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?
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q9f
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Alan Wunsche
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Related: http://ethereum.stackexchange.com/questions/4299/account-uniqueness-guaranteed – eth Nov 26 '16 at 09:08
4 Answers
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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.
nessence
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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 Apr 16 '18 at 01:47
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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.
bekah
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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. – Tjaden Hess Nov 26 '16 at 18:04
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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 Nov 26 '16 at 18:16
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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
linagee
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When the account is created, is there a check to see if any other transactions have used this address previously? – paulmorriss Feb 08 '16 at 13:17
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1@paulmorriss I couldn't find one, but it's possible I just missed something. – linagee Feb 08 '16 at 18:05
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Nope, if you create an account that points to an existing wallet then you can spend all the ETH that's in there – Marklar Jan 09 '18 at 09:07
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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
Steve
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