9.1 Public Key Cryptography Principles

Public key cryptography revolutionized secure communication. It uses two keys: a public one for encryption and a private one for decryption. This system eliminates the need for secure key exchange, making it safer than symmetric encryption.

This section covers the math behind public key crypto, key management, and its many applications. From digital signatures to secure web browsing, public key cryptography is essential for modern online security and privacy.

Key Concepts

Fundamentals of Asymmetric Encryption

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• Asymmetric encryption uses two distinct keys for encryption and decryption
• Public key can be freely distributed and used by anyone to encrypt messages
• Private key remains secret and is used by the owner to decrypt messages
• Key pair consists of mathematically related public and private keys
• Provides stronger security compared to symmetric encryption, eliminating the need for secure key exchange

Mathematical Foundations

• One-way function forms the basis of asymmetric encryption algorithms
  • Easy to compute in one direction but computationally infeasible to reverse
  • Enables secure key generation and encryption processes
• Trapdoor function extends one-way function concept
  • Includes a secret "trapdoor" that allows easy computation of the inverse
  • Enables efficient decryption for the private key holder while maintaining security

Key Management and Security

• Public key can be widely distributed without compromising security
  • Often published in directories or shared through digital certificates
• Private key must be kept strictly confidential
  • Stored securely on the owner's device or in a hardware security module
• Key pair generation involves complex mathematical operations
  • Ensures the mathematical relationship between public and private keys
  • Utilizes prime numbers and modular arithmetic in many algorithms (RSA)

Applications

Secure Communication and Data Protection

• Digital signatures provide message integrity and authentication
  • Sender signs a message with their private key
  • Recipients verify the signature using the sender's public key
  • Ensures message hasn't been tampered with and confirms sender's identity
• Key exchange facilitates secure communication over insecure channels
  • Allows parties to establish a shared secret key without prior communication
  • Diffie-Hellman key exchange protocol commonly used for this purpose
• Confidentiality achieved through public key encryption
  • Sender encrypts message with recipient's public key
  • Only the intended recipient can decrypt using their private key

Authentication and Trust Mechanisms

• Non-repudiation prevents denial of message origin or content
  • Combines digital signatures with secure timestamping
  • Provides legal weight to electronic transactions and communications
• Authentication verifies the identity of communicating parties
  • Can be achieved through challenge-response protocols
  • Often combined with digital certificates for added trust
• Public Key Infrastructure (PKI) establishes trust in public keys
  • Utilizes Certificate Authorities to issue and manage digital certificates
  • Enables secure web browsing (HTTPS) and email encryption (S/MIME)

Advanced Applications and Protocols

• Secure Shell (SSH) uses public key cryptography for remote access
  • Provides encrypted terminal connections and secure file transfers
• Pretty Good Privacy (PGP) employs asymmetric encryption for email security
  • Combines public key cryptography with symmetric encryption for efficiency
• Blockchain technology relies on public key cryptography
  • Secures cryptocurrency transactions and maintains user anonymity
• Transport Layer Security (TLS) uses asymmetric encryption for initial handshake
  • Establishes secure connections for various internet protocols (HTTPS, FTPS)