Quantum Cryptography and Post-Quantum Cryptography

Quantum Cryptography and Post-Quantum Cryptography represent two distinct approaches to securing information in the era of quantum computing. Quantum Cryptography, such as Quantum Key Distribution (QKD), utilizes the principles of quantum mechanics to create provably secure communication channels where any attempt to eavesdrop is immediately detectable due to the disturbance of the quantum state. In contrast, Post-Quantum Cryptography (PQC), or quantum-resistant cryptography, involves the development of new classical algorithms that can run on conventional computers but are mathematically designed to be secure against attacks from both classical and future quantum computers, ensuring the long-term security of data against the threat of quantum code-breaking.

1. Foundations of Modern Cryptography
   1. Classical Cryptography Fundamentals
      1. Symmetric-Key Cryptography
         1. Definition and Basic Principles
         2. Block Ciphers
            1. Structure and Operation
            2. Advanced Encryption Standard (AES)
            3. Data Encryption Standard (DES)
            4. Triple DES (3DES)
            5. Modes of Operation
               1. Electronic Codebook (ECB)
               2. Cipher Block Chaining (CBC)
               3. Counter (CTR)
               4. Galois/Counter Mode (GCM)
               5. Output Feedback (OFB)
               6. Cipher Feedback (CFB)
         3. Stream Ciphers
            1. Structure and Operation
            2. RC4 Algorithm
            3. Salsa20 and ChaCha20
            4. Linear Feedback Shift Registers
         4. Key Distribution Problem
            1. Challenges in Secure Key Exchange
            2. Historical Solutions
            3. Trusted Third Party Approaches
      2. Asymmetric-Key Cryptography
         1. Definition and Basic Principles
         2. Key Pairs
            1. Public Key Properties
            2. Private Key Properties
            3. Key Generation Algorithms
            4. Key Management Practices
         3. RSA Cryptosystem
            1. Mathematical Foundation
            2. Key Generation Process
            3. Encryption and Decryption
            4. Security Analysis
         4. Elliptic Curve Cryptography
            1. Mathematical Foundation
            2. Elliptic Curve Operations
            3. Key Generation
            4. Encryption and Decryption
         5. Digital Signatures
            1. Signing Process
            2. Verification Process
            3. RSA Signatures
            4. DSA and ECDSA
            5. Authentication Properties
            6. Integrity Properties
         6. Key Exchange Protocols
            1. Diffie-Hellman Key Exchange
            2. Elliptic Curve Diffie-Hellman
            3. Security Considerations
            4. Man-in-the-Middle Vulnerabilities
      3. Cryptographic Hash Functions
         1. Properties
            1. Preimage Resistance
            2. Second Preimage Resistance
            3. Collision Resistance
         2. SHA-2 Family
         3. SHA-3 Family
         4. MD5 and SHA-1 Vulnerabilities
         5. Applications
            1. Data Integrity Verification
            2. Digital Signature Support
            3. Password Hashing
            4. Merkle Trees
      4. Security Assumptions in Classical Cryptography
         1. Integer Factorization Problem
            1. Mathematical Definition
            2. Role in RSA Security
            3. Computational Complexity
            4. Best Known Classical Algorithms
         2. Discrete Logarithm Problem
            1. Mathematical Definition
            2. Role in Diffie-Hellman Security
            3. Role in DSA Security
            4. Computational Complexity
         3. Elliptic Curve Discrete Logarithm Problem
            1. Mathematical Definition
            2. Role in ECC Security
            3. Computational Complexity
            4. Advantages over Standard DLP