My reply to CfB and smooth follows.

The Byzantine Generals Problem (BGP) is at its generate essence (i.e. conditions IC1 and IC2 in the white paper) whether a commanding general can collect the vote (e.g. 'attack' or 'retreat', or other information subject to a consensus) of the other generals and relay that result to other decentralized generals and have the vote of the loyal generals reflect the consensus, but without trusting that the commanding general is loyal. This is functionally equivalent to the case of each loyal general computing the vote independently (i.e. conditions 1 and 2 of the white paper).

Afaics the paper has an important omission which is that when the disloyal generals (traitors) are not colluding (i.e. can't trust each other) then they have no reliable means to disrupt the loyal consensus. So my analysis will focus on the case where the disloyal generals are colluding.

The paper does not also explicitly state that at any number of loyal generals other than exactly 2/3 (wherein the result will be inconclusive 50/50 conflict and failure of consensus), then it is undecidable (from the perspective of each general) whether the consensus result reflects loyalty or disloyalty.

Thus although the paper is correct to state that BGP is solvable if the 2/3 + 1 of the generals are loyal (i.e. 3m + 1 total generals for m traitors), the only way to know that precondition is for the system to be centralized so that the count of the traitors is known. Thus the white paper is poorly written (w.r.t. this issue) because it does not explain that there is no decentralized, trustless solution to the BGP and insinuates the opposite in the mind of the naive reader.

No loyal general ever knows if the system is loyal or not.

There is no decentralized solution to the BGP problem. Period.

(note also that the definition of oral messages assumes conditions A1, A2, and A3 which can't exist in a decentralized network where Sybil attacks are possible)


Damn my illness really restricts me. Normally I would go off on a tangent thinking about how such points ripple into the Halting theorem and unbounded recursion of Turing completeness, but I can barely sustain the mental focus to do the above. I need to get cured. This is really fucking me up.