# Bitcoin:

A Peer-to-Peer Electronic Cash System

## Abstract

A purely peer-to-peer version of electronic cash would permit online payments to be sent directly from one party to another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be switched without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power. As long as a majority of CPU power is managed by knots that are not cooperating to attack the network, they’ll generate the longest chain and outpace attackers. The network itself requires minimal structure. Messages are broadcast on a best effort basis, and knots can leave and rejoin the network at will, accepting the longest proof-of-work chain as proof of what happened while they were gone.

## 1. Introduction

Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments. While the system works well enough for most transactions, it still suffers from the inherent weaknesses of the trust based model. Fully non-reversible transactions are not indeed possible, since financial institutions cannot avoid mediating disputes. The cost of mediation increases transaction costs, limiting the minimum practical transaction size and cutting off the possibility for puny casual transactions, and there is a broader cost in the loss of capability to make non-reversible payments for non-reversible services. With the possibility of reversal, the need for trust spreads. Merchants must be wary of their customers, hassling them for more information than they would otherwise need. A certain percentage of fraud is accepted as unavoidable. These costs and payment uncertainties can be avoided in person by using physical currency, but no mechanism exists to make payments over a communications channel without a trusted party.

What is needed is an electronic payment system based on cryptographic proof instead of trust, permitting any two willing parties to transact directly with each other without the need for a trusted third party. Transactions that are computationally impractical to switch sides would protect sellers from fraud, and routine escrow mechanisms could lightly be implemented to protect buyers. In this paper, we propose a solution to the double-spending problem using a peer-to-peer distributed timestamp server to generate computational proof of the chronological order of transactions. The system is secure as long as fair knots collectively control more CPU power than any cooperating group of attacker knots.

## Two. Transactions

We define an electronic coin as a chain of digital signatures. Each holder transfers the coin to the next by digitally signing a hash of the previous transaction and the public key of the next holder and adding these to the end of the coin. A payee can verify the signatures to verify the chain of ownership.

The problem of course is the payee can’t verify that one of the owners did not double-spend the coin. A common solution is to introduce a trusted central authority, or mint, that checks every transaction for dual spending. After each transaction, the coin must be returned to the mint to issue a fresh coin, and only coins issued directly from the mint are trusted not to be double-spent. The problem with this solution is that the fate of the entire money system depends on the company running the mint, with every transaction having to go through them, just like a bank.

We need a way for the payee to know that the previous owners did not sign any earlier transactions. For our purposes, the earliest transaction is the one that counts, so we don’t care about later attempts to double-spend. The only way to confirm the absence of a transaction is to be aware of all transactions. In the mint based model, the mint was aware of all transactions and determined which arrived very first. To accomplish this without a trusted party, transactions must be publicly announced [1] , and we need a system for participants to agree on a single history of the order in which they were received. The payee needs proof that at the time of each transaction, the majority of knots agreed it was the very first received.

## Trio. Timestamp Server

The solution we propose commences with a timestamp server. A timestamp server works by taking a hash of a block of items to be timestamped and widely publishing the hash, such as in a newspaper or Usenet post [2-5] . The timestamp proves that the data must have existed at the time, obviously, in order to get into the hash. Each timestamp includes the previous timestamp in its hash, forming a chain, with each extra timestamp reinforcing the ones before it.

## Four. Proof-of-Work

To implement a distributed timestamp server on a peer-to-peer basis, we will need to use a proof-of-work system similar to Adam Back’s Hashcash [6] , rather than newspaper or Usenet posts. The proof-of-work involves scanning for a value that when hashed, such as with SHA-256, the hash starts with a number of zero bits. The average work required is exponential in the number of zero bits required and can be verified by executing a single hash.

For our timestamp network, we implement the proof-of-work by incrementing a nonce in the block until a value is found that gives the block’s hash the required zero bits. Once the CPU effort has been expended to make it sate the proof-of-work, the block cannot be switched without redoing the work. As later blocks are chained after it, the work to switch the block would include redoing all the blocks after it.

The proof-of-work also solves the problem of determining representation in majority decision making. If the majority were based on one-IP-address-one-vote, it could be subverted by anyone able to allocate many IPs. Proof-of-work is essentially one-CPU-one-vote. The majority decision is represented by the longest chain, which has the greatest proof-of-work effort invested in it. If a majority of CPU power is managed by fair knots, the fair chain will grow the fastest and outpace any contesting chains. To modify a past block, an attacker would have to redo the proof-of-work of the block and all blocks after it and then catch up with and surpass the work of the fair knots. We will showcase later that the probability of a slower attacker catching up diminishes exponentially as subsequent blocks are added.

