Under the assumption of unlimited computing power, is a private key collision truly impossible?

Imagine this scenario: a hacker trains a massive number of quantum AI models, attempting to brute-force and collide with a database. From a probability theory perspective, this is an impossible event—the collision probability of a 256-bit private key is far lower than the total number of atoms in the universe. But what if the computing power is truly infinite?

Of course, this is purely a theoretical hypothesis. In reality, what we need to do is recognize the nature of the risk.

**Why Multi-Signature is Essential for Large-Scale Funds**

Even if a quantum computer could actually find your private key (theoretically negligible probability), what about the probability of cracking three different private keys you hold? That’s an exponential level of difficulty. This is the power of multi-signature (Multisig)—it transforms single-point risk into distributed protection. For any large holdings, multi-signature is not optional.

**Time Locks Provide a Second Line of Defense**

Suppose the worst-case scenario occurs and a private key is compromised. If your transfer has a 24-hour time lock, that period is enough for you to transfer funds to a secure location using other private keys, emergency governance mechanisms, or community intervention. Time is protection.

**The Simple Logic of Whitelists**

Restrict funds to only transfer to pre-approved addresses. Even if a private key is compromised, the flow of funds remains locked within your approved targets.

The security of 256-bit encryption is not based on "impossibility," but on "the time and cost required are beyond imagination." In practical applications, we never rely on a single line of defense. Instead, we build a robust protection system through combinations like multi-signature, time locks, and whitelists.