Hi what is time for finding privatekey in range up to max 2**63 bit :
- BSGS
- pollard rho
and CPU vs GPU
do any of you have know good implementation?
This depends on all what your targeting/aiming for.
For 63 bits upwards it's always pollard that is faster by using GPU, and i assume also slightly by using CPU than BSGS.
BUT if you have multiple public keys and you want to target them all, then its definitely BSGS the way to go. BSGS searches all pubkeys at once by going sequential or random and it makes sure that it goes around all keys to check if the target key has been found, with Pollard, the whole search process restarts as soon as you find a public key searching for next one and unlike BSGS it's probabilistic.
With a normal CPU, you can solve 2^63 bits on average in 5 min using BSGS. With GPU Pollard, in less than 30 seconds on avg. CPU Pollard, on average 7 min. It depends on your hardware too!
Checkout the best Pollard and BSGS programs made by Alberto And JeanLuc.
Pollard by JeanLuc: https://github.com/JeanLucPons/Kangaroo
BSGS by Alberto: https://github.com/albertobsd/keyhunt