How can we be sure that monero wallet addresses are unique?

Question

This question is probably not necessarily limited to monero wallets, but I have been playing around with the Monero Offline Wallet Generator and wanted to know how anyone could ever be sure that a wallet address is unique? Specifically, say I create an offline wallet, and transfer some xmr into it. Is it possible that someone else could ever randomly generate an identical wallet address in the future? If so, wouldn't they have the spend keys to transfer the existing balance of that address once they see the existing balance and think "hot damn, free xmr"?

My brief research has not definitely answered this question, and I assume the answer is that it would be possible but so improbable as to be virtually impossible. I also assume that part of the address creation process involves using things local time when address is being created or other factors to create the initial parameters for creating the wallet addresses and keys, but just wanted to see if anyone more knowledgeable could provide a more clear answer.

Answer 1

Two people might independently generate the same address. As Matt2048 says, this is cryptographically negligible, assuming perfectly equiprobable distribution.

If someone else was to generate an address, they'd have to check whether there are any Monero on it though, and that isn't free. It can take about 20 minutes to scan the blockchain for a new address. However, that person could also not do so, but scan new blocks only, and would see any incoming funds. At that point, the address is known "live", and a full scan is warranted.

Local time is not used directly by the Monero offline address generator. The entropy comes either from the browser's Crypto API (cryptographically sound PRNG, which may or may not use local time), or user defined entropy (and the user is responsible for the amount of entropy supplied). The latter is to be used when a deterministic wallet is required, but the former is recommended.

Answer 2

The question should be answered here: Monero private key collision

TL;DR: There are 2^256 possible private spend keys, which would take 3.67×10^66 years to generate all of them at a rate of 1000 per second.

So while it is theoretically possible to have someone else generate the same key, as long as there is a large enough entropy pool for the random generation, you should be fine.