cryptographic Concepts

10.1.

Post-Quantum Cryptography

10.1.1.

Quantum Computing Threat

10.1.1.1.

Shor's Algorithm

10.1.1.1.1.

Integer Factorization

10.1.1.1.2.

Discrete Logarithm Problem

10.1.1.1.3.

Impact on RSA and ECC

10.1.1.1.4.

Quantum Resource Requirements

10.1.1.2.

Grover's Algorithm

10.1.1.2.1.

Unstructured Search

10.1.1.2.2.

Impact on Symmetric Cryptography

10.1.1.2.3.

Quadratic Speedup

10.1.1.2.4.

Key Size Implications

10.1.2.

Post-Quantum Cryptographic Approaches

10.1.2.1.

Lattice-based Cryptography

10.1.2.1.1.

Learning With Errors Problem

10.1.2.1.2.

Ring Learning With Errors

10.1.2.1.3.

Module Learning With Errors

10.1.2.1.4.

NTRU Cryptosystem

10.1.2.1.5.

Key Exchange Mechanisms

10.1.2.1.6.

Digital Signatures

10.1.2.2.

Code-based Cryptography

10.1.2.2.1.

Error-Correcting Codes

10.1.2.2.2.

McEliece Cryptosystem

10.1.2.2.3.

Niederreiter Cryptosystem

10.1.2.2.4.

Syndrome Decoding Problem

10.1.2.3.

Multivariate Cryptography

10.1.2.3.1.

Multivariate Quadratic Equations

10.1.2.3.2.

Hidden Field Equations

10.1.2.3.3.

Oil and Vinegar Schemes

10.1.2.3.4.

Rainbow Signature Scheme

10.1.2.4.

Hash-based Cryptography

10.1.2.4.1.

Merkle Signature Schemes

10.1.2.4.2.

XMSS and XMSS^MT

10.1.2.4.3.

10.1.2.4.4.

Stateful vs. Stateless Signatures

10.1.2.5.

Isogeny-based Cryptography

10.1.2.5.1.

Supersingular Isogeny Graphs

10.1.2.5.2.

10.1.2.5.3.

Recent Cryptanalytic Developments

10.1.3.

NIST Post-Quantum Standardization

10.1.3.1.

Standardization Process

10.1.3.2.

Selected Algorithms

10.1.3.3.

Implementation Considerations

10.1.3.4.

Migration Strategies

10.2.

Quantum Cryptography

10.2.1.

Quantum Key Distribution

10.2.1.1.

10.2.1.1.1.

Quantum Bit Preparation

10.2.1.1.2.

Measurement Bases

10.2.1.1.3.

Error Detection

10.2.1.1.4.

Privacy Amplification

10.2.1.2.

10.2.1.3.

10.2.1.4.

Quantum Key Distribution Security

10.2.1.4.1.

Information-Theoretic Security

10.2.1.4.2.

Eavesdropping Detection

10.2.1.4.3.

Practical Limitations

10.2.2.

Quantum Random Number Generation

10.2.2.1.

Quantum Entropy Sources

10.2.2.2.

Measurement-based Generation

10.2.2.3.

Device-Independent Protocols

10.2.3.

Quantum Digital Signatures

10.2.3.1.

Quantum Signature Schemes

10.2.3.2.

Non-repudiation Properties

10.2.3.3.

Implementation Challenges

10.3.

Advanced Encryption Techniques

10.3.1.

Homomorphic Encryption

10.3.1.1.

Partially Homomorphic Encryption

10.3.1.1.1.

Additive Homomorphism

10.3.1.1.2.

Multiplicative Homomorphism

10.3.1.1.3.

RSA and ElGamal Properties

10.3.1.2.

Somewhat Homomorphic Encryption

10.3.1.2.1.

Limited Operations

10.3.1.2.2.

Noise Management

10.3.1.3.

Fully Homomorphic Encryption

10.3.1.3.1.

Gentry's Construction

10.3.1.3.2.

Bootstrapping Technique

10.3.1.3.3.

Lattice-based Schemes

10.3.1.3.4.

Performance Considerations

10.3.1.4.

10.3.1.4.1.

Cloud Computing

10.3.1.4.2.

Privacy-Preserving Computation

10.3.1.4.3.

Secure Outsourcing

10.3.2.

Functional Encryption

10.3.2.1.

Attribute-Based Encryption

10.3.2.1.1.

10.3.2.1.2.

Ciphertext-Policy ABE

10.3.2.1.3.

Access Structures

10.3.2.2.

Identity-Based Encryption

10.3.2.2.1.

Bilinear Pairings

10.3.2.2.2.

