Hi,

This is a pretty big departure from cumulative POW.

Could you explain to me what you see happening if a node with this patch 
and no history starts to sync, and some random node gives it a block 
with a better fitness test for say height 250,000? No other solution 
will have a better fitness test at that height, so from my understanding 
its going to stop syncing. How about even later - say this proposal is 
activated at block 750,000. At 850,000, someone decides it'd be fun to 
publish a new block 800,000 with a better fitness test. What happens the 
50,000 blocks?

I can imagine the miners not being particularly happy about it - their 
previously 50:50 chance (well, sort of, it's based on resources- 
connectivity, validation overheads, etc) their tied block would succeed, 
vs the situation with this change - blocks that are inherently more or 
less valid than others.

I think these days people are more focused on improving defences at the 
networking layer than in the consensus layer - especially when it 
affects mining incentives. I don't see how people will take this 
seriously - especially when you regard how often consensus changes are 
made to _fix_ something as opposed to add something new.

Best regards,

Thomas

On 9/24/20 8:40 PM, Mike Brooks via bitcoin-dev wrote:
>   Hey Everyone,
>
>  A lot of work has gone into this paper, and the current revision has 
> been well received and there is a lot of excitement on this side to be 
> sharing it with you today. There are so few people that truly 
> understand this topic, but we are all pulling in the same direction to 
> make Bitcoin better and it shows.  It is wildly underrated that future 
> proofing was never really a consideration in the initial design - but 
> here we are a decade later with amazing solutions like SegWit 
> which gives us a real future-proofing framework.  The fact that 
> future-proofing was added to Bitcoin with a softfork gives me 
> goosebumps. I'd just like to take the time to thank the people who 
> worked on SegWit and it is an appreciation that comes up in 
> conversation of how difficult and necessary that process was, and this 
> appreciation may not be vocalized to the great people who worked on 
> it. The fact that Bitcoin keeps improving and is able to respond to 
> new threats is nothing short of amazing - thank you everyone for a 
> great project.
>
> This current proposal really has nothing to do with SegWit - but it is 
> an update that will make the network a little better for the future, 
> and we hope you enjoy the paper.
>
> PDF:
> https://github.com/in-st/Floating-Point-Nakamoto-Consensus/blob/master/Floating-Point%20Nakamoto%20Consensus.pdf
> Pull Request:
> https://github.com/bitcoin/bitcoin/pull/19665/files
>
> ---
>
>
> Floating-Point Nakamoto Consensus
>
>
> Abstract — It has been shown that Nakamoto Consensus is very useful in 
> the formation of long-term global agreement — and has issues with 
> short-term disagreement which can lead to re-organization (“or-org”) 
> of the blockchain.  A malicious miner with knowledge of a specific 
> kind of denial-of-service (DoS) vulnerability can gain an unfair 
> advantage in the current Bitcoin network, and can be used to undermine 
> the security guarantees that developers rely upon.  Floating-Point 
> Nakamoto consensu makes it more expensive to replace an already mined 
> block vs. creation of a new block, and by resolving ambiguity of 
> competition solutions it helps achieve global consumers more quickly.  
> A floating-point fitness test strongly incentivises the correct 
> network behavior, and prevents disagreement from ever forming in the 
> first place.
>
>
>         Introduction
>
> The Bitcoin protocol was created to provide a decentralized consensus 
> on a fully distributed p2p network.  A problem arises when more than 
> one proof-of-work is presented as the next solution block in the 
> blockchain.  Two solutions of the same height are seen as 
> authoritative equals which is the basis of a growing disagreement. A 
> node will adopt the first solution seen, as both solutions propagate 
> across the network a race condition of disagreement is formed. This 
> race condition can be controlled by byzentiene fault injection 
> commonly referred to as an “eclipsing” attack.  When two segments of 
> the network disagree it creates a moment of weakness in which less 
> than 51% of the network’s computational resources are required to keep 
> the network balanced against itself.
