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((("pycoin library")))The Python library http://github.com/richardkiss/pycoin[+pycoin+], originally written and maintained by Richard Kiss, is a Python-based library that supports manipulation of bitcoin keys and transactions, even supporting the scripting language enough to properly deal with nonstandard transactions.
The pycoin library supports both Python 2 (2.7.x) and Python 3 (after 3.3) and comes with some handy command-line utilities, +ku+ and +tx+.
The pycoin library supports both Python 2 (2.7.x) and Python 3 (3.3 and later) and comes with some handy command-line utilities, +ku+ and +tx+.
=== Key Utility (KU)

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@ -150,7 +150,7 @@ Bitcoin transactions are irreversible. Most electronic payment networks such as
[role="pagebreak-before"]
Here are some methods for getting bitcoin as a new user:
* Find a friend who has bitcoin and buy some from him or her directly. Many bitcoin users start this way. This method is the least complicated. One way to meet people with bitcoin is to attend a local bitcoin meetup listed at https://meetup.com[Meetup.com].
* Find a friend who has bitcoin and buy some from him or her directly. Many bitcoin users start this way. This method is the least complicated. One way to meet people with bitcoin is to attend a local bitcoin meetup listed at https://bitcoin.meetup.com[Meetup.com].
* Use a classified service such as pass:[<a class="orm:hideurl" href="https://localbitcoins.com/">localbitcoins.com</a>] to find a seller in your area to buy bitcoin for cash in an in-person transaction.
* Earn bitcoin by selling a product or service for bitcoin. If you are a programmer, sell your programming skills. If you're a hairdresser, cut hair for bitcoin.
* ((("Coin ATM Radar")))((("ATMs, locating")))Use a bitcoin ATM in your city. A bitcoin ATM is a machine that accepts cash and sends bitcoin to your smartphone bitcoin wallet. Find a bitcoin ATM close to you using an online map from http://coinatmradar.com[Coin ATM Radar].

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=== Transactions, Blocks, Mining, and the Blockchain
((("bitcoin", "overview of", id="BCover02")))((("central trusted authority")))((("decentralized systems", "bitcoin overview", id="DCSover02")))The bitcoin system, unlike traditional banking and payment systems, is based on decentralized trust. Instead of a central trusted authority, in bitcoin, trust is achieved as an emergent property from the interactions of different participants in the bitcoin system. In this chapter, we will examine bitcoin from a high level by tracking a single transaction through the bitcoin system and watch as it becomes "trusted" and accepted by the bitcoin mechanism of distributed consensus and is finally recorded on the blockchain, the distributed ledger of all transactions. Subsequent chapters will delve into the technology behind transactions, the network, and mining.
((("bitcoin", "overview of", id="BCover02")))((("central trusted authority")))((("decentralized systems", "bitcoin overview", id="DCSover02")))The bitcoin system, unlike traditional banking and payment systems, is based on decentralized trust. Instead of a central trusted authority, in bitcoin, trust is achieved as an emergent property from the interactions of different participants in the bitcoin system. In this chapter, we will examine bitcoin from a high level by tracking a single transaction through the bitcoin system and watch as it becomes "trusted" and accepted by the bitcoin mechanism of distributed consensus and is finally recorded on the blockchain, the distributed ledger of all transactions. Subsequent chapters will delve into the technology behind transactions, the network, and mining.
==== Bitcoin Overview
In the overview diagram shown in <<bitcoin-overview>>, we see that the bitcoin system consists of users with wallets containing keys, transactions that are propagated across the network, and miners who produce (through competitive computation) the consensus blockchain, which is the authoritative ledger of all transactions.
In the overview diagram shown in <<bitcoin-overview>>, we see that the bitcoin system consists of users with wallets containing keys, transactions that are propagated across the network, and miners who produce (through competitive computation) the consensus blockchain, which is the authoritative ledger of all transactions.
((("blockchain explorer sites")))Each example in this chapter is based on an actual transaction made on the bitcoin network, simulating the interactions between the users (Joe, Alice, Bob, and Gopesh) by sending funds from one wallet to another. While tracking a transaction through the bitcoin network to the blockchain, we will use a _blockchain explorer_ site to visualize each step. A blockchain explorer is a web application that operates as a bitcoin search engine, in that it allows you to search for addresses, transactions, and blocks and see the relationships and flows between them.
@ -16,9 +16,8 @@ In the overview diagram shown in <<bitcoin-overview>>, we see that the bitcoin s
.Bitcoin overview
image::images/mbc2_0201.png["Bitcoin Overview"]
((("Bitcoin Block Explorer")))((("BlockCypher Explorer")))((("blockchain.info")))((("BitPay Insight")))Popular blockchain explorers include:
((("Bitcoin Block Explorer")))((("BlockCypher Explorer")))((("blockchain.info")))((("BitPay Insight")))Popular blockchain explorers include:
* https://blockexplorer.com[Bitcoin Block Explorer]
* https://live.blockcypher.com[BlockCypher Explorer]
* https://blockchain.info[blockchain.info]
* https://insight.bitpay.com[BitPay Insight]
@ -29,7 +28,7 @@ Each of these has a search function that can take a bitcoin address, transaction
[[cup_of_coffee]]
==== Buying a Cup of Coffee
((("use cases", "buying coffee", id="UCcoffee02")))Alice, introduced in the previous chapter, is a new user who has just acquired her first bitcoin. In <<getting_first_bitcoin>>, Alice met with her friend Joe to exchange some cash for bitcoin. The transaction created by Joe funded Alice's wallet with 0.10 BTC. Now Alice will make her first retail transaction, buying a cup of coffee at Bob's coffee shop in Palo Alto, California.
((("use cases", "buying coffee", id="UCcoffee02")))Alice, introduced in the previous chapter, is a new user who has just acquired her first bitcoin. In <<getting_first_bitcoin>>, Alice met with her friend Joe to exchange some cash for bitcoin. The transaction created by Joe funded Alice's wallet with 0.10 BTC. Now Alice will make her first retail transaction, buying a cup of coffee at Bob's coffee shop in Palo Alto, California.
((("exchange rates", "determining")))Bob's Cafe recently started accepting bitcoin payments by adding a bitcoin option to its point-of-sale system. The prices at Bob's Cafe are listed in the local currency (US dollars), but at the register, customers have the option of paying in either dollars or bitcoin. Alice places her order for a cup of coffee and Bob enters it into the register, as he does for all transactions. The point-of-sale system automatically converts the total price from US dollars to bitcoin at the prevailing market rate and displays the price in both currencies:
@ -44,7 +43,7 @@ $1.50 USD
((("payment requests")))((("QR codes", "payment requests")))Bob's point-of-sale system will also automatically create a special QR code containing a _payment request_ (see <<payment-request-QR>>).
Unlike a QR code that simply contains a destination bitcoin address, a payment request is a QR-encoded URL that contains a destination address, a payment amount, and a generic description such as "Bob's Cafe." This allows a bitcoin wallet application to prefill the information used to send the payment while showing a human-readable description to the user. You can scan the QR code with a bitcoin wallet application to see what Alice would see.
Unlike a QR code that simply contains a destination bitcoin address, a payment request is a QR-encoded URL that contains a destination address, a payment amount, and a generic description such as "Bob's Cafe." This allows a bitcoin wallet application to prefill the information used to send the payment while showing a human-readable description to the user. You can scan the QR code with a bitcoin wallet application to see what Alice would see.
[[payment-request-QR]]
@ -53,7 +52,7 @@ image::images/mbc2_0202.png["payment-request"]
[TIP]
====
((("QR codes", "warnings and cautions")))((("transactions", "warnings and cautions")))((("warnings and cautions", "avoid sending money to addresses appearing in book")))Try to scan this with your wallet to see the address and amount but DO NOT SEND MONEY.
((("QR codes", "warnings and cautions")))((("transactions", "warnings and cautions")))((("warnings and cautions", "avoid sending money to addresses appearing in book")))Try to scan this with your wallet to see the address and amount but DO NOT SEND MONEY.
====
[[payment-request-URL]]
.The payment request QR code encodes the following URL, defined in BIP-21:
@ -63,7 +62,7 @@ amount=0.015&
label=Bob%27s%20Cafe&
message=Purchase%20at%20Bob%27s%20Cafe
Components of the URL
Components of the URL
A bitcoin address: "1GdK9UzpHBzqzX2A9JFP3Di4weBwqgmoQA"
The payment amount: "0.015"
@ -77,31 +76,31 @@ In the following sections, we will examine this transaction in more detail. We'l
[NOTE]
====
((("fractional values")))((("milli-bitcoin")))((("satoshis")))The bitcoin network can transact in fractional values, e.g., from millibitcoin (1/1000th of a bitcoin) down to 1/100,000,000th of a bitcoin, which is known as a satoshi. Throughout this book, we’ll use the term “bitcoin” to refer to any quantity of bitcoin currency, from the smallest unit (1 satoshi) to the total number (21,000,000) of all bitcoin that will ever be mined.