To compensate for enlargening hardware speed and varying interest in running knots over time, the proof-of-work difficulty is determined by a moving average targeting an average number of blocks per hour. If they’re generated too prompt, the difficulty increases.

## Five. Network

The steps to run the network are as goes after:

1. Fresh transactions are broadcast to all knots.
2. Each knot collects fresh transactions into a block.
3. Each knot works on finding a difficult proof-of-work for its block.
4. When a knot finds a proof-of-work, it broadcasts the block to all knots.
5. Knots accept the block only if all transactions in it are valid and not already spent.
6. Knots express their acceptance of the block by working on creating the next block in the chain, using the hash of the accepted block as the previous hash.

Knots always consider the longest chain to be the correct one and will keep working on extending it. If two knots broadcast different versions of the next block at the same time, some knots may receive one or the other very first. In that case, they work on the very first one they received, but save the other branch in case it becomes longer. The tie will be cracked when the next proof-of-work is found and one branch becomes longer; the knots that were working on the other branch will then switch to the longer one.

Fresh transaction broadcasts do not necessarily need to reach all knots. As long as they reach many knots, they will get into a block before long. Block broadcasts are also tolerant of dropped messages. If a knot does not receive a block, it will request it when it receives the next block and realizes it missed one.

## 6. Incentive

By convention, the very first transaction in a block is a special transaction that starts a fresh coin possessed by the creator of the block. This adds an incentive for knots to support the network, and provides a way to primarily distribute coins into circulation, since there is no central authority to issue them. The stable addition of a constant of amount of fresh coins is analogous to gold miners expending resources to add gold to circulation. In our case, it is CPU time and violet wand that is expended.

The incentive can also be funded with transaction fees. If the output value of a transaction is less than its input value, the difference is a transaction fee that is added to the incentive value of the block containing the transaction. Once a predetermined number of coins have entered circulation, the incentive can transition entirely to transaction fees and be fully inflation free.

The incentive may help encourage knots to stay fair. If a greedy attacker is able to assemble more CPU power than all the fair knots, he would have to choose inbetween using it to defraud people by stealing back his payments, or using it to generate fresh coins. He ought to find it more profitable to play by the rules, such rules that favour him with more fresh coins than everyone else combined, than to undermine the system and the validity of his own wealth.

## 7. Reclaiming Disk Space

Once the latest transaction in a coin is buried under enough blocks, the spent transactions before it can be discarded to save disk space. To facilitate this without cracking the block’s hash, transactions are hashed in a Merkle Tree [7] [Two] [Five] , with only the root included in the block’s hash. Old blocks can then be compacted by stubbing off branches of the tree. The interior hashes do not need to be stored.

A block header with no transactions would be about eighty bytes. If we suppose blocks are generated every ten minutes, eighty bytes * six * twenty four * three hundred sixty five = Four.2MB per year. With computer systems typically selling with 2GB of RAM as of 2008, and Moore’s Law predicting current growth of 1.2GB per year, storage should not be a problem even if the block headers must be kept in memory.

## 8. Simplified Payment Verification

It is possible to verify payments without running a total network knot. A user only needs to keep a copy of the block headers of the longest proof-of-work chain, which he can get by querying network knots until he’s coaxed he has the longest chain, and obtain the Merkle branch linking the transaction to the block it’s timestamped in. He can’t check the transaction for himself, but by linking it to a place in the chain, he can see that a network knot has accepted it, and blocks added after it further confirm the network has accepted it.

As such, the verification is reliable as long as fair knots control the network, but is more vulnerable if the network is overpowered by an attacker. While network knots can verify transactions for themselves, the simplified method can be fooled by an attacker’s fabricated transactions for as long as the attacker can proceed to overpower the network. One strategy to protect against this would be to accept alerts from network knots when they detect an invalid block, prompting the user’s software to download the utter block and alerted transactions to confirm the inconsistency. Businesses that receive frequent payments will most likely still want to run their own knots for more independent security and quicker verification.

## 9. Combining and Splitting Value

Albeit it would be possible to treat coins individually, it would be unwieldy to make a separate transaction for every cent in a transfer. To permit value to be split and combined, transactions contain numerous inputs and outputs. Normally there will be either a single input from a larger previous transaction or numerous inputs combining smaller amounts, and at most two outputs: one for the payment, and one returning the switch, if any, back to the sender.

