[Cryptography] Electronic currency revived after 20-year hiatus

[Jerry Leichter]

> Just like how Bitcoin solved the unsolvable Byzantine General's problem by ignoring the original problem statement and going for a probabilistic approximation, Bitcoin's got a solution here too.
> 
Wow.  How many false statements can we pack in here in an attempt to make Bitcoin into some bit of magic?

1.  The Byzantine Generals problem was never considered unsolvable.  In fact, the very paper that introduced it also provided a solution.
2.  Ignoring the problem statement doesn't solve a problem.  It may or may not solve a different problem, but let's stick to reasonable use of language here.
3.  The original paper shows that a deterministic solution in a completely general model had no solutions if 1/3 of the participants were traitors.  That's just true, and no amount of "probabilistic approximation" (whatever exactly that is) changes it.
4.  The original paper also shows that given the assumption of unforgeable message signatures, a deterministic solution exists with any number of traitors.  It's not clear what cryptographic assumptions whatever parts of Bitcoin you want to use actually need, but if they include enough to have unforgeable message signatures, a complete solution without any kind of approximation is at hand - and has been for years.  (BTW, this result is generally stated in terms of signatures, but I suspect that secure keyed MAC's are sufficient, though the message get much larger:  I need to prove to myself that any message alleged to come from any sender S actually *did* come from S.  I don't need to prove that to anyone else - I need merely forward such messages along.)

                                                        -- Jerry


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