((("fractional values")))((("milli-bitcoin")))((("satoshis")))The bitcoin network can transact in fractional values, e.g., from millibitcoin (1/1000th of a bitcoin) down to 1/100,000,000th of a bitcoin, which is known as a satoshi. Throughout this book, we’ll use the term “bitcoin” to refer to any quantity of bitcoin currency, from the smallest unit (1 satoshi) to the total number (21,000,000) of all bitcoin that will ever be mined.
====
You can examine Alice's transaction to Bob's Cafe on the blockchain using a block explorer site (<<view_alice_transaction>>):
[[view_alice_transaction]]
.View Alice's transaction on https://blockexplorer.com/tx/0627052b6f28912f2703066a912ea577f2ce4da4caa5a5fbd8a57286c345c2f2[blockexplorer.com]
.View Alice's transaction on https://blockchain.info/tx/0627052b6f28912f2703066a912ea577f2ce4da4caa5a5fbd8a57286c345c2f2[blockchain.info]
====
----
https://blockexplorer.com/tx/0627052b6f28912f2703066a912ea577f2ce4da4caa5a5fbd8a57286c345c2f2
https://blockchain.info/tx/0627052b6f28912f2703066a912ea577f2ce4da4caa5a5fbd8a57286c345c2f2
----
====
=== Bitcoin Transactions
((("transactions", "defined")))In simple terms, a transaction tells the network that the owner of some bitcoin value has authorized the transfer of that value to another owner. The new owner can now spend the bitcoin by creating another transaction that authorizes the transfer to another owner, and so on, in a chain of ownership.
((("transactions", "defined")))In simple terms, a transaction tells the network that the owner of some bitcoin value has authorized the transfer of that value to another owner. The new owner can now spend the bitcoin by creating another transaction that authorizes the transfer to another owner, and so on, in a chain of ownership.
==== Transaction Inputs and Outputs
((("transactions", "overview of", id="Tover02")))((("outputs and inputs", "basics of")))Transactions are like lines in a double-entry bookkeeping ledger. Each transaction contains one or more "inputs," which are like debits against a bitcoin account. On the other side of the transaction, there are one or more "outputs," which are like credits added to a bitcoin account. ((("fees", "transaction fees")))The inputs and outputs (debits and credits) do not necessarily add up to the same amount. Instead, outputs add up to slightly less than inputs and the difference represents an implied _transaction fee_, which is a small payment collected by the miner who includes the transaction in the ledger. A bitcoin transaction is shown as a bookkeeping ledger entry in <<transaction-double-entry>>.
((("transactions", "overview of", id="Tover02")))((("outputs and inputs", "basics of")))Transactions are like lines in a double-entry bookkeeping ledger. Each transaction contains one or more "inputs," which are like debits against a bitcoin account. On the other side of the transaction, there are one or more "outputs," which are like credits added to a bitcoin account. ((("fees", "transaction fees")))The inputs and outputs (debits and credits) do not necessarily add up to the same amount. Instead, outputs add up to slightly less than inputs and the difference represents an implied _transaction fee_, which is a small payment collected by the miner who includes the transaction in the ledger. A bitcoin transaction is shown as a bookkeeping ledger entry in <<transaction-double-entry>>.
The transaction also contains proof of ownership for each amount of bitcoin (inputs) whose value is being spent, in the form of a digital signature from the owner, which can be independently validated by anyone. ((("spending bitcoin", "defined")))In bitcoin terms, "spending" is signing a transaction that transfers value from a previous transaction over to a new owner identified by a bitcoin address.
[[transaction-double-entry]]
.Transaction as double-entry bookkeeping
.Transaction as double-entry bookkeeping
image::images/mbc2_0203.png["Transaction Double-Entry"]
==== Transaction Chains
@ -114,7 +113,7 @@ image::images/mbc2_0204.png["Transaction chain"]
==== Making Change
((("change, making")))((("change addresses")))((("addresses", "change addresses")))Many bitcoin transactions will include outputs that reference both an address of the new owner and an address of the current owner, called the _change_ address. This is because transaction inputs, like currency notes, cannot be divided. If you purchase a $5 US dollar item in a store but use a $20 US dollar bill to pay for the item, you expect to receive $15 US dollars in change. The same concept applies to bitcoin transaction inputs. If you purchased an item that costs 5 bitcoin but only had a 20 bitcoin input to use, you would send one output of 5 bitcoin to the store owner and one output of 15 bitcoin back to yourself as change (less any applicable transaction fee). Importantly, the change address does not have to be the same address as that of the input and for privacy reasons is often a new address from the owner's wallet.
((("change, making")))((("change addresses")))((("addresses", "change addresses")))Many bitcoin transactions will include outputs that reference both an address of the new owner and an address of the current owner, called the _change_ address. This is because transaction inputs, like currency notes, cannot be divided. If you purchase a $5 US dollar item in a store but use a $20 US dollar bill to pay for the item, you expect to receive $15 US dollars in change. The same concept applies to bitcoin transaction inputs. If you purchased an item that costs 5 bitcoin but only had a 20 bitcoin input to use, you would send one output of 5 bitcoin to the store owner and one output of 15 bitcoin back to yourself as change (less any applicable transaction fee). Importantly, the change address does not have to be the same address as that of the input and for privacy reasons is often a new address from the owner's wallet.
Different wallets may use different strategies when aggregating inputs to make a payment requested by the user. They might aggregate many small inputs, or use one that is equal to or larger than the desired payment. Unless the wallet can aggregate inputs in such a way to exactly match the desired payment plus transaction fees, the wallet will need to generate some change. This is very similar to how people handle cash. If you always use the largest bill in your pocket, you will end up with a pocket full of loose change. If you only use the loose change, you'll always have only big bills. People subconsciously find a balance between these two extremes, and bitcoin wallet developers strive to program this balance.
@ -134,7 +133,7 @@ Another common form of transaction is one that aggregates several inputs into a
.Transaction aggregating funds
image::images/mbc2_0206.png["Aggregating Transaction"]
Finally, another transaction form that is seen often on the bitcoin ledger is a transaction that distributes one input to multiple outputs representing multiple recipients (see <<transaction-distributing>>). This type of transaction is sometimes used by commercial entities to distribute funds, such as when processing payroll payments to multiple employees.((("", startref="Tover02")))
Finally, another transaction form that is seen often on the bitcoin ledger is a transaction that distributes one input to multiple outputs representing multiple recipients (see <<transaction-distributing>>). This type of transaction is sometimes used by commercial entities to distribute funds, such as when processing payroll payments to multiple employees.((("", startref="Tover02")))
[[transaction-distributing]]
.Transaction distributing funds
@ -146,9 +145,9 @@ image::images/mbc2_0207.png["Distributing Transaction"]
==== Getting the Right Inputs
((("outputs and inputs", "locating and tracking inputs")))Alice's wallet application will first have to find inputs that can pay the amount she wants to send to Bob. Most wallets keep track of all the available outputs belonging to addresses in the wallet. Therefore, Alice's wallet would contain a copy of the transaction output from Joe's transaction, which was created in exchange for cash (see <<getting_first_bitcoin>>). A bitcoin wallet application that runs as a full-node client actually contains a copy of every unspent output from every transaction in the blockchain. This allows a wallet to construct transaction inputs as well as quickly verify incoming transactions as having correct inputs. However, because a full-node client takes up a lot of disk space, most user wallets run "lightweight" clients that track only the user's own unspent outputs.
If the wallet application does not maintain a copy of unspent transaction outputs, it can query the bitcoin network to retrieve this information using a variety of APIs available by different providers or by asking a full-node using an application programming interface (API) call. <<example_2-2>> shows a API request, constructed as an HTTP GET command to a specific URL. This URL will return all the unspent transaction outputs for an address, giving any application the information it needs to construct transaction inputs for spending. We use the simple command-line HTTP client _cURL_ to retrieve the response.