>
>
>         Nakamoto Consensus
>
> Nakamoto Consensus is the process of proving computational resources 
> in order to determine eligibility to participate in the decision 
> making process.  If the outcome of an election were based on one node 
> (or one-IP-address-one-vote), then representation could be subverted 
> by anyone able to allocate many IPs. A consensus is only formed when 
> the prevailing decision has the greatest proof-of-work effort invested 
> in it. In order for a Nakamoto Consensus to operate, the network must 
> ensure that incentives are aligned such that the resources needed to 
> subvert a proof-of-work based consensus outweigh the resources gained 
> through its exploitation. In this consensus model, the proof-of-work 
> requirements for the creation of the next valid solution has the exact 
> same cost as replacing the current solution. There is no penalty for 
> dishonesty, and this has worked well in practice because the majority 
> of the nodes on the network are honest and transparent, which is a 
> substantial barrier for a single dishonest node to overcome.
>
>
> A minimal network peer-to-peer structure is required to support 
> Nakamoto Conesus, and for our purposes this is entirely decentralized. 
> Messages are broadcast on a best-effort basis, and nodes can leave and 
> rejoin the network at will, accepting the longest proof-of-work chain 
> as proof of what happened while they were gone.  This design makes no 
> guarantees that the peers connected do not misrepresent the network or 
> so called “dishonest nodes.” Without a central authority or central 
> view - all peers depend on the data provided by neighboring peers - 
> therefore a dishonest node can continue until a peer is able to make 
> contact an honest node.
>
>
>         Security
>
> In this threat model let us assume a malicious miner possesses 
> knowledge of an unpatched DoS vulnerability (“0-day”) which will 
> strictly prevent honest nodes from communicating to new members of the 
> network - a so-called “total eclipse.”  The kind of DoS vulnerability 
> needed to conduct an eclipse does not need to consume all CPU or 
> computaitly ability of target nodes - but rather prevent target nodes 
> from forming new connections that would undermine the eclipsing 
> effect. These kinds of DoS vulnerabilities are somewhat less 
> substional than actually knocking a powerful-mining node offline.  
> This class of attacks are valuable to an adversary because in order 
> for an honest node to prove that a dishonest node is lying - they 
> would need to form a connection to a segment of the network that isn’t 
> entirely suppressed. Let us assume a defense-in-depth strategy and 
> plan on this kind of failure.
>
>
> Let us now consider that the C++ Bitcoind has a finite number of 
> worker threads and a finite number of connections that can be serviced 
> by these workers.  When a rude client occupies all connections - then 
> a pidgin-hole principle comes into play. If a network's maximum 
> capacity for connection handlers ‘k’, is the sum of all available 
> worker threads for all nodes in the network, establishing ‘k+1’ 
> connections by the pidgin-hole principle will prevent any new 
> connections from being formed by honest nodes - thereby creating a 
> perfect eclipse for any new miners joining the network would only be 
> able to form connections with dishonest nodes.
>
>
> Now let’s assume a dishonest node is modified in two ways - it 
> increases the maximum connection handles to hundreds of thousands 
> instead of the current value which is about 10. Then this node is 
> modified to ignore any solution blocks found by honest nodes - thus 
> forcing the dishonest side of the network to keep searching for a 
> competitive-solution to split the network in two sides that disagree 
> about which tip of the chain to use.  Any new solution propagates 
> through nodes one hop at a time. This propagation can be predicted and 
> shaped by dishonest non-voting nodes that are being used to pass 
> messages for honest nodes.
>
>
> At this point an attacker can expedite the transmission of one 
> solution, while slowing another. If ever a competing proof-of-work is 
> broadcasted to the network, the adversary will use their network 
> influence to split knowledge of the proof-of-work as close to ½ as 
> possible. If the network eclipse is perfect then an adversary can 
> leverage an eigen-vector of computational effort to keep the 
> disagreement in balance for as long as it is needed. No mechanism is 
> stopping the attacker from adding additional computation resources or 
> adjusting the eclipsing effect to make sure the system is in balance. 
