Same seed being generated twice?

[buzzlight]

Please forgive me for the stupid question, the answer is probably obvious, but I need to build my confidence about cold storage.

I'm moving to cold storage with Electrum. However one thing occurred to me when the seed was generated on my offline computer. Even ever so unlikely, cannot Electrum provide the same 12 word seed to more than one individual?

I understand the chances being slim is an understatement, however it is possible isn't it? If that happens, a lucky person might end up with someone else's holdings... Again please forgive my ignorance and thanks for any advice.

[dabura667]

There is no way to 100% protect your Bitcoins.

As long as Bitcoin is based on ECDSA which is based on random numbers, there will always be a probability that someone generates the same key as you.

Electrum seeds are one in 346 trillion trillion trillion (rounded down thats 3 with 38 zeros)

[shorena]

There is no way to 100% protect your Bitcoins.

As long as Bitcoin is based on ECDSA which is based on random numbers, there will always be a probability that someone generates the same key as you.

Electrum seeds are one in 346 trillion trillion trillion (rounded down thats 3 with 38 zeros)

There is also the chance that all air molecules in your room spontaneously gather in the half that you are not in and you die. Do you worry about that? Maybe you should if you worry about ECDSA collisions, because it in the same ballpark of likelyhood. Its the ballpark of likelyhood where people get struck by lightning 13 days in a row and survive to tell the story how they won the lottery the week after.

IIRC electum uses this list[1] of 1626 words. Since there are 12 of them, so we are talking about 1626¹² ~ 3.41*10³⁸ different combinations. Bitcoin itself has 2¹⁶⁰ ~ 1.46 *10⁴⁸ different private keys. Which is way more secure than the seed, but it makes no difference. Even considering the birthday paradoxon[2], even if every machine on earth would generate nothing but new private keys (while we still somehow manage a working society) until the sun burns out a collision is very unlikely.


[1] https://raw.githubusercontent.com/spesmilo/electrum/master/lib/mnemonic.py
[2] https://en.wikipedia.org/wiki/Birthday_problem

[buzzlight]

Haha. Fantastic. Thanks for the peace of mind!

[jonald_fyookball]

you can always have TWO electrum wallets
That way, even if some astronomically improbable
event happens and someone generates the same
same seed, you still have the other wallet.

Also, Electrum uses key stretching to make
100,000 more difficult to try to brute force
the 128 bit seed.