Key Escrow Issues

10.3.2.2.3.

Hierarchical IBE

10.3.2.3.

Predicate Encryption

10.3.2.3.1.

Inner Product Encryption

10.3.2.3.2.

10.3.3.

Searchable Encryption

10.3.3.1.

Symmetric Searchable Encryption

10.3.3.2.

Public Key Searchable Encryption

10.3.3.3.

Multi-keyword Search

10.3.3.4.

Privacy Considerations

10.4.

Zero-Knowledge Proofs

10.4.1.

Zero-Knowledge Proof Concepts

10.4.1.1.

10.4.1.2.

10.4.1.3.

Zero-Knowledge Property

10.4.2.

Interactive Zero-Knowledge Proofs

10.4.2.1.

Graph Isomorphism Protocol

10.4.2.2.

Commitment Schemes

10.4.2.3.

Challenge-Response Structure

10.4.3.

Non-Interactive Zero-Knowledge Proofs

10.4.3.1.

Common Reference String Model

10.4.3.2.

Random Oracle Model

10.4.3.3.

10.4.3.3.1.

Succinct Proofs

10.4.3.3.2.

Setup Requirements

10.4.3.3.3.

Applications in Blockchain

10.4.3.4.

10.4.3.4.1.

Transparent Setup

10.4.3.4.2.

Post-Quantum Security

10.4.3.4.3.

Scalability Properties

10.4.4.

10.4.4.1.

Authentication Systems

10.4.4.2.

Privacy-Preserving Protocols

10.4.4.3.

Blockchain Privacy

10.4.4.4.

Verifiable Computation

10.5.

Secure Multi-Party Computation

10.5.1.

Secret Sharing Schemes

10.5.1.1.

Shamir's Secret Sharing

10.5.1.1.1.

Polynomial Interpolation

10.5.1.1.2.

Threshold Properties

10.5.1.2.

Additive Secret Sharing

10.5.1.3.

Verifiable Secret Sharing

10.5.2.

Multi-Party Computation Protocols

10.5.2.1.

10.5.2.2.

10.5.2.3.

Garbled Circuits

10.5.2.3.1.

Circuit Garbling

10.5.2.3.2.

Oblivious Transfer

10.5.3.

10.5.3.1.

Private Set Intersection

10.5.3.2.

Secure Auctions

10.5.3.3.

Privacy-Preserving Statistics

10.5.4.

Security Models

10.5.4.1.

Semi-honest Adversaries

10.5.4.2.

Malicious Adversaries

10.5.4.3.

Covert Adversaries

10.6.

Blockchain and Cryptocurrency Cryptography

10.6.1.

Blockchain Fundamentals

10.6.1.1.

10.6.1.2.

10.6.1.2.1.

Binary Tree Structure

10.6.1.2.2.

Root Hash Computation

10.6.1.2.3.

Inclusion Proofs

10.6.1.3.

Block Structure

10.6.1.4.

Chain Integrity

10.6.2.

Consensus Mechanisms

10.6.2.1.

10.6.2.1.1.

Hash-based Puzzles

10.6.2.1.2.

Difficulty Adjustment

10.6.2.1.3.

10.6.2.1.4.

Energy Considerations

10.6.2.2.

10.6.2.2.1.

Validator Selection

10.6.2.2.2.

Slashing Conditions

10.6.2.2.3.

Nothing-at-Stake Problem

10.6.2.3.

Other Consensus Mechanisms

10.6.2.3.1.

Proof of Authority

10.6.2.3.2.

Delegated Proof of Stake

10.6.2.3.3.

Practical Byzantine Fault Tolerance

10.6.3.

Cryptocurrency Cryptography

10.6.3.1.

Digital Signatures in Transactions

10.6.3.1.1.

10.6.3.1.2.

Transaction Signing

10.6.3.1.3.

Multi-signature Transactions

10.6.3.2.

Address Generation

10.6.3.2.1.

Public Key Hashing

10.6.3.2.2.

Base58 Encoding

10.6.3.2.3.

Address Formats

10.6.3.3.

Privacy Enhancements

10.6.3.3.1.

Ring Signatures

10.6.3.3.2.

Stealth Addresses

10.6.3.3.3.

Zero-Knowledge Proofs

10.6.3.3.4.

Mixing Services

10.6.4.

Smart Contract Security

10.6.4.1.

Execution Environment Security

10.6.4.2.

Common Vulnerabilities

10.6.4.3.

Formal Verification

10.6.4.4.

Audit Practices

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9. Applied Cryptography and Security Protocols

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11. Cryptographic Standards and Compliance