>   As long as two sides of the network are perfectly in disagreement 
> and generating new blocks - the attacker has intentionally created a 
> hard-fork against the will of the network architects and operators. 
> The disagreement needs to be kept open until the adversary’s 
> transactions have been validated on the honest chain - at which point 
> the attacker will add more nodes to the dishonest chain to make sure 
> it is the ultimate winner - thus replacing out the honest chain with 
> the one generated by dishonest miners.
>
>
> This attack is convenient from the adversary’s perspective,  Bitcoin 
> being a broadcast network advertises the IP addresses of all active 
> nodes - and Shodan and the internet scanning project can find all 
> passive nodes responding on TCP 8333.  This should illuminate all 
> honest nodes on the network, and even honest nodes that are trying to 
> obscure themselves by not announcing their presence.  This means that 
> the attacker doesn’t need to know exactly which node is used by a 
> targeted exchange - if the attacker has subdued all nodes then the 
> targeted exchange must be operating a node within this set of targeted 
> honest nodes.
>
>
> During a split in the blockchain, each side of the network will honor 
> a separate merkel-tree formation and therefore a separate ledger of 
> transactions. An adversary will then broadcast currency deposits to 
> public exchanges, but only on the weaker side, leaving the stronger 
> side with no transaction from the adversary. Any exchange that 
> confirms one of these deposits is relying upon nodes that have been 
> entirely eclipsed so that they cannot see the competing chain - at 
> this point anyone looking to confirm a transaction is vulnerable to a 
> double-spend. With this currency deposited on a chain that will become 
> ephemeral, the attacker can wire out the account balance on a 
> different blockchain - such as Tether which is an erc20 token on the 
> Ethereum network which would be unaffected by this attack.  When the 
> weaker chain collapses, the transaction that the exchange acted upon 
> is no longer codified in Bitcoin blockchain's global ledger, and will 
> be replaced with a version of the that did not contain these deposits.
>
>
> Nakamoto Consensus holds no guarantees that it’s process is 
> deterministic.  In the short term, we can observe that the Nakamoto 
> Consensus is empirically non-deterministic which is evident by 
> re-organizations (re-org) as a method of resolving disagreements 
> within the network.   During a reorganization a blockchain network is 
> at its weakest point, and a 51% attack to take the network becomes 
> unnecessary. An adversary who can eclipse honest hosts on the network 
> can use this as a means of byzantine fault-injection to disrupt the 
> normal flow of messages on the network which creates disagreement 
> between miners.
>
>
> DeFi (Decentralized Finance) and smart-contract obligations depend on 
> network stability and determinism.  Failure to pay contracts, such as 
> what happened on “black thursday” resulted in secured loans 
> accidentally falling into redemption.  The transactions used by a 
> smart contract are intended to be completed quickly and the outcome is 
> irreversible.  However, if the blockchain network has split then a 
> contract may fire and have it’s side-effects execute only to have the 
> transaction on the ledger to be replaced.  Another example is that a 
> hard-fork might cause the payer of a smart contract to default - as 
> the transaction that they broadcasted ended up being on the weaker 
> chain that lost. Some smart contracts, such as collateral backed loans 
> have a redemption clause which would force the borrower on the loan to 
> lose their deposit entirely.
>
>
> With two sides of the network balanced against each other - an 
> attacker has split the blockchain and this hard-fork can last for as 
> long as the attacker is able to exert the computational power to 
> ensure that proof-of-work blocks are regularly found on both sides of 
> the network.  The amount of resources needed to balance the network 
> against itself is far less than a 51% attack - thereby undermining the 
> security guarantees needed for a decentralized untrusted payment 
> network to function.  An adversary with a sufficiently large network 
> of dishonest bots could use this to take a tally of which miners are 
> participating in which side of the network split. This will create an 
> attacker-controlled hard fork of the network with two mutually 
> exclusive merkle trees. Whereby the duration of this split is 
> arbitrary, and the decision in which chain to collapse is up to the 
> individual with the most IP address, not the most computation.