((("outputs and inputs", "locating and tracking inputs")))Alice's wallet application will first have to find inputs that can pay the amount she wants to send to Bob. Most wallets keep track of all the available outputs belonging to addresses in the wallet. Therefore, Alice's wallet would contain a copy of the transaction output from Joe's transaction, which was created in exchange for cash (see <<getting_first_bitcoin>>). A bitcoin wallet application that runs as a full-node client actually contains a copy of every unspent output from every transaction in the blockchain. This allows a wallet to construct transaction inputs as well as quickly verify incoming transactions as having correct inputs. However, because a full-node client takes up a lot of disk space, most user wallets run "lightweight" clients that track only the user's own unspent outputs.
If the wallet application does not maintain a copy of unspent transaction outputs, it can query the bitcoin network to retrieve this information using a variety of APIs available by different providers or by asking a full-node using an application programming interface (API) call. <<example_2-2>> shows an API request, constructed as an HTTP GET command to a specific URL. This URL will return all the unspent transaction outputs for an address, giving any application the information it needs to construct transaction inputs for spending. We use the simple command-line HTTP client _cURL_ to retrieve the response.
[[example_2-2]]
.Look up all the unspent outputs for Alice's bitcoin address
@ -162,19 +161,19 @@ $ curl https://blockchain.info/unspent?active=1Cdid9KFAaatwczBwBttQcwXYCpvK8h7FK
[source,json]
----
{
"unspent_outputs":[
{
"tx_hash":"186f9f998a5...2836dd734d2804fe65fa35779",
"tx_index":104810202,
"tx_output_n": 0,
"tx_output_n": 0,
"script":"76a9147f9b1a7fb68d60c536c2fd8aeaa53a8f3cc025a888ac",
"value": 10000000,
"value_hex": "00989680",
"confirmations":0
}
]
}
----
@ -192,7 +191,7 @@ As you can see, Alice's wallet contains enough bitcoin in a single unspent outpu
==== Creating the Outputs
((("outputs and inputs", "creating outputs")))A transaction output is created in the form of a script that creates an encumbrance on the value and can only be redeemed by the introduction of a solution to the script. In simpler terms, Alice's transaction output will contain a script that says something like, "This output is payable to whoever can present a signature from the key corresponding to Bob's public address." Because only Bob has the wallet with the keys corresponding to that address, only Bob's wallet can present such a signature to redeem this output. Alice will therefore "encumber" the output value with a demand for a signature from Bob.
((("outputs and inputs", "creating outputs")))A transaction output is created in the form of a script that creates an encumbrance on the value and can only be redeemed by the introduction of a solution to the script. In simpler terms, Alice's transaction output will contain a script that says something like, "This output is payable to whoever can present a signature from the key corresponding to Bob's public address." Because only Bob has the wallet with the keys corresponding to that address, only Bob's wallet can present such a signature to redeem this output. Alice will therefore "encumber" the output value with a demand for a signature from Bob.
This transaction will also include a second output, because Alice's funds are in the form of a 0.10 BTC output, too much money for the 0.015 BTC cup of coffee. Alice will need 0.085 BTC in change. Alice's change payment is created by Alice's wallet as an output in the very same transaction as the payment to Bob. Essentially, Alice's wallet breaks her funds into two payments: one to Bob and one back to herself. She can then use (spend) the change output in a subsequent transaction.
@ -234,7 +233,7 @@ If Bob's bitcoin wallet application is directly connected to Alice's wallet appl
=== Bitcoin Mining
((("mining and consensus", "overview of", id="MACover02")))((("blockchain (the)", "overview of mining", id="BToverview02")))Alice's transaction is now propagated on the bitcoin network. It does not become part of the _blockchain_ until it is verified and included in a block by a process called _mining_. See <<mining>> for a detailed explanation.
((("mining and consensus", "overview of", id="MACover02")))((("blockchain (the)", "overview of mining", id="BToverview02")))Alice's transaction is now propagated on the bitcoin network. It does not become part of the _blockchain_ until it is verified and included in a block by a process called _mining_. See <<mining>> for a detailed explanation.
The bitcoin system of trust is based on computation. Transactions are bundled into _blocks_, which require an enormous amount of computation to prove, but only a small amount of computation to verify as proven. The mining process serves two purposes in bitcoin:
@ -258,7 +257,7 @@ Transactions are added to the new block, prioritized by the highest-fee transact
((("candidate blocks")))((("blocks", "candidate blocks")))Alice's transaction was picked up by the network and included in the pool of unverified transactions. Once validated by the mining software it was included in a new block, called a _candidate block_, generated by Jing's mining pool. All the miners participating in that mining pool immediately start computing Proof-of-Work for the candidate block. Approximately five minutes after the transaction was first transmitted by Alice's wallet, one of Jing's ASIC miners found a solution for the candidate block and announced it to the network. Once other miners validated the winning block they started the race to generate the next block.
Jing's winning block became part of the blockchain as block #277316, containing 420 transactions, including Alice's transaction. The block containing Alice's transaction is counted as one "confirmation" of that transaction.
Jing's winning block became part of the blockchain as block #277316, containing 419 transactions, including Alice's transaction. The block containing Alice's transaction is counted as one "confirmation" of that transaction.
[TIP]
====
@ -275,10 +274,10 @@ image::images/mbc2_0209.png["Alice's transaction included in a block"]
=== Spending the Transaction
((("spending bitcoin", "simple-payment-verification (SPV)")))((("simple-payment-verification (SPV)")))Now that Alice's transaction has been embedded in the blockchain as part of a block, it is part of the distributed ledger of bitcoin and visible to all bitcoin applications. Each bitcoin client can independently verify the transaction as valid and spendable. Full-node clients can track the source of the funds from the moment the bitcoin were first generated in a block, incrementally from transaction to transaction, until they reach Bob's address. Lightweight clients can do what is called a simplified payment verification (see <<spv_nodes>>) by confirming that the transaction is in the blockchain and has several blocks mined after it, thus providing assurance that the miners accepted it as valid.
Bob can now spend the output from this and other transactions. For example, Bob can pay a contractor or supplier by transferring value from Alice's coffee cup payment to these new owners. Most likely, Bob's bitcoin software will aggregate many small payments into a larger payment, perhaps concentrating all the day's bitcoin revenue into a single transaction. This would aggregate the various payments into a single output (and a single address). For a diagram of an aggregating transaction, see <<transaction-aggregating>>.
((("spending bitcoin", "simple-payment-verification (SPV)")))((("simple-payment-verification (SPV)")))Now that Alice's transaction has been embedded in the blockchain as part of a block, it is part of the distributed ledger of bitcoin and visible to all bitcoin applications. Each bitcoin client can independently verify the transaction as valid and spendable. Full-node clients can track the source of the funds from the moment the bitcoin were first generated in a block, incrementally from transaction to transaction, until they reach Bob's address. Lightweight clients can do what is called a simplified payment verification (see <<spv_nodes>>) by confirming that the transaction is in the blockchain and has several blocks mined after it, thus providing assurance that the miners accepted it as valid.
Bob can now spend the output from this and other transactions. For example, Bob can pay a contractor or supplier by transferring value from Alice's coffee cup payment to these new owners. Most likely, Bob's bitcoin software will aggregate many small payments into a larger payment, perhaps concentrating all the day's bitcoin revenue into a single transaction. This would aggregate the various payments into a single output (and a single address). For a diagram of an aggregating transaction, see <<transaction-aggregating>>.
As Bob spends the payments received from Alice and other customers, he extends the chain of transactions. Let's assume that Bob pays his web designer Gopesh((("use cases", "offshore contract services"))) in Bangalore for a new website page. Now the chain of transactions will look like <<block-alice2>>.
[[block-alice2]]

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@ -222,7 +222,7 @@ $ which bitcoin-cli
((("Bitcoin Core", "running core nodes", id="BCnode03")))((("bitcoin nodes", "running core nodes", id="BNcore03")))Bitcoin's peer-to-peer network is composed of network "nodes," run mostly by volunteers and some of the businesses that build bitcoin applications. Those running bitcoin nodes have a direct and authoritative view of the bitcoin blockchain, with a local copy of all the transactions, independently validated by their own system. By running a node, you don't have to rely on any third party to validate a transaction. Moreover, by running a bitcoin node you contribute to the bitcoin network by making it more robust.
Running a node, however, requires a permanently connected system with enough resources to process all bitcoin transactions. Depending on whether you choose to index all transactions and keep a full copy of the blockchain, you may also need a lot of disk space and RAM. As of late 2016, a full-index node needs 2 GB of RAM and 125 GB of disk space so that it has room to grow. Bitcoin nodes also transmit and receive bitcoin transactions and blocks, consuming internet bandwidth. If your internet connection is limited, has a low data cap, or is metered (charged by the gigabit), you should probably not run a bitcoin node on it, or run it in a way that constrains its bandwidth (see <<constrained_resources>>).
