How do Ethereum clients, like Ethereum Wallet or Eth-Lightwallet, generate unique addresses that haven't been used before, and what is the likelihood that these addresses have been used?


4 Answers 4


The address is derived from a random private key. The client does not check if it has been previously used because the chance of that happening is nearly zero.

  • Well lets not forget the golden rule of Murphy law - what can happen - will happen or as he said "whatever can go wrong, will go wrong."
    – Tommixoft
    Commented Apr 16, 2018 at 1:47

I think the most important phrase in your question is 'what is the likelihood'.

The other answers are correct in determining that there is a 1 in 2^160 likelihood of finding a collision with 100% probability.

Due to the birthday paradox, cryptographers give a hash function with output bitlength 160 a bitwise security rating of 80. This is because with 2^80 addresses, it is more likely than not (i.e the probability is over 50%) that you will have an address collision.

For visual comparison with the above answers, the birthday problem implies a collision will occur with probability 1 in 1,208,925,819,614,629,174,706,176, yikes.

  • What the birthday problem says is that if you generate addresses using 2^80 random seeds, the chance of some pair of generated addresses being the same is ~50%. That's different than saying that if you generate a new address the chance that it will have been used before is 1 in 2^80. The correct probability is 1 in 2^160 times the number of addresses that have already been generated. Commented Nov 26, 2016 at 18:04
  • Ah yeah I get the distinction, I guess interpreted the question as more 'when are we likely to get an address collision' and less 'what is the likelihood that each new address generation (starting from 0 addresses) will result in a collision'.
    – bekah
    Commented Nov 26, 2016 at 18:16

Ethereum Wallet (the official wallet that will use Mist) uses web3.personal.newAccount to create an account. This is a web3.js call that does the equivalent of geth account new.

The address space in Ethereum is a 20-byte value (160-bit address space, same as Bitcoin).

what is the likelihood that these addresses have been used?

2^160 or about 1 in 1,461,501,637,330,902,918,203,684,832,716,283,019,655,932,542,976

  • When the account is created, is there a check to see if any other transactions have used this address previously? Commented Feb 8, 2016 at 13:17
  • 1
    @paulmorriss I couldn't find one, but it's possible I just missed something.
    – linagee
    Commented Feb 8, 2016 at 18:05
  • Nope, if you create an account that points to an existing wallet then you can spend all the ETH that's in there
    – Marklar
    Commented Jan 9, 2018 at 9:07

Ethereum uses addresses that are 160 bits long. The chance that any one address is the same as any other given address is therefore 1 in 2^160. However, due to the birthday paradox the chance that a new Ethereum address is the same as any already existing Ethereum address rises exponentially with every new Ethereum address and is calculated as following:

Number of possible pairs: (number of unique Ethereum addresses + 1 / number of unique Ethereum addresses) = ((4,807,984 + 1) * 4,807,984) / 2 = 11,558,357,476,120

Chance of a unique pair: ((2^160)-1) / 2^160) = 0.999999999999999999999999999999999999999999999999315772234

Chance of 11,558,357,476,120 unique pairs = 0.999999999999999999999999999999999999999999999999315772234 ^ 11,558,357,476,120 = 0.999999999999999999999999999999999992091451

Chance of some match = 1 - 0.999999999999999999999999999999999992091451 = 7.908549 × 10^-36

As of today (26 Jul 2017) the chance of a new Ethereum address being the same as an already existing Ethereum address is ~8 × 10^-36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.