It should be noted that fan-out, where a transaction depends on several transactions, and those transactions depend on many more, is not a problem here. There is never the need to extract a finish standalone copy of a transaction’s history.

## Ten. Privacy

The traditional banking model achieves a level of privacy by limiting access to information to the parties involved and the trusted third party. The necessity to announce all transactions publicly precludes this method, but privacy can still be maintained by violating the flow of information in another place: by keeping public keys anonymous. The public can see that someone is sending an amount to someone else, but without information linking the transaction to anyone. This is similar to the level of information released by stock exchanges, where the time and size of individual trades, the “gauze”, is made public, but without telling who the parties were.

As an extra firewall, a fresh key pair should be used for each transaction to keep them from being linked to a common possessor. Some linking is still unavoidable with multi-input transactions, which necessarily expose that their inputs were possessed by the same holder. The risk is that if the proprietor of a key is exposed, linking could expose other transactions that belonged to the same possessor.

## 11. Calculations

We consider the script of an attacker attempting to generate an alternate chain swifter than the fair chain. Even if this is accomplished, it does not throw the system open to arbitrary switches, such as creating value out of skinny air or taking money that never belonged to the attacker. Knots are not going to accept an invalid transaction as payment, and fair knots will never accept a block containing them. An attacker can only attempt to switch one of his own transactions to take back money he recently spent.

The race inbetween the fair chain and an attacker chain can be characterized as a Binomial Random Walk. The success event is the fair chain being extended by one block, enlargening its lead by +1, and the failure event is the attacker’s chain being extended by one block, reducing the gap by -1.

The probability of an attacker catching up from a given deficit is analogous to a Gambler’s Ruin problem. Suppose a gambler with unlimited credit starts at a deficit and plays potentially an infinite number of trials to attempt to reach breakeven. We can calculate the probability he ever reaches breakeven, or that an attacker ever catches up with the fair chain, as goes after [8] :

Given our assumption that $p \gt q$, the probability drops exponentially as the number of blocks the attacker has to catch up with increases. With the odds against him, if he doesn’t make a fortunate lunge forward early on, his chances become vanishingly petite as he falls further behind.

We now consider how long the recipient of a fresh transaction needs to wait before being reasonably certain the sender can’t switch the transaction. We assume the sender is an attacker who wants to make the recipient believe he paid him for a while, then switch it to pay back to himself after some time has passed. The receiver will be alerted when that happens, but the sender hopes it will be too late.

The receiver generates a fresh key pair and gives the public key to the sender shortly before signing. This prevents the sender from preparing a chain of blocks ahead of time by working on it continuously until he is fortunate enough to get far enough ahead, then executing the transaction at that moment. Once the transaction is sent, the dishonest sender starts working in secret on a parallel chain containing an alternate version of his transaction.

The recipient waits until the transaction has been added to a block and $z$ blocks have been linked after it. He doesn’t know the exact amount of progress the attacker has made, but assuming the fair blocks took the average expected time per block, the attacker’s potential progress will be a Poisson distribution with expected value:

$$\large \lambda = z \frac qp$$

To get the probability the attacker could still catch up now, we multiply the Poisson density for each amount of progress he could have made by the probability he could catch up from that point:

Rearranging to avoid summing the infinite tail of the distribution.

Converting to C code.

Running some results, we can see the probability drop off exponentially with $z$.

Solving for P less than 0.1%.

## 12. Conclusion

We have proposed a system for electronic transactions without relying on trust. We commenced with the usual framework of coins made from digital signatures, which provides strong control of ownership, but is incomplete without a way to prevent double-spending. To solve this, we proposed a peer-to-peer network using proof-of-work to record a public history of transactions that quickly becomes computationally impractical for an attacker to switch if fair knots control a majority of CPU power. The network is sturdy in its unstructured plainness. Knots work all at once with little coordination. They do not need to be identified, since messages are not routed to any particular place and only need to be delivered on a best effort basis. Knots can leave and rejoin the network at will, accepting the proof-of-work chain as proof of what happened while they were gone. They vote with their CPU power, voicing their acceptance of valid blocks by working on extending them and rejecting invalid blocks by refusing to work on them. Any needed rules and incentives can be enforced with this consensus mechanism.

