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My (censored) comment on the CAP Theorem (https://en.wikipedia.org/wiki/CAP_theorem) distributed systems limitation:

https://www.goland.org/blockchain_and_cap/comment-page-1/#comment-2681576

https://www.goland.org/blockchain_and_cap/#comment-2681576

“Bitcoin is always and forever only probabilistically consistent, thus never CP [but always AP in the CAP]. This blog is incorrect, although it does illustrate a point about trading off availability latency for [a naively computed? c.f. below…] probability of consistency. Unfortunately the blog does not even mention probability.”

Bitcoin’s partition tolerance doesn’t mean partitioning is nice. Imagine aliens mining Bitcoin on Mars exploiting some technology for nearly free energy, at a million times the hash rate of on Earth.

Later when they broadcast their chain to Earth, all earthly Bitcoin wealth will be erased and fleeced (https://paulkernfeld.com/2016/01/15/bitcoin-cap-theorem.html#big-partitions).[1] Thus Bitcoin is only ever probabilistically consistent.[7] Bitcoin wealth is not absolute.

[1] For n00bs, the Nakamoto consensus protocol rule is that the partition (i.e. fork) with the longest chain (actually to be more precise the highest cumulative proof-of-work difficulty) always wins and the other fork is orphaned.

Competing forks are resolved probabilistically w\high probability (by orphaning all but one) typically within up to ~6 blocks; but not if network partitioned such that the forks aren’t aware of the other (until much later).

This is an example of lying w\Probability & Statistics (https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics)— why I emphasize the true independent random variable is often the unaccounted (even unknowable) factor that can lead to such egregiously incorrect computations. The long-tail distribution (aka Black Swan event) is essentially failure of assumptions about the independent variable due to appearance of a Black Swan outlier. Accumulated inertia of such assumptions is the antithesis of Taleb’s antifragility.

[Technobabble minutiae: probability of finality (https://math.stackexchange.com/questions/2356763/the-probability-behind-bitcoin) (i.e. consistency, c.f. also (https://bitcoil.co.il/Doublespend.pdf#page=7)) in Nakamoto consensus is normally calculated (https://ems.press/content/serial-article-files/11512#page=2) (actually approximated (https://arxiv.org/pdf/1801.07447#section.5)) as a (continuous (https://archive.ph/https://suhailsaqan.medium.com/explaining-bitcoin-mining-as-a-poisson-distribution-92b2481fb80f)) Poisson process with an exponential distribution of time between blocks (https://bitcoin.stackexchange.com/questions/25293/probablity-distribution-of-mining) and the (discrete) Poisson distribution (https://en.wikipedia.org/wiki/Poisson_distribution) for blocks per period, wherein the average constant rate of events is given by the average time to find a proof-of-work hash solution given the current level of mining difficulty and the network’s cumulative hash rate.]

But the Poisson process (i.e. a probabilistic) model is unaware of a partition running (e.g. on Mars by aliens) at a different hashrate. The “independent” random variable in the Poisson model is actually dependent on the probability distribution of partition events (i.e. an orthogonal probabilistic model)— something you will never see mentioned in any mathematical discussion of Bitcoin. Heck this isn’t merely theoretical nor so far-fetched given the radio signal propagation delay between Mars and Earth ranges from 4.3 to 21 minutes, making Bitcoin entirely unsuitable for an interstellar mined blockchain.

[7] In an asynchronous network,[8] footnote #1 in Andrew Poelstra’s On Stake and Consensus (https://download.wpsoftware.net/bitcoin/pos.pdf) correctly cited that absolute termination (i.e. final consistency) is impossible unless **dysfunctionally partition intolerant** (http://web.archive.org/web/20130312052529/http://blog.cloudera.com/blog/2010/04/cap-confusion-problems-with-partition-tolerance/). Nakamoto consensus sidesteps that FLP85 impossibility theorem by (its transactions) being only probabilistically (and thus never absolutely) final.

Proof-of-stake requires a synchronous network assumption enabling “dysfunctionally partition intolerant” deterministic finality (https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery/comment/56466346) but forsaking on-chain objectivity (https://blog.ethereum.org/2014/11/25/proof-stake-learned-love-weak-subjectivity) (c.f. also (https://www.reddit.com/r/CryptoTechnology/comments/od9ves/proof_of_stake_how_i_learned_to_love_weak/) and §4.3 “Long-Range” vs “Short-Range” Attacks (https://download.wpsoftware.net/bitcoin/pos.pdf#subsection.4.3)) inter alia.[9]

[8] Asynchronous networks have no max message arrival latency. Actually Bitcoin’s 10 min block period is a synchrony assumption, but the (propagation delay) network diameter is so much smaller; it’s for practical purposes almost (https://tik-old.ee.ethz.ch/file//49318d3f56c1d525aabf7fda78b23fc0/P2P2013_041.pdf#page=8) equivalent to an asynchronous assumption. C.f. 1 (https://www.reddit.com/r/btc/comments/gxng23/comment/ft97xgd/), 2 (https://www.reddit.com/r/btc/comments/gxng23/comment/ft3qgsi/) and Vitalik’s summary w\less exact equation (https://blog.ethereum.org/2014/07/11/toward-a-12-second-block-time#stales-efficiency-and-centralization).

