[bitcoin-dev] Compact Block Relay BIP
Peter R
peter_r at gmx.com
Mon May 9 23:37:00 UTC 2016
Greg Maxwell wrote:
> What are you talking about? You seem profoundly confused here...
>
> I obtain some txouts. I write a transaction spending them in malleable
> form (e.g. sighash single and an op_return output).. then grind the
> extra output to produce different hashes. After doing this 2^32 times
> I am likely to find two which share the same initial 8 bytes of txid.
[9 May 16 @ 4:30 PDT]
I’m trying to understand the collision attack that you're explaining to Tom Zander.
Mathematica is telling me that if I generated 2^32 random transactions, that the chances that the initial 64-bits on one of the pairs of transactions is about 40%. So I am following you up to this point. Indeed, there is a good chance that a pair of transactions from a set of 2^32 will have a collision in the first 64 bits.
But how do you actually find that pair from within your large set? The only way I can think of is to check if the first 64-bits is equal for every possible pair until I find it. How many possible pairs are there?
It is a standard result that there are
m! / [n! (m-n)!]
ways of picking n numbers from a set of m numbers, so there are
(2^32)! / [2! (2^32 - 2)!] ~ 2^63
possible pairs in a set of 2^32 transactions. So wouldn’t you have to perform approximately 2^63 comparisons in order to identify which pair of transactions are the two that collide?
Perhaps I made an error or there is a faster way to scan your set to find the collision. Happy to be corrected…
Best regards,
Peter
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