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This question is inspired after reading How are ethereum addresses generated?

This is the section of interest

There are three main steps to get from private -> address:

  1. Create a random private key (64 (hex) characters / 256 bits / 32 bytes)
  2. Derive the public key from this private key (128 (hex) characters / 512 bits / 64 bytes)
  3. Derive the address from this public key. (40 (hex) characters / 160 bits / 20 bytes)

From this simplified explanation, it seems that if you create a random private key that someone previously generated, you would be able to gain access to their account. This is clearly not the case since many accounts have been created and I have never heard of this happening. So, what exactly am I missing here?

Aryan Jain
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Everything is about probably of collision to happen. Fast answer, no you can't find a collision by chance (an existing randomly generated private key) as the probability is far too small.

See this Reddit thread where people give some comparisons of the numbers and probability to find one by chance.

The entire cryptographic world, almost every robust cryptographic algorithm ever written in computer code, relies on pure chance to avoid key collisions. The key space is simply chosen to be large enough to make collisions unlikely before the heat death of the universe. But unlikely is not the same as impossible. It's not something I'm worried about at all but I've always found it fascinating.

An interesting non technical article for you could be https://www.wired.com/story/blockchain-bandit-ethereum-weak-private-keys/

the odds of guessing a randomly generated Ethereum private key is 1 in 115 quattuorvigintillion. (Or, as a fraction: 1/2256.) That denominator is very roughly around the number of atoms in the universe. Bednarek compares the task of identifying a random Ethereum key to choosing a grain of sand on a beach, and later asking a friend to find that same grain among a "billion gazillion" beaches.

But note that even not by chance, even if you try hard to find one, it would take you so much time that you would be dead long before even having as much chance to find one than for the entire humanity to find a winning lottery number at the same time.

Nicolas Massart
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    Thanks for the answer. This really puts things into perspective but unlike the above author, this does worry me. I rather not take an 1 in 115 quattuorvigintillion chance (albeit much lesser than that since thats the probability of guessing any ethereum wallet, not specifically mine) when it comes to my retirement savings.

    Anyhoo, I’d take this risk any day over the risk of staying in dollars and losing to inflation. Cheers

     – Aryan Jain Nov 25 '21 at 07:18
  • The risk is far far lower than having a car accident or just die instantly for no reason. The numbers are hard to figure because they are out of our usual range of numbers, even a billion is hard to think about. So here really, you can trust this maths. For info the maths you use every day with your credit card is far far less secure. And you don't think much about it. Only quantum computing could provide hope to find a collision. But in many years and we are working on resistant crypto already. If you should fear for your retirement it's about Inflation or crypto volatility. Not keys. – Nicolas Massart Nov 25 '21 at 10:08