In order to use the Bitcoin network, a wallet is needed. It can take the form of an application on a computer or phone, or that of a hardware wallet such as the Ledger Wallet Nano S. By the decentralized nature of the Bitcoin network, or most cryptocurrencies, the addresses that control the funds are not registered anywhere: you cannot register an address as your own property with any organization or bank.
So how do wallets determine if an address belongs to you?
They simply draw them at random. This means, of course, that two different Bitcoin wallets could theoretically generate the same address, and that the two owners could then spend the same funds. Shocking? Yes, but you will be told that such an event is unlikely to happen. Let’s examine together the probability for such an event to happen.
The total number of possible Bitcoin addresses is 2^160. By performing statistical calculations, it is possible to determine the probability that two wallets will randomly generate the same address. For mathematical details, please refer to this article.
We can therefore conclude the following: the probability of having a 99.9999% chance of having an address collision, ie. your wallet randomly generating the same address as another is one in 6.35.10^24. But such a large figure is relatively difficult to conceptualize.
What does it match to?
Let’s try to evaluate the size of such a figure through an analogy. Imagine that you have a computer capable of generating 400,000 Bitcoin addresses per second, which already requires significant computing power.
Start the computer, and go for a walk. For example, complete the Tour of France (6397 km), walking at a normal pace of 4 km/h. Once you have finished your walk, say hello to a random person, and start your walk again. Once you have said hello to 66 million inhabitants, and completed the Tour de France each time, visit one of the 36,000 French municipalities.
Now repeat your tours of France, your greetings to each inhabitant, and when you have finished visiting all of the French municipalities, you will probably have generated a Bitcoin address collision with your computer.
The computer in question would then need 10 million billion of hard drives to store such a large amount of data. Unfortunately, here is the bad news: there is no guarantee that the address on which you generated a collision contains bitcoins: at present, only 10 million addresses have been used on the network.
The probability of generating a collision on an address containing bitcoins is therefore much lower, and it is highly likely that the Earth would have disappeared well before you finish your tours of France.
Conclusion: Don’t worry
All this is simply to say that one should not worry about the possibility that an address collision is generated by two different wallets. The creator of the Bitcoin network has devised a particularly well-adapted system, which, through decentralization, ensures that everyone has the opportunity to use the network without having to register the addresses of their wallets with anyone, and this without fear that two people will ever use the same address.