Thank you for the insightful responses. I’ll be looking into everything that’s been mentioned here. One point I’d like to clarify, though, is that in the protocol I’m working on, private key collisions are expected to be a regular occurrence. I understand this might seem unconventional.
In that case, the simplest way I can think of is to maintain a centralized database of all already generated private keys. This would allow you to check for collisions before assigning a new key, similar to how web applications verify the uniqueness of usernames or email addresses. However, this approach has its drawbacks. Even with encryption and security measures in place, there's always a risk of data breaches or unauthorized access.
Decentralized protocols like Bitcoin and Tor have successfully addressed this issue by eliminating the need for a central authority. They employ cryptographic techniques that make it virtually impossible for two private keys to collide, even with a massive number of keys in circulation. The probability of a collision is so low that it's considered negligible.