Proof of Stake

Proof of Stake is a propose alternative mechanism to Proof of Work as a way to mine Bitcoin and sign transactions. It was probablly first proposed here by Quantum Mechanic. With Proof of Work, the probability of mining a block depends on the work done by the miner (e.g. CPU/GPU cycles spent checking hashes). With Proof of Stake, the resource that's compared is the amount of Bitcoin a miner holds - someone holding 1% of the Bitcoin can mine 1% of the "Proof of Stake blocks".

Some argue that methods based on Proof of Work alone might lead to a low network security due to Tragedy of the Commons, and Proof of Stake is one way of changing the miner's incentives in favor of higher network security.

Here is one attempt to describe an implementation of Proof of Stake.

Motivation For Proof of Stake

• A proof-of-stake system might provide increased protection from a malicious attack on the network.
• When block rewards are produced through txn fees, a proof of stake system would result in lower equilibrium txn fees. Lower long-run fees would increase the competiveness of bitcoin relative to alternative payments systems.

The Monopoly Problem

If a single entity (hereafter a monopolist) took control of the majority of txn verification resources, he could use these resources to impose conditions on the rest of the network. Potentially, the monopolist could choose to do this in malicious ways, such as double spending or denying service. If the monopolist chose a malicious strategy and maintained his control for a long period, confidence in bitcoin would be undermined and bitcoin purchasing power would collapse. Alternatively, the monopolist could choose to act benevolently. A benevolent monopolist would exclude all other txn verifiers from fee collection and currency generation, but would not try to exploit currency holders in any way. In order to maintain a good reputation, he would refrain from double spends and maintain service provision. In this case, confidence in Bitcoin could be maintained under monopoly since all of its basic functionality would not be affected.

Both benevolent and malevolent monopoly are potentially profitable, so there are reasons to suspect that an entrepreneurial miner might attempt to become a monopolist at some point. Due to the Tragedy of the Commons effect, attempts at monopoly become increasingly likely over time.

How Proof of Stake Addresses Monopoly Problems

Monopoly is still possible under proof-of-stake. However, proof-of-stake would be more secure against malicious attacks for two reasons.

Firstly, proof-of-stake makes establishing a verification monopoly more difficult. At the time of writing, an entrepreneur could achieve monopoly over proof-of-work by investing at most 10 million USD in computing hardware. The actual investment necessary might be less than this because other miners will exit as difficulty increases, but it is difficult to predict exactly how much exit will occur. If price remained constant in the face of extremely large purchases (unlikely), such an entrepreneur would need to invest at least 20 million USD to obtain monopoly under proof-of-stake. Since such a large purchase would dramatically increase bitcoin price, the entrepreneur would likely need to invest several times this amount. Thus, even now proof-of-stake monopoly would be several-fold more costly to achieve than proof-of-work monopoly. Over time the comparison of monopoly costs will become more and more dramatic. The ratio of bitcoin's mining rewards to market value is programmed to decline exponentially. As this happens, proof-of-work monopoly will become easier and easier to obtain, whereas obtaining proof-of-stake monopoly will become progressively more difficult as more of the total money supply is released into circulation.

Secondly, and perhaps more importantly, a proof-of-stake monopolist is more likely to behave benevolently exactly because of his stake in Bitcoin. In a benevolent monopoly, the currency txn continue as usual, but the monopolist earns all txn fees and coin generations. Other txn verifiers are shut out of the system, however. Since mining is not source of demand for bitcoin, bitcoin might retain most of its value in the event of a benevolent attack. Earnings from a benevolent attack are similar regardless of whether the attack occurs under proof-of-stake or proof-of-work. In a malicious attack, the attacker has some outside opportunity which allows profit from bitcoin's destruction (simple double-spends are not a plausible motivation; ownership of a competing payment platform is). At the same time, the attacker faces costs related to losses on bitcoin-specific investments which are necessary for the attack. It can be assumed that a malicious attack causes the purchasing power of bitcoin to fall to zero. Under such an attack, the proof-of-stake monopolist will lose his entire investment. By contrast, a malicious proof-of-work monopolist will be able to recover much of their hardware investment through resale. Recall also, that the necessary proof-of-work investment is much smaller than the proof-of-stake investment. Thus, the costs of a malicious attack are several-fold lower under proof-of-work. The low costs associated with malicious attack make a malicious attack more likely to occur.

Why Proof of Stake Would Likely Decrease Long-run Txn Fees By An Order of Magnitude

In a competitive market equilibrium, the total volume of txn fees must be equal to opportunity cost of all resources used to verify txns. Under proof-of-work mining, opportunity cost can be calculated as the total sum spent on mining electricity, mining equipment depreciation, mining labor, and a market rate of return on mining capital. Electricity costs, returns on mining equipment, and equipment depreciation costs are likely to dominate here. If these costs are not substantial, then it will be exceptionally easy to monopolize the mining network. The fees necessary to prevent monopolization will be onerous, possibly in excess of the 3% fee currently charged for credit card purchases. Under pure proof-of-stake, opportunity cost can be calculated as the total sum spent on mining labor and the market interest rate for risk-free bitcoin lending (hardware-related costs will be negligible). Since bitcoins are designed to appreciate over time due to hard-coded supply limitations, interest rates on risk-free bitcoin-denominated loans are likely to be negligible. Therefore, the total volume of txn fees under pure proof-of-stake will just need to be just sufficient to compensate labor involved in maintaining bandwidth and storage space. The associated txn fees will be exceptionally low. Despite these exceptionally low fees, a proof-of-stake network will be many times more costly to exploit than the proof-of-work network. Approximately, a proof-of-work network can be exploited using expenditure equal to about one years worth of currency generation and txn fees. By constrast, exploitation of a proof-of-stake network requires purchase of a majority or near majority of all extant coins.

Cunicula's Implementation of Mixed Proof-of-Work and Proof-of-Stake

Cunicula suggests that proof-of-stake could be implemented through a mixed Proof-of-Work / Proof-of-Stake system.

Useful Definitions

Coin-confirmations are defined as the product of the number of coins in an account multiplied by the number of confirmations on this account.

Confirmations are defined as the number of blocks mined since this account's private key was last used to send coins or sign a newly mined block.

Description of System

Each block must be signed by its miner using a single bitcoin account. The account used to sign a block must also be the recipient of txn fees and generation from this block. Blocks are mined by proof-of-work hashing as before, but with modified difficulty criteria. The difficulty criterion for block validity is modified as follows:

Hash generates valid block if and only if

Hash Difficulty >= (Aggregate difficulty)^{1/((1-p)}/({max(Coin-confirmations used to sign block,100 satoshi-confirmations)})^{p/(1-p)}

, where 0 <= p < 1. Stake becomes more and more important as p approaches 1. p=0.8 is suggested as an appropriate choice. p=0 is identical to the current proof-of-work system.

The maximum criteria allows for valid blocks to be generated even if no stakeholders exist, solving the problem of initial distribution.

As before aggregate difficulty is periodically adjusted to maintain a target generation rate of 1 block every 10 minutes.

Space for Criticism and Questions About Cunicula's Proposal [Cunicula promises not to edit this section, though others are free to do so as they feel.]

== Space for Response to Criticism and Questions About Cunicula's proposal [Cunicula will edit this.]

== Meni's Proposal for Proof-of-Stake == [This space is reserved for Meni to describe his system for proof-of-stake].