Running a node, however, requires a permanently connected system with enough resources to process all bitcoin transactions. Depending on whether you choose to index all transactions and keep a full copy of the blockchain, you may also need a lot of disk space and RAM. As of early 2018, a full-index node needs 2 GB of RAM and a minimum of 160 GB of disk space (see https://blockchain.info/charts/blocks-size). Bitcoin nodes also transmit and receive bitcoin transactions and blocks, consuming internet bandwidth. If your internet connection is limited, has a low data cap, or is metered (charged by the gigabit), you should probably not run a bitcoin node on it, or run it in a way that constrains its bandwidth (see <<constrained_resources>>).
[TIP]
====

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@ -1,15 +1,15 @@
[[ch04_keys_addresses]]
== Keys, Addresses
((("cryptography", "defined")))((("cryptography", see="also keys and addresses")))You may have heard that bitcoin is based on _cryptography_, which is a branch of mathematics used extensively in computer security. Cryptography means "secret writing" in Greek, but the science of cryptography encompasses more than just secret writing, which is referred to as encryption. Cryptography can also be used to prove knowledge of a secret without revealing that secret (digital signature), or prove the authenticity of data (digital fingerprint). These types of cryptographic proofs are the mathematical tools critical to bitcoin and used extensively in bitcoin applications. ((("encryption")))((("encryption", see="also keys and addresses")))Ironically, encryption is not an important part of bitcoin, as its communications and transaction data are not encrypted and do not need to be encrypted to protect the funds. In this chapter we will introduce some of the cryptography used in bitcoin to control ownership of funds, in the form of keys, addresses, and wallets.
((("cryptography", "defined")))((("cryptography", see="also keys and addresses")))You may have heard that bitcoin is based on _cryptography_, which is a branch of mathematics used extensively in computer security. Cryptography means "secret writing" in Greek, but the science of cryptography encompasses more than just secret writing, which is referred to as encryption. Cryptography can also be used to prove knowledge of a secret without revealing that secret (digital signature), or prove the authenticity of data (digital fingerprint). These types of cryptographic proofs are the mathematical tools critical to bitcoin and used extensively in bitcoin applications. ((("encryption")))((("encryption", see="also keys and addresses")))Ironically, encryption is not an important part of bitcoin, as its communications and transaction data are not encrypted and do not need to be encrypted to protect the funds. In this chapter we will introduce some of the cryptography used in bitcoin to control ownership of funds, in the form of keys, addresses, and wallets.
=== Introduction
((("digital keys", see="keys and addresses")))((("keys and addresses", "overview of", id="KAover04")))((("digital signatures", "purpose of")))Ownership of bitcoin is established through _digital keys_, _bitcoin addresses_, and _digital signatures_. The digital keys are not actually stored in the network, but are instead created and stored by users in a file, or simple database, called a _wallet_. The digital keys in a user's wallet are completely independent of the bitcoin protocol and can be generated and managed by the user's wallet software without reference to the blockchain or access to the internet. Keys enable many of the interesting properties of bitcoin, including decentralized trust and control, ownership attestation, and the cryptographic-proof security model.
((("digital keys", see="keys and addresses")))((("keys and addresses", "overview of", id="KAover04")))((("digital signatures", "purpose of")))Ownership of bitcoin is established through _digital keys_, _bitcoin addresses_, and _digital signatures_. The digital keys are not actually stored in the network, but are instead created and stored by users in a file, or simple database, called a _wallet_. The digital keys in a user's wallet are completely independent of the bitcoin protocol and can be generated and managed by the user's wallet software without reference to the blockchain or access to the internet. Keys enable many of the interesting properties of bitcoin, including decentralized trust and control, ownership attestation, and the cryptographic-proof security model.
Most bitcoin transactions require a valid digital signature to be included in the blockchain, which can only be generated with a secret key; therefore, anyone with a copy of that key has control of the bitcoin. ((("witnesses")))The digital signature used to spend funds is also referred to as a _witness_, a term used in cryptography. The witness data in a bitcoin transaction testifies to the true ownership of the funds being spent.
((("public and private keys", "key pairs")))((("public and private keys", see="also keys and addresses")))Keys come in pairs consisting of a private (secret) key and a public key. Think of the public key as similar to a bank account number and the private key as similar to the secret PIN, or signature on a check, that provides control over the account. These digital keys are very rarely seen by the users of bitcoin. For the most part, they are stored inside the wallet file and managed by the bitcoin wallet software.
((("public and private keys", "key pairs")))((("public and private keys", see="also keys and addresses")))Keys come in pairs consisting of a private (secret) key and a public key. Think of the public key as similar to a bank account number and the private key as similar to the secret PIN, or signature on a check, that provides control over the account. These digital keys are very rarely seen by the users of bitcoin. For the most part, they are stored inside the wallet file and managed by the bitcoin wallet software.
In the payment portion of a bitcoin transaction, the recipient's public key is represented by its digital fingerprint, called a _bitcoin address_, which is used in the same way as the beneficiary name on a check (i.e., "Pay to the order of"). In most cases, a bitcoin address is generated from and corresponds to a public key. However, not all bitcoin addresses represent public keys; they can also represent other beneficiaries such as scripts, as we will see later in this chapter. This way, bitcoin addresses abstract the recipient of funds, making transaction destinations flexible, similar to paper checks: a single payment instrument that can be used to pay into people's accounts, pay into company accounts, pay for bills, or pay to cash. The bitcoin address is the only representation of the keys that users will routinely see, because this is the part they need to share with the world.
@ -20,7 +20,7 @@ First, we will introduce cryptography and explain the mathematics used in bitcoi
((("keys and addresses", "overview of", "public key cryptography")))((("digital currencies", "cryptocurrency")))Public key cryptography was invented in the 1970s and is a mathematical foundation for computer and information security.
Since the invention of public key cryptography, several suitable mathematical functions, such as prime number exponentiation and elliptic curve multiplication, have been discovered. These mathematical functions are practically irreversible, meaning that they are easy to calculate in one direction and infeasible to calculate in the opposite direction. Based on these mathematical functions, cryptography enables the creation of digital secrets and unforgeable digital signatures. Bitcoin uses elliptic curve multiplication as the basis for its cryptography.
In bitcoin, we use public key cryptography to create a key pair that controls access to bitcoin. The key pair consists of a private key and--derived from it--a unique public key. The public key is used to receive funds, and the private key is used to sign transactions to spend the funds.
There is a mathematical relationship between the public and the private key that allows the private key to be used to generate signatures on messages. This signature can be validated against the public key without revealing the private key.
@ -49,7 +49,7 @@ image::images/mbc2_0401.png["privk_to_pubK_to_addressA"]
[[private_keys]]
==== Private Keys
((("keys and addresses", "overview of", "private key generation")))((("warnings and cautions", "private key protection")))A private key is simply a number, picked at random. Ownership and control over the private key is the root of user control over all funds associated with the corresponding bitcoin address. The private key is used to create signatures that are required to spend bitcoin by proving ownership of funds used in a transaction. The private key must remain secret at all times, because revealing it to third parties is equivalent to giving them control over the bitcoin secured by that key. The private key must also be backed up and protected from accidental loss, because if it's lost it cannot be recovered and the funds secured by it are forever lost, too.
((("keys and addresses", "overview of", "private key generation")))((("warnings and cautions", "private key protection")))A private key is simply a number, picked at random. Ownership and control over the private key is the root of user control over all funds associated with the corresponding bitcoin address. The private key is used to create signatures that are required to spend bitcoin by proving ownership of funds used in a transaction. The private key must remain secret at all times, because revealing it to third parties is equivalent to giving them control over the bitcoin secured by that key. The private key must also be backed up and protected from accidental loss, because if it's lost it cannot be recovered and the funds secured by it are forever lost, too.
[TIP]
====
@ -60,8 +60,8 @@ The bitcoin private key is just a number. You can pick your private keys randoml
The first and most important step in generating keys is to find a secure source of entropy, or randomness. Creating a bitcoin key is essentially the same as "Pick a number between 1 and 2^256^." The exact method you use to pick that number does not matter as long as it is not predictable or repeatable. Bitcoin software uses the underlying operating system's random number generators to produce 256 bits of entropy (randomness). Usually, the OS random number generator is initialized by a human source of randomness, which is why you may be asked to wiggle your mouse around for a few seconds.