>
>
> In Satoshi Nakamoto’s original paper it was stated that the electorate 
> should be represented by computational effort in the form of a 
> proof-of-work, and only these nodes can participate in the consues 
> process.  However, the electorate can be misled by non-voting nodes 
> which can reshape the network to benefit an individual adversary.
>
>
>         Chain Fitness
>
> Any solution to byzantine fault-injection or the intentional formation 
> of disagreements must be fully decentralized. A blockchain is allowed 
> to split because there is ambiguity in the Nakamoto proof-of-work, 
> which creates the environment for a race-condition to form. To resolve 
> this, Floating-Point Nakamoto Consensus makes it increasingly more 
> expensive to replace the current winning block. This added cost comes 
> from a method of disagreement resolution where not every solution 
> block is the same value, and a more-fit solution is always chosen over 
> a weaker solution. Any adversary attempting to have a weaker chain to 
> win out would have to overcome a kind of relay-race, whereby the 
> winning team’s strength is carried forward and the loser will have to 
> work harder and harder to maintain the disagreement.  In most cases 
> Floating-Point Nakamoto Consensus will prevent a re-org blockchain 
> from ever going past a single block thereby expediting the formation 
> of a global consensus.  Floating-Point Nakamoto Consensus cements the 
> lead of the winner and to greatly incentivize the network to adopt the 
> dominant chain no matter how many valid solutions are advertised, or 
> what order they arrive.
>
>
> The first step in Floating-Point Nakamoto Consensus is that all nodes 
> in the network should continue to conduct traditional Nakamoto 
> Consensus and the formation of new blocks is dictated by the same 
> zero-prefix proof-of-work requirements.  If at any point there are two 
> solution blocks advertised for the same height - then a floating-point 
> fitness value is calculated and the solution with the higher fitness 
> value is the winner which is then propagated to all neighbors. Any 
> time two solutions are advertised then a re-org is inevitable and it 
> is in the best interest of all miners to adopt the most-fit block, 
> failing to do so risks wasting resources on a mining of a block that 
> would be discarded.  To make sure that incentives are aligned, any 
> zero-prefix proof of work could be the next solution, but now in order 
> to replace the current winning solution an adversary would need a 
> zero-prefix block that is also more fit that the current solution - 
> which is much more computationally expensive to produce.
>
> Any changes to the current tip of the blockchain must be avoided as 
> much as possible. To avoid thrashing between two or more competitive 
> solutions, each replacement can only be done if it is more fit, 
> thereby proving that it has an increased expense.  If at any point two 
> solutions of the same height are found it means that eventually some 
> node will have to replace their tip - and it is better to have it done 
> as quickly as possible so that consensus is maintained.
>
>
> In order to have a purely decentralized solution, this kind of 
> agreement must be empirically derived from the existing proof-of-work 
> so that it is universally and identically verifiable by all nodes on 
> the network.  Additionally, this fitness-test evaluation needs to 
> ensure that no two competing solutions can be numerically equivalent.
>
>
> Let us suppose that two or more valid solutions will be proposed for 
> the same block.  To weigh the value of a given solution, let's 
> consider a solution for block 639254, in which the following hash was 
> proposed:
>
>     00000000000000000008e33faa94d30cc73aa4fd819e58ce55970e7db82e10f8
>
>
> There are 19 zeros, and the remaining hash in base 16 starts with 9e3 
> and ends with f8.  This can value can be represented in floating point as:
>
>     19.847052573336114130069196154809453027792121882588614904
>
>
> To simplify further lets give this block a single whole number to 
> represent one complete solution, and use a rounded floating-point 
> value to represent some fraction of additional work exerted by the miner.
