Cryptography

  1. Advanced Cryptographic Concepts
    1. Post-Quantum Cryptography
      1. Quantum Computing Threat
        1. Shor's Algorithm
          1. Integer Factorization
            1. Discrete Logarithm Problem
              1. Impact on RSA and ECC
                1. Quantum Resource Requirements
                2. Grover's Algorithm
                  1. Unstructured Search
                    1. Impact on Symmetric Cryptography
                      1. Quadratic Speedup
                        1. Key Size Implications
                      2. Post-Quantum Cryptographic Approaches
                        1. Lattice-based Cryptography
                          1. Learning With Errors Problem
                            1. Ring Learning With Errors
                              1. Module Learning With Errors
                                1. NTRU Cryptosystem
                                  1. Key Exchange Mechanisms
                                    1. Digital Signatures
                                    2. Code-based Cryptography
                                      1. Error-Correcting Codes
                                        1. McEliece Cryptosystem
                                          1. Niederreiter Cryptosystem
                                            1. Syndrome Decoding Problem
                                            2. Multivariate Cryptography
                                              1. Multivariate Quadratic Equations
                                                1. Hidden Field Equations
                                                  1. Oil and Vinegar Schemes
                                                    1. Rainbow Signature Scheme
                                                    2. Hash-based Cryptography
                                                      1. Merkle Signature Schemes
                                                        1. XMSS and XMSS^MT
                                                          1. SPHINCS Family
                                                            1. Stateful vs. Stateless Signatures
                                                            2. Isogeny-based Cryptography
                                                              1. Supersingular Isogeny Graphs
                                                                1. SIDH and SIKE
                                                                  1. Recent Cryptanalytic Developments
                                                                2. NIST Post-Quantum Standardization
                                                                  1. Standardization Process
                                                                    1. Selected Algorithms
                                                                      1. Implementation Considerations
                                                                        1. Migration Strategies
                                                                      2. Quantum Cryptography
                                                                        1. Quantum Key Distribution
                                                                          1. BB84 Protocol
                                                                            1. Quantum Bit Preparation
                                                                              1. Measurement Bases
                                                                                1. Error Detection
                                                                                  1. Privacy Amplification
                                                                                  2. B92 Protocol
                                                                                    1. E91 Protocol
                                                                                      1. Quantum Key Distribution Security
                                                                                        1. Information-Theoretic Security
                                                                                          1. Eavesdropping Detection
                                                                                            1. Practical Limitations
                                                                                          2. Quantum Random Number Generation
                                                                                            1. Quantum Entropy Sources
                                                                                              1. Measurement-based Generation
                                                                                                1. Device-Independent Protocols
                                                                                                2. Quantum Digital Signatures
                                                                                                  1. Quantum Signature Schemes
                                                                                                    1. Non-repudiation Properties
                                                                                                      1. Implementation Challenges
                                                                                                    2. Advanced Encryption Techniques
                                                                                                      1. Homomorphic Encryption
                                                                                                        1. Partially Homomorphic Encryption
                                                                                                          1. Additive Homomorphism
                                                                                                            1. Multiplicative Homomorphism
                                                                                                              1. RSA and ElGamal Properties
                                                                                                              2. Somewhat Homomorphic Encryption
                                                                                                                1. Limited Operations
                                                                                                                  1. Noise Management
                                                                                                                  2. Fully Homomorphic Encryption
                                                                                                                    1. Gentry's Construction
                                                                                                                      1. Bootstrapping Technique
                                                                                                                        1. Lattice-based Schemes
                                                                                                                          1. Performance Considerations
                                                                                                                          2. Applications
                                                                                                                            1. Cloud Computing
                                                                                                                              1. Privacy-Preserving Computation
                                                                                                                                1. Secure Outsourcing
                                                                                                                              2. Functional Encryption
                                                                                                                                1. Attribute-Based Encryption
                                                                                                                                  1. Key-Policy ABE
                                                                                                                                    1. Ciphertext-Policy ABE
                                                                                                                                      1. Access Structures
                                                                                                                                      2. Identity-Based Encryption
                                                                                                                                        1. Bilinear Pairings
                                                                                                                                          1. Key Escrow Issues
                                                                                                                                            1. Hierarchical IBE
                                                                                                                                            2. Predicate Encryption
                                                                                                                                              1. Inner Product Encryption
                                                                                                                                                1. Range Queries
                                                                                                                                              2. Searchable Encryption
                                                                                                                                                1. Symmetric Searchable Encryption
                                                                                                                                                  1. Public Key Searchable Encryption
                                                                                                                                                    1. Privacy Considerations
                                                                                                                                                  2. Zero-Knowledge Proofs
                                                                                                                                                    1. Zero-Knowledge Proof Concepts
                                                                                                                                                      1. Completeness
                                                                                                                                                        1. Soundness
                                                                                                                                                          1. Zero-Knowledge Property
                                                                                                                                                          2. Interactive Zero-Knowledge Proofs
                                                                                                                                                            1. Graph Isomorphism Protocol
                                                                                                                                                              1. Commitment Schemes
                                                                                                                                                                1. Challenge-Response Structure
                                                                                                                                                                2. Non-Interactive Zero-Knowledge Proofs
                                                                                                                                                                  1. Common Reference String Model
                                                                                                                                                                    1. Random Oracle Model
                                                                                                                                                                      1. zk-SNARKs
                                                                                                                                                                        1. Succinct Proofs
                                                                                                                                                                          1. Setup Requirements
                                                                                                                                                                            1. Applications in Blockchain
                                                                                                                                                                            2. zk-STARKs
                                                                                                                                                                              1. Transparent Setup
                                                                                                                                                                                1. Post-Quantum Security
                                                                                                                                                                                  1. Scalability Properties
                                                                                                                                                                                2. Applications
                                                                                                                                                                                  1. Authentication Systems
                                                                                                                                                                                    1. Privacy-Preserving Protocols
                                                                                                                                                                                      1. Blockchain Privacy
                                                                                                                                                                                        1. Verifiable Computation
                                                                                                                                                                                      2. Secure Multi-Party Computation
                                                                                                                                                                                        1. Secret Sharing Schemes
                                                                                                                                                                                          1. Shamir's Secret Sharing
                                                                                                                                                                                            1. Polynomial Interpolation
                                                                                                                                                                                              1. Threshold Properties