More precisely, the private key can be any number between +0+ and +n - 1+ inclusive, where n is a constant (n = 1.158 * 10^77^, slightly less than 2^256^) defined as the order of the elliptic curve used in bitcoin (see <<elliptic_curve>>). To create such a key, we randomly pick a 256-bit number and check that it is less than +n+. In programming terms, this is usually achieved by feeding a larger string of random bits, collected from a cryptographically secure source of randomness, into the SHA256 hash algorithm, which will conveniently produce a 256-bit number. If the result is less than +n+, we have a suitable private key. Otherwise, we simply try again with another random number.
More precisely, the private key can be any number between +0+ and +n - 1+ inclusive, where n is a constant (n = 1.1578 * 10^77^, slightly less than 2^256^) defined as the order of the elliptic curve used in bitcoin (see <<elliptic_curve>>). To create such a key, we randomly pick a 256-bit number and check that it is less than +n+. In programming terms, this is usually achieved by feeding a larger string of random bits, collected from a cryptographically secure source of randomness, into the SHA256 hash algorithm, which will conveniently produce a 256-bit number. If the result is less than +n+, we have a suitable private key. Otherwise, we simply try again with another random number.
[WARNING]
====
((("random numbers", "random number generation")))((("entropy", "random number generation")))Do not write your own code to create a random number or use a "simple" random number generator offered by your programming language. Use a cryptographically secure pseudorandom number generator (CSPRNG) with a seed from a source of sufficient entropy. Study the documentation of the random number generator library you choose to make sure it is cryptographically secure. Correct implementation of the CSPRNG is critical to the security of the keys.
@ -88,15 +88,15 @@ $ bitcoin-cli dumpprivkey 1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy
KxFC1jmwwCoACiCAWZ3eXa96mBM6tb3TYzGmf6YwgdGWZgawvrtJ
----
The +dumpprivkey+ command opens the wallet and extracts the private key that was generated by the +getnewaddress+ command. It is not possible for +bitcoind+ to know the private key from the public key unless they are both stored in the wallet.
The +dumpprivkey+ command opens the wallet and extracts the private key that was generated by the +getnewaddress+ command. It is not possible for +bitcoind+ to know the private key from the public key unless they are both stored in the wallet.
[TIP]
=====================================================================
The +dumpprivkey+ command does not generate a private key from a public key, as this is impossible. The command simply reveals the private key that is already known to the wallet and which was generated by the +getnewaddress+ command.
The +dumpprivkey+ command does not generate a private key from a public key, as this is impossible. The command simply reveals the private key that is already known to the wallet and which was generated by the +getnewaddress+ command.
=====================================================================
[role="pagebreak-before"]
You can also use the Bitcoin Explorer command-line tool (see <<appdx_bx>>) to generate and display private keys with the commands +seed+, +ec-new+, and +ec-to-wif+:
You can also use the Bitcoin Explorer command-line tool (see <<appdx_bx>>) to generate and display private keys with the commands +seed+, +ec-new+, and +ec-to-wif+:
----
$ bx seed | bx ec-new | bx ec-to-wif
@ -106,7 +106,7 @@ $ bx seed | bx ec-new | bx ec-to-wif
[[pubkey]]
==== Public Keys
((("keys and addresses", "overview of", "public key calculation")))((("generator point")))The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: _K_ = _k_ * _G_, where _k_ is the private key, _G_ is a constant point called the _generator point_, and _K_ is the resulting public key. The reverse operation, known as "finding the discrete logarithm"—calculating _k_ if you know __K__—is as difficult as trying all possible values of _k_, i.e., a brute-force search. Before we demonstrate how to generate a public key from a private key, let's look at elliptic curve cryptography in a bit more detail.
((("keys and addresses", "overview of", "public key calculation")))((("generator point")))The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: _K_ = _k_ * _G_, where _k_ is the private key, _G_ is a constant point called the _generator point_, and _K_ is the resulting public key. The reverse operation, known as "finding the discrete logarithm"—calculating _k_ if you know __K__—is as difficult as trying all possible values of _k_, i.e., a brute-force search. Before we demonstrate how to generate a public key from a private key, let's look at elliptic curve cryptography in a bit more detail.
[TIP]
====
@ -116,7 +116,7 @@ Elliptic curve multiplication is a type of function that cryptographers call a "
[[elliptic_curve]]
==== Elliptic Curve Cryptography Explained
((("keys and addresses", "overview of", "elliptic curve cryptography")))((("elliptic curve cryptography", id="eliptic04")))((("cryptography", "elliptic curve cryptography", id="Celliptic04")))Elliptic curve cryptography is a type of asymmetric or public key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve.
((("keys and addresses", "overview of", "elliptic curve cryptography")))((("elliptic curve cryptography", id="eliptic04")))((("cryptography", "elliptic curve cryptography", id="Celliptic04")))Elliptic curve cryptography is a type of asymmetric or public key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve.
<<ecc-curve>> is an example of an elliptic curve, similar to that used by bitcoin.
@ -134,7 +134,7 @@ Bitcoin uses a specific elliptic curve and set of mathematical constants, as def
\end{equation}
++++
or
or
[latexmath]
++++
@ -143,9 +143,9 @@ or
\end{equation}
++++
The _mod p_ (modulo prime number p) indicates that this curve is over a finite field of prime order _p_, also written as latexmath:[\( \mathbb{F}_p \)], where p = 2^256^ – 2^32^ – 2^9^ – 2^8^ – 2^7^ – 2^6^ – 2^4^ – 1, a very large prime number.
The _mod p_ (modulo prime number p) indicates that this curve is over a finite field of prime order _p_, also written as latexmath:[\( \mathbb{F}_p \)], where p = 2^256^ – 2^32^ – 2^9^ – 2^8^ – 2^7^ – 2^6^ – 2^4^ – 1, a very large prime number.
Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical to that of an elliptic curve over real numbers. As an example, <<ecc-over-F17-math>> shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid.
Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical to that of an elliptic curve over real numbers. As an example, <<ecc-over-F17-math>> shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid.
[[ecc-over-F17-math]]
[role="smallersixty"]
@ -155,7 +155,7 @@ image::images/mbc2_0403.png["ecc-over-F17-math"]
So, for example, the following is a point P with coordinates (x,y) that is a point on the +secp256k1+ curve:
----
P = (55066263022277343669578718895168534326250603453777594175500187360389116729240, 32670510020758816978083085130507043184471273380659243275938904335757337482424)
P = (55066263022277343669578718895168534326250603453777594175500187360389116729240, 32670510020758816978083085130507043184471273380659243275938904335757337482424)
----
<<example_4_1>> shows how you can check this yourself using Python:
@ -190,14 +190,14 @@ In some cases (i.e., if P~1~ and P~2~ have the same x values but different y val
If P~1~ is the "point at infinity," then P~1~ + P~2~ = P~2~. Similarly, if P~2~ is the point at infinity, then P~1~ + P~2~ = P~1~. This shows how the point at infinity plays the role of zero.
It turns out that pass:[+] is associative, which means that (A pass:[+] B) pass:[+] C = A pass:[+] (B pass:[+] C). That means we can write A pass:[+] B pass:[+] C without parentheses and without ambiguity.
It turns out that pass:[+] is associative, which means that (A pass:[+] B) pass:[+] C = A pass:[+] (B pass:[+] C). That means we can write A pass:[+] B pass:[+] C without parentheses and without ambiguity.
