Crypto-Current (065)

§5.8613 — As differences accumulate in a decentralized database, it tends naturally to divergence. No authoritative tribunal exists in which to resolve disagreements. Not only is trustlessness the default, but the space for malicious deception is not easily limitable. Since contracts are agreements, a decentralized system without trusted third parties is a challenging place to do business of any kind. Those special – if typically momentary – contracts which are monetary transactions are no less profoundly problematized than any other. More specifically, insoluble controversies over their unique execution would generate double spending problems, which no money system could tolerate. Without an effective consensus mechanism, the basic compatibility of commerce with radical decentralization is plausibly questionable.

§5.86131 — The general solution space for dissensus and double-spending problems in decentralized systems has been explored under the name of Byzantine fault-tolerance (BFT).[1] This measures the resilience of a network in respect to the operation of treacherous nodes. ‘Byzantine’ references the Byzantine Generals Problem, which was conceptually formulated in the late 1970s, although the name itself is a few years more recent.[2] The Byzantine Generals Problem belongs to a larger class of ‘Generals Problems’ in computer science, all of which address questions of coordination between independent networked modules or agencies, especially when complicated by trustless communication. The joint work of Leslie Lamport, Robert Shostak, and Marshall Pease is the crucial reference.[3]  

§5.86132 — When apprehended teleologically, which is to say given Bitcoin, the Byzantine Generals Problem and Proof-of-work fit together like lock and key. Current discussion thus tends to scramble the two together, with the term ‘Byzantine Fault Tolerance’ serving as something close to a synonym for proof-of-work validation. Satoshi Nakamoto’s engagement with the Byzantine Generals Problem inaugurates the genre.[4] The consequence is an obscured synthesis. Something is brought together by Bitcoin Byzantine Fault-Tolerance whose original geneses were quite distinct.

§5.86133 — The central concern of Lamport, Shostak, and Pease is to determine the cost of reliability in insecure systems. Since fault-tolerance – in their estimation – is attained only through redundancy, it has a price determined by the measure of necessary message duplication. The message validation algorithm they propose requires that at least two-thirds of the communicating nodes are trustworthy (without – of course – knowing in advance which ones). No appeal is made to proof-of-work credentials, or in general to any kind of intrinsic message credibility.[5]

§5.86134 — Beyond their function as a technical designation, the Byzantine Generals mark the emergence of a rare modern myth. They plot an assault upon a city, under conditions that typify the ‘nomad war-machine’ in its philosophical acceptance – that is, dominance of external relations.[6] Having no interiority, the attackers have no default information security. Their domain is trustless, and primordially disunited. Integration is never given, but only strategically produced, as a precarious synthesis. It is this condition that the word ‘Byzantine’ is hijacked for, irrespective of the historical incongruity involved. The attack is – strictly – a critique. We have then, in the Byzantine Generals Problem, the mythical image of an assault upon centralization, unity, and interiority, staged from the Outside. Computer science, and later a far wider audience, is drawn into dramatic sympathy with this attack, and its ‘Byzantine’ heroes. In tackling the problem, or watching it tackled, we root for the unnamed city to fall.


[1] See §4.08+

[2] The Byzantine Generals Problem was immediately preceded  According to a comment appended to the 1982 article, the ‘generals’ confronted by this archetypal network coordination problem were Chinese, and then Albanian, before finally being identified – for reasons of diplomacy – as Byzantine.

See: https://www.microsoft.com/en-us/research/publication/byzantine-generals-problem/

[3] See in particular Lamport, Leslie; Shostak, Robert; and Pease, Marshall; ‘Reaching Agreement in the Presence of Faults’ (April 1980) and

‘The Byzantine Generals Problem’ (1982).

https://www.microsoft.com/en-us/research/uploads/prod/2016/12/The-Byzantine-Generals-Problem.pdf

[4] See §4.08

[5] Some qualification of this claim might be suggested by the fact that in their 1982 paper, Lamport, Shostak, and Pease entertain the possibility that secure digital signatures could contribute to Byzantine solutions.

[6] “As for the war machine in itself, it seems to be irreducible to the State apparatus, to be outside its sovereignty and prior to its law: it comes from elsewhere.” (Deleuze & Guattari, A Thousand Plateaus, p.352)