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 Author Topic: There are 2^256 private keys out there: how big is that number?  (Read 691 times)
pooya87
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 January 08, 2020, 05:24:54 AMMerited by fillippone (2)

Now, in Bitcoin, I'm thinking of a number between one and 2^160 (in fact, it's a little less, but let's not delve into technical details too much).
there is a tiny mistake here. that "number" that we choose in bitcoin (aka private key) is between 1 and a little less than 2256 then that number is "converted" and "compressed" using one way operations to a smaller size (2160).
It's actually a little more complicated than that.
There is (AFAIK) no really good answer to how many "guesses" we're talking about in this "game".
There are indeed 2^256 private keys (or slightly less), but they translate to a "mere" 2^160 addresses.
More than one private key translates to one address, but it's not as simple as saying "x private keys translate to one address".
that's a different topic though.
if we are talking about collision then it is not just about finding a hash collision in 2160 range, that would be pointless. we have to find two "private keys" that collide to the same hash result. so the bounds for the loop that is used to choose the keys are from 1 to 2256 instead.

now how many keys should be checked before we find a collision is what you are pointing out here. and in cryptography it usually is half of the final size meaning theoretically after checking 280 keys we may start seeing collisions.

At this moment the hash rate of bitcoin network is about 2^67 hashes/s, i.e. about 2^92 hashes/year.
that is a good number but also a bit of an unfair comparison. the hashrate is the result of computing double SHA256 of a mostly fixed 80 bytes message whereas a collision is going to be computing multiple things starting from an elliptic curve multiplication then 1 SHA256 followed by 1 RIPEMD160 of either a 33 byte input or a 65 byte input. most of the optimization that has gone into mining won't work here not to mention that there isn't much room to optimize RIPE-MD algorithm. the result should be a lot less than 292 for this process even if ASICs were made for it.

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qwk
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 January 12, 2020, 12:47:40 PMMerited by fillippone (2)

How much energy would be necessary? Well, a lot, according to this infographic:

I was never truly happy with that picture, so your thread got me thinking how to explain the energy requirements in a different way:

"If you had a computer that could do those calculations within a human's lifetime and were the size of the earth or smaller, and you actually somehow had an energy source to power it, as soon as you'd turn it on, you'd turn the earth into a supernova."