Now that we have defined addition, we can define multiplication in the standard way that extends addition. For a point P on the elliptic curve, if k is a whole number, then kP = P + P + P + ... + P (k times). Note that k is sometimes confusingly called an "exponent" in this case.((("", startref="eliptic04")))((("", startref="Celliptic04")))
Now that we have defined addition, we can define multiplication in the standard way that extends addition. For a point P on the elliptic curve, if k is a whole number, then kP = P + P + P + ... + P (k times). Note that k is sometimes confusingly called an "exponent" in this case.((("", startref="eliptic04")))((("", startref="Celliptic04")))
[[public_key_derivation]]
==== Generating a Public Key
==== Generating a Public Key
((("keys and addresses", "overview of", "public key generation")))((("generator point")))Starting with a private key in the form of a randomly generated number _k_, we multiply it by a predetermined point on the curve called the _generator point_ _G_ to produce another point somewhere else on the curve, which is the corresponding public key _K_. The generator point is specified as part of the +secp256k1+ standard and is always the same for all keys in bitcoin:
((("keys and addresses", "overview of", "public key generation")))((("generator point")))Starting with a private key in the form of a randomly generated number _k_, we multiply it by a predetermined point on the curve called the _generator point_ _G_ to produce another point somewhere else on the curve, which is the corresponding public key _K_. The generator point is specified as part of the +secp256k1+ standard and is always the same for all keys in bitcoin:
[latexmath]
++++
@ -206,7 +206,7 @@ Now that we have defined addition, we can define multiplication in the standard
\end{equation}
++++
where _k_ is the private key, _G_ is the generator point, and _K_ is the resulting public key, a point on the curve. Because the generator point is always the same for all bitcoin users, a private key _k_ multiplied with _G_ will always result in the same public key _K_. The relationship between _k_ and _K_ is fixed, but can only be calculated in one direction, from _k_ to _K_. That's why a bitcoin address (derived from _K_) can be shared with anyone and does not reveal the user's private key (_k_).
where _k_ is the private key, _G_ is the generator point, and _K_ is the resulting public key, a point on the curve. Because the generator point is always the same for all bitcoin users, a private key _k_ multiplied with _G_ will always result in the same public key _K_. The relationship between _k_ and _K_ is fixed, but can only be calculated in one direction, from _k_ to _K_. That's why a bitcoin address (derived from _K_) can be shared with anyone and does not reveal the user's private key (_k_).
[TIP]
====
@ -222,7 +222,7 @@ K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD * G
Public key _K_ is defined as a point +K = (x,y)+:
----
K = (x, y)
K = (x, y)
where,
@ -230,7 +230,7 @@ x = F028892BAD7ED57D2FB57BF33081D5CFCF6F9ED3D3D7F159C2E2FFF579DC341A
y = 07CF33DA18BD734C600B96A72BBC4749D5141C90EC8AC328AE52DDFE2E505BDB
----
To visualize multiplication of a point with an integer, we will use the simpler elliptic curve over real numbers&#x2014;remember, the math is the same. Our goal is to find the multiple _kG_ of the generator point _G_, which is the same as adding _G_ to itself, _k_ times in a row. In elliptic curves, adding a point to itself is the equivalent of drawing a tangent line on the point and finding where it intersects the curve again, then reflecting that point on the x-axis.
To visualize multiplication of a point with an integer, we will use the simpler elliptic curve over real numbers&#x2014;remember, the math is the same. Our goal is to find the multiple _kG_ of the generator point _G_, which is the same as adding _G_ to itself, _k_ times in a row. In elliptic curves, adding a point to itself is the equivalent of drawing a tangent line on the point and finding where it intersects the curve again, then reflecting that point on the x-axis.
<<ecc_illustrated>> shows the process for deriving _G_, _2G_, _4G_, as a geometric operation on the curve.
@ -254,7 +254,7 @@ image::images/mbc2_0404.png["ecc_illustrated"]
The bitcoin address is what appears most commonly in a transaction as the "recipient" of the funds. If we compare a bitcoin transaction to a paper check, the bitcoin address is the beneficiary, which is what we write on the line after "Pay to the order of." On a paper check, that beneficiary can sometimes be the name of a bank account holder, but can also include corporations, institutions, or even cash. Because paper checks do not need to specify an account, but rather use an abstract name as the recipient of funds, they are very flexible payment instruments. Bitcoin transactions use a similar abstraction, the bitcoin address, to make them very flexible. A bitcoin address can represent the owner of a private/public key pair, or it can represent something else, such as a payment script, as we will see in <<p2sh>>. For now, let's examine the simple case, a bitcoin address that represents, and is derived from, a public key.
((("addresses", "algorithms used to create")))The bitcoin address is derived from the public key through the use of one-way cryptographic hashing. A "hashing algorithm" or simply "hash algorithm" is a one-way function that produces a fingerprint or "hash" of an arbitrary-sized input. Cryptographic hash functions are used extensively in bitcoin: in bitcoin addresses, in script addresses, and in the mining Proof-of-Work algorithm. The algorithms used to make a bitcoin address from a public key are the Secure Hash Algorithm (SHA) and the RACE Integrity Primitives Evaluation Message Digest (RIPEMD), specifically SHA256 and RIPEMD160.
((("addresses", "algorithms used to create")))The bitcoin address is derived from the public key through the use of one-way cryptographic hashing. A "hashing algorithm" or simply "hash algorithm" is a one-way function that produces a fingerprint or "hash" of an arbitrary-sized input. Cryptographic hash functions are used extensively in bitcoin: in bitcoin addresses, in script addresses, and in the mining Proof-of-Work algorithm. The algorithms used to make a bitcoin address from a public key are the Secure Hash Algorithm (SHA) and the RACE Integrity Primitives Evaluation Message Digest (RIPEMD), specifically SHA256 and RIPEMD160.
Starting with the public key _K_, we compute the SHA256 hash and then compute the RIPEMD160 hash of the result, producing a 160-bit (20-byte) number:
@ -265,18 +265,18 @@ Starting with the public key _K_, we compute the SHA256 hash and then compute th
\end{equation}
++++
where _K_ is the public key and _A_ is the resulting bitcoin address.
where _K_ is the public key and _A_ is the resulting bitcoin address.
[TIP]
====
A bitcoin address is _not_ the same as a public key. Bitcoin addresses are derived from a public key using a one-way function.
A bitcoin address is _not_ the same as a public key. Bitcoin addresses are derived from a public key using a one-way function.
====
Bitcoin addresses are almost always encoded as "Base58Check" (see <<base58>>), which uses 58 characters (a Base58 number system) and a checksum to help human readability, avoid ambiguity, and protect against errors in address transcription and entry. Base58Check is also used in many other ways in bitcoin, whenever there is a need for a user to read and correctly transcribe a number, such as a bitcoin address, a private key, an encrypted key, or a script hash. In the next section we will examine the mechanics of Base58Check encoding and decoding and the resulting representations. <<pubkey_to_address>> illustrates the conversion of a public key into a bitcoin address.
[[pubkey_to_address]]
.Public key to bitcoin address: conversion of a public key into a bitcoin address
.Public key to bitcoin address: conversion of a public key into a bitcoin address
image::images/mbc2_0405.png["pubkey_to_address"]
[[base58]]
@ -298,12 +298,12 @@ To add extra security against typos or transcription errors, Base58Check is a Ba
To convert data (a number) into a Base58Check format, we first add a prefix to the data, called the "version byte," which serves to easily identify the type of data that is encoded. For example, in the case of a bitcoin address the prefix is zero (0x00 in hex), whereas the prefix used when encoding a private key is 128 (0x80 in hex). A list of common version prefixes is shown in <<base58check_versions>>.
Next, we compute the "double-SHA" checksum, meaning we apply the SHA256 hash-algorithm twice on the previous result (prefix and data):
----
checksum = SHA256(SHA256(prefix+data))
checksum = SHA256(SHA256(prefix+data))
----
From the resulting 32-byte hash (hash-of-a-hash), we take only the first four bytes. These four bytes serve as the error-checking code, or checksum. The checksum is concatenated (appended) to the end.
From the resulting 32-byte hash (hash-of-a-hash), we take only the first four bytes. These four bytes serve as the error-checking code, or checksum. The checksum is concatenated (appended) to the end.
The result is composed of three items: a prefix, the data, and a checksum. This result is encoded using the Base58 alphabet described previously. <<base58check_encoding>> illustrates the Base58Check encoding process.
@ -318,43 +318,14 @@ In bitcoin, most of the data presented to the user is Base58Check-encoded to mak
[options="header"]
|=======
|Type| Version prefix (hex)| Base58 result prefix
| Bitcoin Address | 0x00 | 1
| Pay-to-Script-Hash Address | 0x05 | 3
| Bitcoin Testnet Address | 0x6F | m or n
| Private Key WIF | 0x80 | 5, K, or L
| BIP-38 Encrypted Private Key | 0x0142 | 6P
| BIP-32 Extended Public Key | 0x0488B21E | xpub
| Bitcoin Address | 0x00 | 1
| Pay-to-Script-Hash Address | 0x05 | 3
| Bitcoin Testnet Address | 0x6F | m or n
| Private Key WIF | 0x80 | 5, K, or L
| BIP-38 Encrypted Private Key | 0x0142 | 6P
| BIP-32 Extended Public Key | 0x0488B21E | xpub
|=======
Let's look at the complete process of creating a bitcoin address, from a private key, to a public key (a point on the elliptic curve), to a double-hashed address, and finally, the Base58Check encoding. The C++ code in <<addr_example>> shows the complete step-by-step process, from private key to Base58Check-encoded bitcoin address. The code example uses the libbitcoin library introduced in <<alt_libraries>> for some helper functions.
