Consider the ECDSA protocol, which is applied in different environments e.g. the Bitcoin system (for user addresses, and transaction signing).
What are the greatest threats in terms of algorithms that could solve the underlying discrete log problem for groups over elliptic curves? I found:
- General Number Field Sieve
- Pollard's Rho
(excluding quantum algorithms)
to be the most efficient. Are all of them able to solve the ECDLP and if so, what is their complexity (runtime)?