## References

S. Haber, W.S. Stornetta, “How to time-stamp a digital document,” In Journal of Cryptology, vol Trio, no Two, pages 99-111, 1991. ↩

D. Bayer, S. Haber, W.S. Stornetta, “Improving the efficiency and reliability of digital time-stamping,” In Sequences II: Methods in Communication, Security and Computer Science, pages 329-334, 1993. ↩

S. Haber, W.S. Stornetta, “Secure names for bit-strings,” In Proceedings of the 4th ACM Conference on Computer and Communications Security, pages 28-35, April 1997. ↩ ↩

R.C. Merkle, “Protocols for public key cryptosystems,” In Proc. One thousand nine hundred eighty Symposium on Security and Privacy, IEEE Computer Society, pages 122-133, April 1980. ↩

# What is Multi-Sig, and What Can It Do?

Multi-sig holds enormous potential: trustless escrow, trustless margin, and sturdy security for consumers, businesses, and anyone who holds or wants to hold bitcoins.

## Introduction

Bitcoin is stored in “addresses” which are based on public/private ECDSA key pairs. For most of Bitcoin’s history, each address was based on a single private key. Even at the time of writing (November 2014), 97% of Bitcoin is stored using single-­key addresses. These addresses (aka “standard addresses”), can be recognized by the fact that they always commence with a “1.” Anyone who knows the one private key corresponding to a given single-­key Bitcoin address can stir those funds — period. It’s often said that possession is nine-­tenths of the law, but with Bitcoin, possession of the private key is the law, since transfers are effectively irreversible. As far as the Bitcoin network is worried, if you wield the private key for an address, you are authorized to stir funds. This black-­or-­white nature of single-­key storage has led to a number of critical problems for Bitcoin.

## Problem: Security

At the simplest level, a single-­key Bitcoin wallet is little more than a collection of private keys which permit the user to spend his or her bitcoin, while attempting to keep those keys safe from theft. Keys for a single-­key wallet are typically generated and stored on a single machine, using encryption to secure them while on disk. However, despite taking best practices for securing keys, any machine which stores a single-­key wallet represents a single point of failure. If the wallet file can be stolen, the encryption can be attacked offline, or the hacker or malware can simply lie in wait and key-­log the user’s password. As Bitcoin has grown more valuable, existing malware has been re-­engineered to specifically target Bitcoin wallets. It is this fundamental security risk of single-­key storage that has led to the development of elaborate protocols for generating and storing keys totally offline, in physical vaults (generally referred to as “cold storage” in the industry.) However, cold storage has its own risks and weaknesses. If the random number generator (RNG) on the single machine used to generate the key had weaknesses, funds may be at risk even without any breach of the machine itself. Offline cold storage solutions do alleviate some security concerns, but at the expense of introducing significant operational burdens.

