🔐Cryptography Unit 4 – Public Key Cryptography

What's Public Key Cryptography?

• Cryptographic system that uses pairs of keys: public keys and private keys
• Enables secure communication and data transmission over unsecured channels (internet)
• Public key is widely distributed and used for encrypting messages
• Private key is kept secret by the owner and used for decrypting messages
• Eliminates the need for secure key exchange prior to communication
• Provides confidentiality, integrity, authentication, and non-repudiation
• Fundamental building block of modern secure communication protocols (SSL/TLS, SSH, PGP)

Key Concepts and Terminology

• Asymmetric cryptography: Uses two different keys for encryption and decryption
• Public key: Widely distributed key used for encrypting messages intended for the owner
  • Can be freely shared without compromising security
• Private key: Secret key used for decrypting messages encrypted with the corresponding public key
  • Must be kept secure and never shared
• Key pair: A public key and its corresponding private key
• Digital signatures: Used to verify the authenticity and integrity of messages
  • Created using the sender's private key
  • Verified using the sender's public key
• Cryptographic hash functions: Used to create fixed-size digests of messages (SHA-256, MD5)
  • Ensure data integrity and are used in digital signature schemes

How Public Key Cryptography Works

• Key generation: A key pair (public and private keys) is generated using mathematical algorithms
• Key distribution: The public key is freely distributed, while the private key is kept secret
• Encryption: The sender encrypts the message using the recipient's public key
  • Only the recipient's private key can decrypt the message
• Decryption: The recipient uses their private key to decrypt the message
• Digital signatures:
  • Signing: The sender creates a digital signature using their private key and the message hash
  • Verification: The recipient verifies the signature using the sender's public key and the message hash
• Key management: Proper storage, distribution, and revocation of keys is crucial for maintaining security

Popular Public Key Algorithms

• RSA (Rivest-Shamir-Adleman): Widely used algorithm based on the difficulty of factoring large numbers
  • Suitable for encryption and digital signatures
• Elliptic Curve Cryptography (ECC): Uses algebraic structure of elliptic curves over finite fields
  • Offers similar security to RSA with smaller key sizes
• Diffie-Hellman key exchange: Protocol for securely exchanging cryptographic keys over an unsecured channel
  • Used in conjunction with symmetric encryption for secure communication
• Digital Signature Algorithm (DSA): U.S. Federal Information Processing Standard for digital signatures
  • Variant of the ElGamal signature scheme

Real-World Applications

• Secure web communication: SSL/TLS protocols use public key cryptography for authentication and key exchange
• Email security: PGP and S/MIME use public key cryptography for encrypting and signing emails
• Secure shell (SSH): Uses public key cryptography for authentication and secure remote access
• Cryptocurrencies: Bitcoin and other cryptocurrencies rely on public key cryptography for transaction verification and wallet security
• Code signing: Ensures the authenticity and integrity of software distributions
• Smart card authentication: Uses public key cryptography for secure user identification and access control

Strengths and Weaknesses

• Strengths:
  • Eliminates the need for secure key exchange prior to communication
  • Enables secure communication over unsecured channels
  • Provides authentication, non-repudiation, and integrity through digital signatures
• Weaknesses:
  • Computationally intensive compared to symmetric key cryptography
  • Slower than symmetric key algorithms for encrypting large amounts of data
  • Key management can be complex, especially for large-scale deployments
  • Vulnerable to quantum computing attacks (Shor's algorithm)

Implementation Challenges

• Key management: Ensuring proper generation, distribution, storage, and revocation of keys
  • Public Key Infrastructure (PKI) is used to manage keys and digital certificates
• Certificate Authorities (CAs): Trusted third parties that issue and manage digital certificates
  • Verifying the identity of key owners and maintaining certificate revocation lists (CRLs)
• Interoperability: Ensuring compatibility between different implementations and platforms
• Performance: Optimizing algorithms and implementations for efficient computation
• Side-channel attacks: Protecting against attacks that exploit physical implementation weaknesses (timing, power consumption)

Future of Public Key Cryptography

• Post-quantum cryptography: Developing algorithms resistant to quantum computing attacks
  • Lattice-based, code-based, and multivariate cryptography are promising candidates
• Elliptic Curve Cryptography (ECC) adoption: Increasing use due to smaller key sizes and improved performance
• Blockchain and decentralized systems: Public key cryptography plays a crucial role in securing these emerging technologies
• Integration with Internet of Things (IoT) devices: Lightweight public key algorithms for resource-constrained devices
• Advancements in secure multi-party computation and homomorphic encryption
  • Enabling computation on encrypted data without revealing the underlying information