[[addr_example]]
.Creating a Base58Check-encoded bitcoin address from a private key
====
[role="c_less_space"]
[source, cpp]
----
include::code/addr.cpp[]
----
====
The code uses a predefined private key to produce the same bitcoin address every time it is run, as shown in <<addr_example_run>>.((("", startref="base5804")))((("", startref="Abase5804")))
[[addr_example_run]]
.Compiling and running the addr code
====
[source,bash]
----
# Compile the addr.cpp code
$ g++ -o addr addr.cpp $(pkg-config --cflags --libs libbitcoin)
# Run the addr executable
$ ./addr
Public key: 0202a406624211f2abbdc68da3df929f938c3399dd79fac1b51b0e4ad1d26a47aa
Address: 1PRTTaJesdNovgne6Ehcdu1fpEdX7913CK
----
====
==== Key Formats
((("keys and addresses", "bitcoin addresses", "key formats")))Both private and public keys can be represented in a number of different formats. These representations all encode the same number, even though they look different. These formats are primarily used to make it easy for people to read and transcribe keys without introducing errors.
@ -382,7 +353,7 @@ Address: 1PRTTaJesdNovgne6Ehcdu1fpEdX7913CK
[options="header"]
|=======
|Format | Private key
| Hex | 1e99423a4ed27608a15a2616a2b0e9e52ced330ac530edcc32c8ffc6a526aedd
| Hex | 1e99423a4ed27608a15a2616a2b0e9e52ced330ac530edcc32c8ffc6a526aedd
| WIF | 5J3mBbAH58CpQ3Y5RNJpUKPE62SQ5tfcvU2JpbnkeyhfsYB1Jcn
| WIF-compressed | KxFC1jmwwCoACiCAWZ3eXa96mBM6tb3TYzGmf6YwgdGWZgawvrtJ
|=======
@ -451,7 +422,7 @@ The resulting WIF-compressed format starts with a "K." This denotes that the pri
===== Public key formats
((("public and private keys", "public key formats")))Public keys are also presented in different ways, usually as either _compressed_ or _uncompressed_ public keys.
((("public and private keys", "public key formats")))Public keys are also presented in different ways, usually as either _compressed_ or _uncompressed_ public keys.
As we saw previously, the public key is a point on the elliptic curve consisting of a pair of coordinates +(x,y)+. It is usually presented with the prefix +04+ followed by two 256-bit numbers: one for the _x_ coordinate of the point, the other for the _y_ coordinate. The prefix +04+ is used to distinguish uncompressed public keys from compressed public keys that begin with a +02+ or a +03+.
@ -479,7 +450,7 @@ K = 04F028892BAD7ED57D2FB57BF33081D5CFCF6F9ED3D3D7F159C2E2FFF579DC341A&#x21b5;
As we saw in the section <<pubkey>>, a public key is a point (x,y) on an elliptic curve. Because the curve expresses a mathematical function, a point on the curve represents a solution to the equation and, therefore, if we know the _x_ coordinate we can calculate the _y_ coordinate by solving the equation y^2^ mod p = (x^3^ + 7) mod p. That allows us to store only the _x_ coordinate of the public key point, omitting the _y_ coordinate and reducing the size of the key and the space required to store it by 256 bits. An almost 50% reduction in size in every transaction adds up to a lot of data saved over time!
Whereas uncompressed public keys have a prefix of +04+, compressed public keys start with either a +02+ or a +03+ prefix. Let's look at why there are two possible prefixes: because the left side of the equation is __y__^2^, the solution for _y_ is a square root, which can have a positive or negative value. Visually, this means that the resulting _y_ coordinate can be above or below the x-axis. As you can see from the graph of the elliptic curve in <<ecc-curve>>, the curve is symmetric, meaning it is reflected like a mirror by the x-axis. So, while we can omit the _y_ coordinate we have to store the _sign_ of _y_ (positive or negative); or in other words, we have to remember if it was above or below the x-axis because each of those options represents a different point and a different public key. When calculating the elliptic curve in binary arithmetic on the finite field of prime order p, the _y_ coordinate is either even or odd, which corresponds to the positive/negative sign as explained earlier. Therefore, to distinguish between the two possible values of _y_, we store a compressed public key with the prefix +02+ if the _y_ is even, and +03+ if it is odd, allowing the software to correctly deduce the _y_ coordinate from the _x_ coordinate and uncompress the public key to the full coordinates of the point. Public key compression is illustrated in <<pubkey_compression>>.
Whereas uncompressed public keys have a prefix of +04+, compressed public keys start with either a +02+ or a +03+ prefix. Let's look at why there are two possible prefixes: because the left side of the equation is __y__^2^, the solution for _y_ is a square root, which can have a positive or negative value. Visually, this means that the resulting _y_ coordinate can be above or below the x-axis. As you can see from the graph of the elliptic curve in <<ecc-curve>>, the curve is symmetric, meaning it is reflected like a mirror by the x-axis. So, while we can omit the _y_ coordinate we have to store the _sign_ of _y_ (positive or negative); or in other words, we have to remember if it was above or below the x-axis because each of those options represents a different point and a different public key. When calculating the elliptic curve in binary arithmetic on the finite field of prime order p, the _y_ coordinate is either even or odd, which corresponds to the positive/negative sign as explained earlier. Therefore, to distinguish between the two possible values of _y_, we store a compressed public key with the prefix +02+ if the _y_ is even, and +03+ if it is odd, allowing the software to correctly deduce the _y_ coordinate from the _x_ coordinate and uncompress the public key to the full coordinates of the point. Public key compression is illustrated in <<pubkey_compression>>.
[[pubkey_compression]]
[role="smallerseventy"]
@ -496,7 +467,7 @@ This compressed public key corresponds to the same private key, meaning it is ge
Compressed public keys are gradually becoming the default across bitcoin clients, which is having a significant impact on reducing the size of transactions and therefore the blockchain. However, not all clients support compressed public keys yet. Newer clients that support compressed public keys have to account for transactions from older clients that do not support compressed public keys. This is especially important when a wallet application is importing private keys from another bitcoin wallet application, because the new wallet needs to scan the blockchain to find transactions corresponding to these imported keys. Which bitcoin addresses should the bitcoin wallet scan for? The bitcoin addresses produced by uncompressed public keys, or the bitcoin addresses produced by compressed public keys? Both are valid bitcoin addresses, and can be signed for by the private key, but they are different addresses!
To resolve this issue, when private keys are exported from a wallet, the WIF that is used to represent them is implemented differently in newer bitcoin wallets, to indicate that these private keys have been used to produce _compressed_ public keys and therefore _compressed_ bitcoin addresses. This allows the importing wallet to distinguish between private keys originating from older or newer wallets and search the blockchain for transactions with bitcoin addresses corresponding to the uncompressed, or the compressed, public keys, respectively. Let's look at how this works in more detail, in the next section.
To resolve this issue, when private keys are exported from a wallet, the WIF that is used to represent them is implemented differently in newer bitcoin wallets, to indicate that these private keys have been used to produce _compressed_ public keys and therefore _compressed_ bitcoin addresses. This allows the importing wallet to distinguish between private keys originating from older or newer wallets and search the blockchain for transactions with bitcoin addresses corresponding to the uncompressed, or the compressed, public keys, respectively. Let's look at how this works in more detail, in the next section.
[[comp_priv]]
===== Compressed private keys
@ -520,7 +491,7 @@ Notice that the hex-compressed private key format has one extra byte at the end
Remember, these formats are _not_ used interchangeably. In a newer wallet that implements compressed public keys, the private keys will only ever be exported as WIF-compressed (with a _K_ or _L_ prefix). If the wallet is an older implementation and does not use compressed public keys, the private keys will only ever be exported as WIF (with a 5 prefix). The goal here is to signal to the wallet importing these private keys whether it must search the blockchain for compressed or uncompressed public keys and addresses.
If a bitcoin wallet is able to implement compressed public keys, it will use those in all transactions. The private keys in the wallet will be used to derive the public key points on the curve, which will be compressed. The compressed public keys will be used to produce bitcoin addresses and those will be used in transactions. When exporting private keys from a new wallet that implements compressed public keys, the WIF is modified, with the addition of a one-byte suffix +01+ to the private key. The resulting Base58Check-encoded private key is called a "compressed WIF" and starts with the letter _K_ or _L_, instead of starting with "5" as is the case with WIF-encoded (noncompressed) keys from older wallets.
