Strength of Public Keys
Elliptic curve / Lucas functions / some others
- Best (known) attacks O(sqrt(N))
- so need 256 bit keys to match 128 bit symmetric
Factoring/Discrete Log
- RSA, El Gamal, Diffie-Hellman, DSA
- Best (known): O(exp(log(N)**1/3 * log(log(N))**2/3))
- for 128 bit symmetric equivalent, need maybe 2048 bit keys or longer