public key to private key using HASH TABLE (Pollard's kangaroo for SECPK1)

Question

I have done a little bit of research on HASH TABLE (Pollard's kangaroo for SECPK1) I was wondering if there is any way to extract the private key range using the public key or the public address..??

Answer 1

In secp256k1 there are 2²⁵⁶ possible keys. Pollard's kangaroo algorithm (and other known algorithms) run in time square root of the number of keys. So the algorithm would take ~2¹²⁸ steps. This is completely infeasible. Just as a comparison: Bitcoin's hashrate is 160M TH/s. That's 160 million * 1 billion hashes per second. Say all of bitcoin's miners would try to find one private key, at a rate of one attempt per hash. It would take them 67 trillion years. As a comparison, the universe has existed for less than 14 billion years. (Also bitcoin's hardware isn't set out to find private keys but let's ignore that).

Caveat: Quantum computers enable special algorithms to solve the discrete logarithm problem exponentially faster. If such a computer existed it could potentially find private keys within seconds. That being said, quantum computers are still far away from reaching this level of maturity and some doubt whether they ever will.