Cryptography Systems Overview

Overview

This lecture covers key asymmetric cryptographic systems, their mechanisms, historical incidents, and the advantages of elliptic curve cryptography.

RSA is an early asymmetric cryptography system named after Ron Rivest, Adi Shamir, and Leonard Adleman.
RSA was patented in 1983 and released to public domain in 2000.
Key generation in RSA requires two large, unique, randomly chosen prime numbers.
RSA is used for encryption and decryption operations via public and private keys.

DSA is an asymmetric cryptography algorithm primarily used for signing and verifying data.
Patented in 1991 and adopted as a U.S. federal standard.
DSA's security relies on choosing a random seed value during signing.
If the random value or prime number is predictable or reused, private keys can be compromised.
Sony's failure to randomize the signing value in 2010 allowed hackers to recover their private key, enabling game piracy.

Asymmetric systems like RSA and DSA are commonly used for secure key exchange.
Diffie-Hellman (DH) is another key exchange algorithm allowing two parties to create a shared secret over an unsecure channel.
DH involves both parties agreeing on a public value and exchanging computed values based on their secret numbers.
The shared secret can be safely established without revealing private information.

ECC uses the algebraic properties of elliptic curves over finite fields to generate keys.
Elliptic curves have unique mathematical properties like horizontal symmetry and specific intersection points for lines.
ECC offers comparable security to traditional systems but with much smaller key sizes (e.g., 256-bit ECC ≈ 3072-bit RSA).
ECC variants include ECDH (Elliptic Curve Diffie-Hellman) and ECDSA (Elliptic Curve Digital Signature Algorithm).
NIST recommends ECC, and NSA authorizes its use for top secret data with 384-bit keys.
There are concerns that ECC could become vulnerable to quantum computing attacks.

RSA — Asymmetric cryptosystem using two large prime numbers for encryption and decryption.
DSA — Digital Signature Algorithm for authenticating data using asymmetric keys.
Diffie-Hellman (DH) — Algorithm for secure key exchange over unsecure channels.
Elliptic Curve Cryptography (ECC) — Public key system using elliptic curves for efficient and strong encryption.
ECDH — Elliptic Curve variant of the Diffie-Hellman key exchange.
ECDSA — Elliptic Curve variant of the Digital Signature Algorithm.

Review the differences between RSA, DSA, and ECC.
Understand the key exchange process in Diffie-Hellman.
Read about real-world cryptographic failures, such as Sony's PS3 signing incident.