Elaborate hash function design in BIP152#397
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luke-jr merged 3 commits intobitcoin:masterfrom Jun 7, 2016
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| In case 1, we're good. In cases 2, 3, or 4, we request the full transaction because we know we're uncertain. Only in case 5, we fail to reconstruct. The chance that case 5 does not occur in any of the ''t'' transactions in a block is ''(1 - (1 - r) * m * (1 - P) * P^(m - 1))^t''. This expression is well approximated by ''1 - m * t * r / 2^B''. Thus, if we want only one in F block transmissions between honest nodes to fail, we need ''log2(F * m * t)'' bits hash functions. | ||
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| This means that ''B = 48'' bits short IDs suffice blocks with up to ''t = 10000'' transactions, mempools up to ''m = 100000'' transactions, with failure to reconstruct up to once every ''F = 281474'' blocks. Since failure to reconstruct just means we fall back to normal inv/header based relay, it isn't necessary to avoid such failure completely. It just needs to be sufficiently rare they have a lower impact than random transmission failures (for example, network disconnection, node overloaded, ...). |
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once every ''F = 281474'' blocks. < needs to mention that every link in the network is multiple comparisons.
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That's already accounted for in the log2(F * m * t) formula. If it's not clear enough, that should be clarified where that formula is introduced.
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Didnt check any of the math, but general text seems reasonable. ACK. |
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ACK |
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