Overview
This lecture introduces major asymmetric cryptography systems, focusing on RSA, DSA, Diffie-Hellman key exchange, and Elliptic Curve Cryptography (ECC), highlighting their mechanisms, uses, and security considerations.
RSA and DSA: Asymmetric Cryptographic Systems
- RSA is an early asymmetric cryptography system named after its inventors and released to the public in 2000.
- RSA involves key generation using two large, random prime numbers for secure encryption and decryption.
- DSA (Digital Signature Algorithm) is used for digital signatures, standard in US government encryption since 1991.
- DSA security depends on a random seed in the signing process; leakage or poor randomness can compromise the private key.
- Real-world example: In 2010, Sony's failure to randomize DSA signature values led to PlayStation 3 private key exposure and piracy.
Key Exchange Algorithms: Diffie-Hellman
- Asymmetric cryptography is commonly used to securely exchange symmetric keys.
- Diffie-Hellman (DH) is a key exchange algorithm where two parties create a shared secret over an unsecured channel.
- DH process: agree on a large public number, each choose a secret number, exchange calculated values, then compute a common secret.
- DH provides a way to establish shared secrets without revealing them to eavesdroppers.
- DH is not used for encryption but for key exchange, and it has been integrated into PKI systems.
Elliptic Curve Cryptography (ECC)
- ECC uses the mathematics of elliptic curves over finite fields to generate secure keys.
- Elliptic curves are described by equations like y² = x³ + ax + b and have unique properties such as horizontal symmetry.
- ECC enables strong security with smaller key sizes compared to traditional systems (e.g., 256-bit ECC ≈ 3072-bit RSA).
- ECC reduces the data required to store and transmit cryptographic keys.
- There are ECC versions of DH and DSA, called ECDH (Elliptic Curve Diffie-Hellman) and ECDSA (Elliptic Curve DSA).
- NIST and NSA endorse EC encryption, but the NSA notes potential vulnerability to future quantum computing attacks.
Key Terms & Definitions
- Asymmetric Cryptography — encryption using different keys for encryption (public) and decryption (private).
- RSA — an encryption system based on factoring large primes.
- DSA — a digital signature algorithm for signing and verifying messages.
- Diffie-Hellman (DH) — an algorithm for exchanging cryptographic keys securely.
- Elliptic Curve Cryptography (ECC) — encryption using the mathematical properties of elliptic curves for secure, efficient key generation.
- ECDH/ECDSA — elliptic curve versions of DH and DSA respectively.
Action Items / Next Steps
- Review the basic process of each asymmetric cryptography method discussed.
- Study example scenarios of RSA, DSA, and DH usage.
- Read about elliptic curve properties and why smaller key sizes are effective in ECC.