[9] Specific (https://web.stanford.edu/class/ee374/lec_notes/lec15.pdf#subsection.1.4) (dubiously (https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery#%C2%A7liveness-attack)-ameliorated (https://web.stanford.edu/class/archive/ee/ee374/ee374.1206/downloads/l18_notes.pdf)) attacks against (https://bitfury.com/content/downloads/pos-vs-pow-1.0.2.pdf#page=16) proof-of-stake consensus distract focus from insoluble deficiencies of lacks cost-of-production (https://steemit.com/bitcoin/@anonymint/secrets-of-bitcoin-s-dystopian-valuation-model) thus no monetary value (https://archive.ph/https://www.zerohedge.com/news/2019-05-25/drop-gold-myths-naturalist-exposition-golds-manifest-superiority-bitcoin-money), inferior liveness (https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery#%C2%A7liveness-attack) (rubber-hose (https://www.google.com/search?q=rubber-hose+cryptography) the whales![10]), can’t distribute decentralized (https://bitfury.com/content/downloads/pos-vs-pow-1.0.2.pdf#subsection.3.2) and cost-free forks (https://bitfury.com/content/downloads/pos-vs-pow-1.0.2.pdf#subsection.3.1) (lack opportunity cost bcz) are equally (in)“secure.”

I wrote (https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery#%C2%A7what-might-work):

“stake is always conserved”

[10] https://www.reddit.com/r/programming/comments/7ph6m/rubberhose_cryptanalysis_russian_name/ (Russian name: "Thermorectal cryptanalysis" 🤣)

===========

Hypothetically even brute-force, nearly cost-free, long-range attacks (analogous to a withheld/uncontactable partition) might someday be viable on Bitcoin employing hypothetically[2] a quantum computer employing Grover’s algorithm for preimage search[3] might be able to orphan the entire Bitcoin history since inception, c.f. *§5 Resistance to quantum computations* of Iota’s Tangle whitepaper[4] although quantum computers are no where near practical yet[3][5] and Daniel J. Bernstein showed that some (at least one) quantum algorithms (e.g. hash collisions) will **never** be more cost-efficient with a quantum computer.[3][6]

Note this posited attack presumes the profit/motivation from/for orphaning the non-quantum history subsumes appending quantum computing mined blocks to said history.

[2] https://www.scottaaronson.com/democritus/lec14.html

[3] https://crypto.stackexchange.com/questions/63236/what-benefits-quantum-offer-over-classical-parallelism

[4] https://assets.ctfassets.net/r1dr6vzfxhev/2t4uxvsIqk0EUau6g2sw0g/45eae33637ca92f85dd9f4a3a218e1ec/iota1_4_3.pdf#page=26

[5] https://viterbischool.usc.edu/news/2023/06/quantum-computers-are-better-at-guessing-new-study-demonstrates/

[6] https://cr.yp.to/papers.html#collisioncost (https://cr.yp.to/hash/collisioncost-20090823.pdf)

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Anonymint's avatar

Reacting to:

https://0xfoobar.substack.com/p/ethereum-proof-of-stake#%C2%A7ethereum-implementation

“Ethereum’s PoS implementation has been teased for the better half of a decade now, but with the beacon chain running for 18 months straight and successful live merges on multiple testnets the initial implementation is largely finalized.”

Dubious whether bugs and corner cases have been exorcised given the high likelihood of the natural oligarchy enforcing a preferred order:

https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery/comment/56417630

“A supermajority (2/3rds) of validators is required to finalize a block, in case of a 50-50 network partition blocks would stop being finalized and attestation rewards would stop. Non-participating validators would slowly leak stake through the inactivity leak until online validators once again had a supermajority. This is the ‘self-healing’ mechanism that allows both safety and liveness.”

THIS ENTIRELY LACKS THE PARTITION TOLERANCE OF THE CAP THEOREM.[1] This design bleeds out the partitioned stake from every partition, so they are permanently forked off from each other unlike for proof-of-work where all but one of the partitions will eventually be orphaned when the network returns to normal.

[1] https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery/comment/57176124

Also this presents either an inferior liveness situation to proof-of-work or means for the natural oligarchy (probably insidiously, surreptitiously) extract value:

https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery/comment/56417630

“Equivocation is punished by slashing up to the validator’s entire stake, so the attacker must commit to destroying at least one-third of all staked ETH. The cost to reorg a finalized block is several billion dollars, even at today’s depressed prices.”

Not that they have any incentive to do so when the natural oligarchy (w\majority stake) can more easily and effectively extract value insidiously instead. There are theoretical long-range attacks for said natural oligarchy in proof-of-stake against lock-up deposit penalty mechanisms, but this simply isn’t the preferred way that proof-of-stake systems mine the FOMO n00bs instead by surreptitious value extraction.

“One key difference is that the honest validators would have to explicitly band together to recognize one another’s attestations and override the fork choice rule, but other than that they can form their own child chain and the malicious supermajority would slowly bleed stake out of the validator set until the honest subminority has once again regained a supermajority.”

The majority stake chain can censor blocks and attestations! The bleeding based on inactivity of attestations is a double-edged sword that can be (even insidiously) turned against the subminority by the malevolent supermajority. The “he said, she said” dilemma of weak subjectivity[2] applies if instead the honest minority band together to create their own fork to bleed out what they claim is the dishonest majority.

[2] https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery/comment/56420675

https://anonymint1.substack.com/p/decentralized-data-storage-and-delivery/comment/56417630

In addition to some additional points I made at the aforelinked, Lyn Alden also refuted (https://www.youtube.com/watch?v=1m12zgJ42dI) the following linked section. Essentially she argued against the highest economies-of-scale have the most proof-of-work profit, because she alleges there’s too much risk (e.g. jurisdictional) and micromanaged opportunity-cost (e.g. making deals in situations where byproduct energy or natural sources are normally discarded/unharvested).

https://0xfoobar.substack.com/p/ethereum-proof-of-stake#%C2%A7pos-rich-get-richer-pow-egalitarian

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