🔒Cybersecurity and Cryptography Unit 9 – Asymmetric Cryptography and PKI

Key Concepts

• Asymmetric cryptography uses two different keys (public and private) for encryption and decryption
• Public key is freely distributed and used for encryption while private key is kept secret and used for decryption
• Relies on mathematical problems that are easy to compute in one direction but difficult to reverse (integer factorization, discrete logarithm)
• Enables secure communication and authentication without the need for a shared secret key
  • Eliminates the key distribution problem associated with symmetric cryptography
• Digital signatures provide authentication, non-repudiation, and integrity
  • Sender signs the message with their private key, and the recipient verifies using the sender's public key
• Key pairs are mathematically related but computationally infeasible to derive the private key from the public key

Historical Context

• Asymmetric cryptography developed in the 1970s to address limitations of symmetric cryptography
• Diffie-Hellman key exchange (1976) introduced the concept of public-key cryptography
  • Allowed two parties to establish a shared secret key over an insecure channel
• RSA algorithm (1977) was the first practical implementation of public-key cryptography
  • Named after its inventors Rivest, Shamir, and Adleman
• Elliptic Curve Cryptography (ECC) proposed in the mid-1980s
  • Offers similar security with smaller key sizes compared to RSA
• Development of PKI in the 1990s provided a framework for managing and distributing public keys
• Adoption of asymmetric cryptography increased with the growth of the internet and e-commerce

Types of Asymmetric Cryptography

• RSA (Rivest-Shamir-Adleman) is the most widely used asymmetric algorithm
  • Based on the difficulty of factoring large composite numbers
  • Typically uses key sizes of 1024, 2048, or 4096 bits
• Elliptic Curve Cryptography (ECC) is based on the algebraic structure of elliptic curves over finite fields
  • Provides similar security to RSA with smaller key sizes (256, 384, or 521 bits)
  • Gaining popularity due to its efficiency and suitability for resource-constrained devices
• Diffie-Hellman key exchange enables two parties to establish a shared secret key
  • Based on the discrete logarithm problem
  • Used in protocols like SSL/TLS for secure communication
• DSA (Digital Signature Algorithm) is a standard for digital signature generation and verification
  • Variant of the ElGamal signature scheme based on the discrete logarithm problem

Public Key Infrastructure (PKI)

• PKI is a framework for creating, managing, distributing, and revoking digital certificates
• Certificates bind public keys to identities and are issued by trusted Certificate Authorities (CAs)
  • Contain information such as the subject's name, public key, validity period, and the issuing CA's digital signature
• Hierarchical trust model with Root CAs at the top and intermediate CAs below
  • Enables scalability and delegation of trust
• Certificate Revocation Lists (CRLs) and Online Certificate Status Protocol (OCSP) provide mechanisms for checking the validity of certificates
• PKI enables secure communication, authentication, and non-repudiation in various applications (SSL/TLS, email, code signing)
• Relies on the security and trustworthiness of the CAs and the proper management of private keys

Algorithms and Protocols

• RSA algorithm involves key generation, encryption, and decryption steps
  • Key generation: select two large prime numbers, compute modulus and public/private key pair
  • Encryption: convert message to an integer, raise to the power of the public key, and compute modulo the modulus
  • Decryption: raise the ciphertext to the power of the private key and compute modulo the modulus
• Elliptic Curve Cryptography (ECC) operations are based on the arithmetic of elliptic curves over finite fields
  • Key generation: select a suitable elliptic curve and base point, generate public/private key pair
  • Encryption: map the message to a point on the curve, perform scalar multiplication with the recipient's public key
  • Decryption: perform scalar multiplication of the ciphertext with the private key to recover the original point
• SSL/TLS protocol uses asymmetric cryptography for key exchange and authentication
  • Diffie-Hellman key exchange or RSA key transport establishes a shared secret key
  • Server authentication using digital certificates signed by trusted CAs
  • Optional client authentication using client certificates
• S/MIME and PGP/GPG are email security protocols that use asymmetric cryptography for encryption and digital signatures
  • Provide confidentiality, authentication, and integrity for email communication

Real-World Applications

• SSL/TLS secures communication on the internet (HTTPS, secure email, VPNs)
  • Ensures confidentiality, integrity, and authentication between clients and servers
• Digital signatures are used for software and firmware verification
  • Code signing certificates issued by CAs to software developers
  • Enables users to verify the authenticity and integrity of the software
• Cryptocurrencies like Bitcoin and Ethereum use asymmetric cryptography for transaction signing and verification
  • Users have public/private key pairs associated with their wallet addresses
  • Transactions are signed with the sender's private key and verified using their public key
• Secure Shell (SSH) uses asymmetric cryptography for remote server authentication and key exchange
  • Server's public key is used to authenticate the server during the initial connection
  • Diffie-Hellman key exchange establishes a shared secret key for symmetric encryption
• Email security protocols (S/MIME, PGP/GPG) provide encryption and digital signatures for email communication
  • Sender encrypts the message using the recipient's public key
  • Sender signs the message with their private key for authentication and non-repudiation

Security Considerations

• Key management is critical for the security of asymmetric cryptography
  • Private keys must be kept secure and confidential
  • Compromise of a private key can lead to impersonation, decryption of past messages, and forged signatures
• Key sizes must be sufficiently large to resist cryptanalytic attacks
  • Recommended minimum key sizes: 2048 bits for RSA, 256 bits for ECC
  • Larger key sizes provide higher security but also increase computational overhead
• Proper implementation and use of cryptographic libraries and protocols are essential
  • Vulnerabilities in implementations can undermine the security of the system
  • Regular updates and patches are necessary to address discovered vulnerabilities
• Trust in the PKI and Certificate Authorities is crucial
  • Compromised or fraudulent CAs can issue false certificates and enable man-in-the-middle attacks
  • Strict validation and auditing of CAs are necessary to maintain the integrity of the PKI
• Quantum computing poses a potential threat to the security of some asymmetric algorithms (RSA, ECC)
  • Shor's algorithm could efficiently solve the integer factorization and discrete logarithm problems
  • Post-quantum cryptography is an active area of research to develop quantum-resistant algorithms

Future Trends

• Adoption of Elliptic Curve Cryptography (ECC) is increasing due to its efficiency and smaller key sizes
  • Suitable for resource-constrained devices and mobile applications
  • Gaining support in various protocols and standards (TLS, SSH, Bitcoin)
• Post-quantum cryptography is being developed to address the potential threat of quantum computing
  • Lattice-based, code-based, and multivariate cryptography are promising candidates
  • Standardization efforts by NIST and other organizations to select and standardize post-quantum algorithms
• Blockchain and decentralized PKI solutions are being explored to address the limitations of traditional PKI
  • Decentralized trust models and certificate transparency to reduce reliance on centralized CAs
  • Smart contracts and decentralized applications (dApps) leveraging asymmetric cryptography for secure transactions and authentication
• Integration of asymmetric cryptography with Internet of Things (IoT) devices and embedded systems
  • Lightweight cryptographic algorithms and protocols for resource-constrained environments
  • Secure firmware updates, device authentication, and data encryption in IoT ecosystems
• Advances in secure multi-party computation and homomorphic encryption
  • Enabling computation on encrypted data without revealing the underlying plaintext
  • Potential applications in privacy-preserving data analysis, machine learning, and secure cloud computing