## Problem: Access Control

How can businesses effectively use Bitcoin? Businesses usually delegate responsibility for technology integration to their IT staff. But offloading responsibility for a Bitcoin wallet to the IT department is like leaving a pile of $100 bills on a table in the middle of the office. Since anyone with access to the keys can stir the money without leaving a trace, if numerous people have access to the keys, there is no real way to achieve accountability or prevent insider theft. Bitcoin’s history is littered with insider thefts which are publicly claimed to be outer hacks. The Bitcoin businesses which have successfully avoided theft have tightly managed the number of people who have access to the keys. They have relied on the principals of the businesses to be the ultimate gatekeepers, as well as using physical safeguards and key-­splitting technologies to ensure a single person cannot transact on his own. But for larger businesses to embrace Bitcoin, it is not a tenable solution to require the CEO and CFO to be involved in every transaction. Organizations need to be able to define their own internal policies on who can transact, for how much, and with whose approval. They need the type of controls that they would be able to have with standard corporate treasury banking software. One way to achieve such controls is to delegate finish custody of the business’s Bitcoin to another entity, essentially a Bitcoin bank. But there is also another way. ## The Solution: Multi-sig Since early 2012, Bitcoin has had an alternative to single-­key addresses. Around that time, a fresh type of address called pay-­to-­script-­hash (P2SH) was defined and standardized. P2SH addresses can be recognized by the fact that they begin with a “3” instead of a “1.” Among the functionality supported by P2SH addresses is the capability to require numerous private keys in order to transact, known as multi-­signature, or more commonly, multi-­sig. A P2SH address can support arbitrary sets of N keys, any M of which are required to transact — this is commonly referred to as “M-­of-­N.” In practice, the blockchain does enforce some boundaries as to the size of N, and by far the most typical multi-­sig implementations are of the form 2-­of-­2 or 2-­of-­3. (Note that using this terminology, a single-­key address would be considered 1-­of-­1.) The easiest real-­world analogy for explaining multi-­sig is a safe deposit box with two keys, one held by the customer, the other held by the bank. In order to open the box, both keys are required, making a safe deposit box analogous to a 2-­of-­2 multi-­sig address. There are some instantaneous advantages that can be gained from using multi-­sig technology. Very first, we can fully eliminate single points of failure by ensuring that the keys for an address are generated and stored on downright separate devices. For example, one key might be generated on the user’s laptop, while the other is generated on the phone, making it necessary to have both devices in order to transact. Malware which infects the laptop cannot steal any funds, because it does not have the key stored on the phone. Secondly, we can achieve redundancy. In the previous screenplay, what happens if the user loses their phone? If a third key were kept offline in a vault, and a 2-­of-­3 scheme were used, then the user could tolerate losing either device, and still manage to recover his funds using the remaining device in conjunction with the offline key. Third, we can begin to address the access control problem. A spouse and wifey can construct a multi-­sig wallet which requires both of them to transact, while a 3-­person partnership can create a wallet which requires at least two of them to be in agreement. Additionally, entirely fresh possibilities can be unlocked by multi-­sig technologies — consider the following scripts. ### Trustless Escrow Alice wants to send Bitcoin to Bob, but only if Bob produces the merchandise he has promised. Bob wants to ensure he is paid for his merchandise. They both trust Trent to adjudicate a dispute but do not wish to trust him with the funds. They create a 2-­of-­3 multi-­sig address with one key each from Alice, Bob and Trent. If the transaction goes slickly, Alice and Bob can jointly release the funds without Trent’s involvement. If there is a dispute, Trent can adjudicate, and can budge the funds in conjunction with either Alice or Bob. During the course of the transaction, the Bitcoin is effectively in a kind of limbo, since no one person can stir the funds on his own. ### Organizational Thresholds A company desires to set up a Bitcoin wallet accessible by three of its employees, but require two of them to be involved on any transaction exceeding$Five,000. In order to do so, it creates a 2-­of-­2 multi-­sig address where it holds one key, and an outside policy-­enforcement service holds the other key.

When one of the three employees wishes to transact, he signs the transaction with the company’s key, authenticates to the service, and requests a co-­signature. The policy service uses the pre-­arranged spending limit to determine whether to co-­sign the transaction or to request a secondary approval from one of the other two employees. The service cannot steal funds, but it can block the company’s capability to transact. If that is not desirable, the company can instead use a 2-­of-­3 configuration in which another employee or security officer retains an extra backup key which permits the company to recover the funds in the case the policy service becomes uncooperative.

### Trustless Margin

A user wishes to trade on an exchange, but does not wish to entrust total custody to the exchange, since he does not fully trust their security measures. He establishes a 2-­of-­2 wallet in which he and the exchange share a single key, and an outside policy-­enforcement service holds the other key. He deposits Bitcoin into the wallet which the exchange permits him to use as margin for trading, loans or other purposes. The role of the policy enforcer in this case is to ensure that the customer cannot withdraw funds while he has outstanding ordersor unsettled trades, while assuring the customer that the exchange cannot unilaterally steal or lose all funds.

As the above scripts demonstrate, multi-­sig can strongly benefit both individuals and organizations in improving security, establishing access controls, and enabling the delegation of partial trust. As exchanges and other businesses begin to enable customers to deposit without fear of loss, there will be enhanced consumer pressure on other businesses to adopt similar technology. And if the risk of loss can be minimized, there should be substantial benefits to transparency and liquidity across the entire ecosystem. For these reasons, it is anticipated that the majority of Bitcoin will, over time, be moved to P2SH multi-­sig addresses.

In the traditional world of finance, a custodian is a trusted third party who holds assets on behalf of another. It’s significant to note that with Bitcoin, there is no longer always a clear custodian of funds. In a 3-­of-­3 multi-­sig wallet where Bank of America, JP Morgan and State Street each hold one key, who is the custodian? With Bitcoin, final custody lies only with the blockchain, which is, of course, decentralized itself. As a consequence, lawmakers and regulators will need to understand this fresh paradigm as they best determine how to adapt existing regulations and create fresh ones.

Ben Davenport is co-­founder and chief product officer of BitGo, a leading multi-­sig Bitcoin security company.

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