>
>    1.847
>
>
> Now let us suppose that a few minutes later another solution is 
> advertised to the network shown in base16 below:
>
>     000000000000000000028285ed9bd2c774136af8e8b90ca1bbb0caa36544fbc2
>
>
> The solution above also has 19 prefixed zeros, and is being broadcast 
> for the same blockheight value of 639254 - and a fitness score of 
> 1.282.  With Nakamoto Consensus both of these solutions would be 
> equivalent and a given node would adopt the one that it received 
> first.  In Floating-Post Nakamoto Consensus, we compare the fitness 
> scores and keep the highest.  In this case no matter what happens - 
> some nodes will have to change their tip and a fitness test makes sure 
> this happens immediately.
>
>
> With both solutions circulating in the network - any node who has 
> received both proof-of-works should know 1.847 is the current highest 
> value, and shouldn’t need to validate any lower-valued solution.  In 
> fact this fitness value has a high degree of confidence that it won’t 
> be unseated by a larger value - being able to produce a proof-of-work 
> with 19 0’s and a decimal component greater than 0.847 is 
> non-trivial.  As time passes any nodes that received a proof-of-work 
> with a value 1.204 - their view of the network should erode as these 
> nodes adopt the 1.847 version of the blockchain.
>
> All nodes are incentivized to support the solution with the highest 
> fitness value - irregardless of which order these proof-of-work were 
> validated. Miners are incentivized to support the dominant chain which 
> helps preserve the global consensus.
>
>
> Let us assume that the underlying cryptographic hash-function used to 
> generate a proof-of-work is an ideal primitive, and therefore a node 
> cannot force the outcome of the non-zero component of their 
> proof-of-work.  Additionally if we assume an ideal cipher then the 
> fitness of all possible solutions is gaussian-random. With these 
> assumptions then on average a new solution would split the keyspace of 
> remaining solutions in half.  Given that the work needed to form a  
> new block remains a constant at 19 blocks for this period - it is 
> cheaper to produce a N+1 block that has any floating point value as 
> this is guaranteed to be adopted by all nodes if it is the first 
> solution.  To leverage a chain replacement on nodes conducting 
> Floating-Point Nakamoto Consensus a malicious miner would have to 
> expend significantly more resources.
>
>
> Each successive n+1 solution variant of the same block-height must 
> therefore on average consume half of the remaining finite keyspace. 
> Resulting in a the n+1 value not only needed to overcome the 19 zero 
> prefix, but also the non-zero fitness test.   It is possible for an 
> adversary to waste their time making a 19 where n+1 was not greater, 
> at which point the entire network will have had a chance to move on 
> with the next solution.  With inductive reasoning, we can see that a 
> demissiniong keyspace increases the amount of work needed to find a 
> solution that also meets this new criteria.
>
>
> Now let us assume a heavily-fragmented network where some nodes have 
> gotten one or both of the solutions.  In the case of nodes that 
> received the proof-of-work solution with a fitness of 1.847, they will 
> be happily mining on this version of the blockchain. The nodes that 
> have gotten both 1.847 and .240 will still be mining for the 1.847 
> domainite version, ensuring a dominant chain.  However, we must assume 
> some parts of the network never got the message about 1.847 proof of 
> work, and instead continued to mine using a value of 1.240 as the 
> previous block.   Now, let’s say this group of isolated miners manages 
> to present a new conflicting proof-of-work solution for 639255:
>
>
>      000000000000000000058d8ebeb076584bb5853c80111bc06b5ada35463091a6
>
>
> The above base16 block has a fitness score of 1.532  The fitness value 
> for the previous block 639254 is added together:
>
>
>      2.772 = 1.240 + 1.532
>
>
> In this specific case, no other solution has been broadcast for block 
> height 639255 - putting the weaker branch in the lead.  If the weaker 
> branch is sufficiently lucky, and finds a solution before the dominant 
> branch then this solution will have a higher overall fitness score, 
> and this solution will propagate as it has the higher value.  This is 
> also important for transactions on the network as they benefit from 
> using the most recently formed block - which will have the highest 
> local fitness score at the time of its discovery.  At this junction, 
> the weaker branch has an opportunity to prevail enterally thus ending 
> the split.