                                                                                                                                                                                              2. Additive Secret Sharing
                                                                                                                                                                                                1. Verifiable Secret Sharing
                                                                                                                                                                                                2. Multi-Party Computation Protocols
                                                                                                                                                                                                  1. BGW Protocol
                                                                                                                                                                                                    1. GMW Protocol
                                                                                                                                                                                                      1. Garbled Circuits
                                                                                                                                                                                                        1. Circuit Garbling
                                                                                                                                                                                                          1. Oblivious Transfer
                                                                                                                                                                                                        2. Applications
                                                                                                                                                                                                          1. Private Set Intersection
                                                                                                                                                                                                            1. Secure Auctions
                                                                                                                                                                                                              1. Privacy-Preserving Statistics
                                                                                                                                                                                                              2. Security Models
                                                                                                                                                                                                                1. Semi-honest Adversaries
                                                                                                                                                                                                                  1. Malicious Adversaries
                                                                                                                                                                                                                    1. Covert Adversaries
                                                                                                                                                                                                                  2. Blockchain and Cryptocurrency Cryptography
                                                                                                                                                                                                                    1. Blockchain Fundamentals
                                                                                                                                                                                                                      1. Hash Pointers
                                                                                                                                                                                                                        1. Merkle Trees
                                                                                                                                                                                                                          1. Binary Tree Structure
                                                                                                                                                                                                                            1. Root Hash Computation
                                                                                                                                                                                                                              1. Inclusion Proofs
                                                                                                                                                                                                                              2. Block Structure
                                                                                                                                                                                                                                1. Chain Integrity
                                                                                                                                                                                                                                2. Consensus Mechanisms
                                                                                                                                                                                                                                  1. Proof of Work
                                                                                                                                                                                                                                    1. Hash-based Puzzles
                                                                                                                                                                                                                                      1. Difficulty Adjustment
                                                                                                                                                                                                                                        1. Mining Process
                                                                                                                                                                                                                                          1. Energy Considerations
                                                                                                                                                                                                                                          2. Proof of Stake
                                                                                                                                                                                                                                            1. Validator Selection
                                                                                                                                                                                                                                              1. Slashing Conditions
                                                                                                                                                                                                                                                1. Nothing-at-Stake Problem
                                                                                                                                                                                                                                                2. Other Consensus Mechanisms
                                                                                                                                                                                                                                                  1. Proof of Authority
                                                                                                                                                                                                                                                    1. Delegated Proof of Stake
                                                                                                                                                                                                                                                      1. Practical Byzantine Fault Tolerance
                                                                                                                                                                                                                                                    2. Cryptocurrency Cryptography
                                                                                                                                                                                                                                                      1. Digital Signatures in Transactions
                                                                                                                                                                                                                                                        1. ECDSA Usage
                                                                                                                                                                                                                                                          1. Transaction Signing
                                                                                                                                                                                                                                                            1. Multi-signature Transactions
                                                                                                                                                                                                                                                            2. Address Generation
                                                                                                                                                                                                                                                              1. Public Key Hashing
                                                                                                                                                                                                                                                                1. Base58 Encoding
                                                                                                                                                                                                                                                                  1. Address Formats
                                                                                                                                                                                                                                                                  2. Privacy Enhancements
                                                                                                                                                                                                                                                                    1. Ring Signatures
                                                                                                                                                                                                                                                                      1. Stealth Addresses
                                                                                                                                                                                                                                                                        1. Zero-Knowledge Proofs
                                                                                                                                                                                                                                                                          1. Mixing Services
                                                                                                                                                                                                                                                                        2. Smart Contract Security
                                                                                                                                                                                                                                                                          1. Execution Environment Security
                                                                                                                                                                                                                                                                            1. Common Vulnerabilities
                                                                                                                                                                                                                                                                              1. Formal Verification
                                                                                                                                                                                                                                                                                1. Audit Practices

                                                                                                                                                                                                                                                                            Previous

                                                                                                                                                                                                                                                                            9. Applied Cryptography and Security Protocols

                                                                                                                                                                                                                                                                            Go to top

                                                                                                                                                                                                                                                                            Next

                                                                                                                                                                                                                                                                            11. Cryptographic Standards and Compliance