Example of How a Filter Works:
We want to exclude private keys that contain triple repeating characters (e.g., “aaa”, “111”, etc.), because no valid Bitcoin private key from Puzzles 1-70 has had this pattern.
Without Filter:
• Generate Private Key
• Convert Private Key to Public Key (elliptic curve multiplication).
• Check Public Key: Convert to Bitcoin address, compare with target.
• If Invalid: Discard the result.
With Filter (Efficiency Gain):
• Generate Private Key
• Filter Check: Check if the private key contains any triple repeating characters.
• If the key fails the filter (e.g., contains “aaa” or “111”), skip the public key calculation.
• If the key passes the filter, proceed to the next step.
• Convert Private Key to Public Key (elliptic curve multiplication).
• Check Public Key: Convert to Bitcoin address, compare with target.
• If Invalid: Discard the result.
We need to update filter with every new private keys…
You only save the cost of EC multiplication and address conversion for filtered keys, but you still have to generate and scan every private key.
The global search space and thus the brute-force difficulty remains the same. Filtering helps a bit, but doesn’t make miracle.