>
>
> Now let us return to the DoS threat model and explore the worst-case 
> scenario created by byzantine fault injection. Let us assume that both 
> the weaker group and the dominant group have produced competing 
> proof-of-work solutions for blocks 639254 and 639255 respectively.  
> Let’s assume that the dominant group that went with the 1.847 fitness 
> score - also produces a solution with a similar fitness value and 
> advertises the following solution to the network:
>
>
> 0000000000000000000455207e375bf1dac0d483a7442239f1ef2c70d050c113
>
> 19.414973649464574877549198290879237036867705594421756179
>
> or
>
> 3.262 = 1.847 + 1.415
>
>
> A total of 3.262 is still dominant over the lesser 2.772 - in order to 
> overcome this - the 2nd winning block needs to make up for all of the 
> losses in the previous block.  In this scenario, in order for the 
> weaker chain to supplant the dominant chain it must overcome a -0.49 
> point deficit. In traditional Nakamoto Consensus the nodes would see 
> both forks as authoritative equals which creates a divide in mining 
> capacity while two groups of miners search for the next block.  In 
> Floating-Point Nakamoto Consensus any nodes receiving both forks, 
> would prefer to mine on the chain with an overall fitness score of 
> +3.262 - making it even harder for the weaker chain to find miners to 
> compete in any future disagreement, thereby eroding support for the 
> weaker chain. This kind of comparison requires an empirical method for 
> determining fitness by miners following the same same system of rules 
> will insure a self-fulfilled outcome.  After all nodes adopt the 
> dominant chain normal Nakamoto Consuess can resume without having to 
> take into consideration block fitness. This example shows how 
> disagreement can be resolved more quickly if the network has a 
> mechanism to resolve ambiguity and de-incentivise dissent.
>
>
>         Soft Fork
>
> Blockchain networks that would like to improve the consensus 
> generation method by adding a fitness test should be able to do so 
> using a “Soft Fork” otherwise known as a compatible software update.  
> By contrast a “Hard-Fork” is a separate incompatible network that does 
> not form the same consensus.  Floating-Point Nakamoto Consensus can be 
> implemented as a soft-fork because both patched, and non-patched nodes 
> can co-exist and non-patched nodes will benefit from a kind of herd 
> immunity in overall network stability.  This is because once a small 
> number of nodes start following the same rules then they will become 
> the deciding factor in which chain is chosen.  Clients that are using 
> only traditional Nakamoto Consensus will still agree with new clients 
> over the total chain length. Miners that adopt the new strategy early, 
> will be less likely to lose out on mining invalid solutions.
>
>
>         Conclusion
>
> Floating-Point Nakamoto consensus allows the network to form a 
> consensus more quickly by avoiding ambiguity allowing for determinism 
> to take hold. Bitcoin has become an essential utility, and attacks 
> against our networks must be avoided and adapting, patching and 
> protecting the network is a constant effort. An organized attack 
> against a cryptocurrency network will undermine the guarantees that 
> blockchain developers are depending on.
>
>
> Any blockchain using Nakamoto Consensus can be modified to use a 
> fitness constraint such as the one used by a Floating-Point Nakamoto 
> Consensus.  An example implementation has been written and submitted 
> as a PR to the bitcoin core which is free to be adapted by other networks.
>
>
>
>
>
>
> A complete implementation of Floating-Point Nakamoto consensus is in 
> the following pull request:
>
> https://github.com/bitcoin/bitcoin/pull/19665/files
>
>
> Paper:
>
> https://github.com/in-st/Floating-Point-Nakamoto-Consensus
>
> https://in.st.capital <https://in.st.capital/>
>
>
>
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