If a bitcoin wallet is able to implement compressed public keys, it will use those in all transactions. The private keys in the wallet will be used to derive the public key points on the curve, which will be compressed. The compressed public keys will be used to produce bitcoin addresses and those will be used in transactions. When exporting private keys from a new wallet that implements compressed public keys, the WIF is modified, with the addition of a one-byte suffix +01+ to the private key. The resulting Base58Check-encoded private key is called a "compressed WIF" and starts with the letter _K_ or _L_, instead of starting with "5" as is the case with WIF-encoded (noncompressed) keys from older wallets.
[TIP]
@ -528,7 +499,42 @@ If a bitcoin wallet is able to implement compressed public keys, it will use tho
"Compressed private keys" is a misnomer! They are not compressed; rather, WIF-compressed signifies that the keys should only be used to derive compressed public keys and their corresponding bitcoin addresses. Ironically, a "WIF-compressed" encoded private key is one byte longer because it has the added +01+ suffix to distinguish it from an "uncompressed" one.((("", startref="KAaddress04")))
====
=== Implementing Keys and Addresses in Python
=== Implementing Keys and Addresses in Cpass:[++]
Let's look at the complete process of creating a bitcoin address, from a private key, to a public key (a point on the elliptic curve), to a double-hashed address, and finally, the Base58Check encoding. The C++ code in <<addr_example>> shows the complete step-by-step process, from private key to Base58Check-encoded bitcoin address. The code example uses the libbitcoin library introduced in <<alt_libraries>> for some helper functions.
[[addr_example]]
.Creating a Base58Check-encoded bitcoin address from a private key
====
[role="c_less_space"]
[source, cpp]
----
include::code/addr.cpp[]
----
====
The code uses a predefined private key to produce the same bitcoin address every time it is run, as shown in <<addr_example_run>>.((("", startref="base5804")))((("", startref="Abase5804")))
[[addr_example_run]]
.Compiling and running the addr code
====
[source,bash]
----
# Compile the addr.cpp code
$ g++ -o addr addr.cpp -std=c++11 $(pkg-config --cflags --libs libbitcoin)
# Run the addr executable
$ ./addr
Public key: 0202a406624211f2abbdc68da3df929f938c3399dd79fac1b51b0e4ad1d26a47aa
Address: 1PRTTaJesdNovgne6Ehcdu1fpEdX7913CK
----
====
[TIP]
====
The example in <<addr_example_run>>, produces a bitcoin address (+1PRTT...+) from a _compressed_ public key (see <<comp_pub>>). If you used the uncompressed public key instead, it would produce a different bitcoin address (+14K1y...+).
====
=== Implementing Keys and Addresses in Python
((("keys and addresses", "implementing in Python", id="KApython04")))((("pybitcointools")))The most comprehensive bitcoin library in Python is https://github.com/vbuterin/pybitcointools[pybitcointools] by Vitalik Buterin. In <<key-to-address_script>>, we use the pybitcointools library (imported as "bitcoin") to generate and display keys and addresses in various formats.
@ -548,28 +554,28 @@ include::code/key-to-address-ecc-example.py[]
====
++++
<pre data-type="programlisting">
$ python key-to-address-ecc-example.py
Private Key (hex) is:
$ python key-to-address-ecc-example.py
Private Key (hex) is:
3aba4162c7251c891207b747840551a71939b0de081f85c4e44cf7c13e41daa6
Private Key (decimal) is:
Private Key (decimal) is:
26563230048437957592232553826663696440606756685920117476832299673293013768870
Private Key (WIF) is:
Private Key (WIF) is:
5JG9hT3beGTJuUAmCQEmNaxAuMacCTfXuw1R3FCXig23RQHMr4K
Private Key Compressed (hex) is:
Private Key Compressed (hex) is:
3aba4162c7251c891207b747840551a71939b0de081f85c4e44cf7c13e41daa601
Private Key (WIF-Compressed) is:
Private Key (WIF-Compressed) is:
KyBsPXxTuVD82av65KZkrGrWi5qLMah5SdNq6uftawDbgKa2wv6S
Public Key (x,y) coordinates is:
(41637322786646325214887832269588396900663353932545912953362782457239403430124L,
Public Key (x,y) coordinates is:
(41637322786646325214887832269588396900663353932545912953362782457239403430124L,
16388935128781238405526710466724741593761085120864331449066658622400339362166L)
Public Key (hex) is:
Public Key (hex) is:
045c0de3b9c8ab18dd04e3511243ec2952002dbfadc864b9628910169d9b9b00ec&#x21b5;
243bcefdd4347074d44bd7356d6a53c495737dd96295e2a9374bf5f02ebfc176
Compressed Public Key (hex) is:
Compressed Public Key (hex) is:
025c0de3b9c8ab18dd04e3511243ec2952002dbfadc864b9628910169d9b9b00ec
Bitcoin Address (b58check) is:
Bitcoin Address (b58check) is:
1thMirt546nngXqyPEz532S8fLwbozud8
Compressed Bitcoin Address (b58check) is:
Compressed Bitcoin Address (b58check) is:
14cxpo3MBCYYWCgF74SWTdcmxipnGUsPw3
</pre>
++++
@ -591,7 +597,7 @@ include::code/ec-math.py[]
[NOTE]
====
<<ec_math>> ((("random numbers", "os.urandom", see="entropy")))((("entropy", "os.urandom", see="random numbers")))((("random numbers", "random number generation")))((("entropy", "random number generation")))uses +os.urandom+, which reflects a cryptographically secure random number generator (CSRNG) provided by the underlying operating system. In the case of a Unix-like operating system such as Linux, it draws from +/dev/urandom+; and in the case of Windows, it calls +CryptGenRandom()+. If a suitable randomness source is not found, +NotImplementedError+ will be raised. While the random number generator used here is for demonstration purposes, it is _not_ appropriate for generating production-quality bitcoin keys as it is not implemented with sufficient security.((("", startref="KApython04")))
<<ec_math>> ((("random numbers", "os.urandom", see="entropy")))((("entropy", "os.urandom", see="random numbers")))((("random numbers", "random number generation")))((("entropy", "random number generation")))uses +os.urandom+, which reflects a cryptographically secure random number generator (CSRNG) provided by the underlying operating system. Caution: Depending on the OS, +os.urandom+ may _not_ be implemented with sufficient security or seeded properly and may _not_ be appropriate for generating production-quality bitcoin keys.((("", startref="KApython04")))
====
[[ec_math_run]]
@ -603,7 +609,7 @@ $ sudo apt-get install python-pip
$ # Install the Python ECDSA library
$ sudo pip install ecdsa
$ # Run the script
$ python ec-math.py
$ python ec-math.py
Secret: 38090835015954358862481132628887443905906204995912378278060168703580660294000
EC point: (70048853531867179489857750497606966272382583471322935454624595540007269312627, 105262206478686743191060800263479589329920209527285803935736021686045542353380)
BTC public key: 029ade3effb0a67d5c8609850d797366af428f4a0d5194cb221d807770a1522873
@ -616,18 +622,18 @@ BTC public key: 029ade3effb0a67d5c8609850d797366af428f4a0d5194cb221d807770a15228
==== Encrypted Private Keys (BIP-38)
((("bitcoin improvement proposals", "Encrypted Private Keys (BIP-38)")))((("keys and addresses", "advanced forms", "encrypted private keys")))((("public and private keys", "encrypted private keys")))((("passwords", "encrypted private keys")))((("security", "passwords")))Private keys must remain secret. The need for _confidentiality_ of the private keys is a truism that is quite difficult to achieve in practice, because it conflicts with the equally important security objective of _availability_. Keeping the private key private is much harder when you need to store backups of the private key to avoid losing it. A private key stored in a wallet that is encrypted by a password might be secure, but that wallet needs to be backed up. At times, users need to move keys from one wallet to another—to upgrade or replace the wallet software, for example. Private key backups might also be stored on paper (see <<paper_wallets>>) or on external storage media, such as a USB flash drive. But what if the backup itself is stolen or lost? These conflicting security goals led to the introduction of a portable and convenient standard for encrypting private keys in a way that can be understood by many different wallets and bitcoin clients, standardized by BIP-38 (see <<appdxbitcoinimpproposals>>).
BIP-38 proposes a common standard for encrypting private keys with a passphrase and encoding them with Base58Check so that they can be stored securely on backup media, transported securely between wallets, or kept in any other conditions where the key might be exposed. The standard for encryption uses the Advanced Encryption Standard (AES), a standard established by the NIST and used broadly in data encryption implementations for commercial and military applications.
((("bitcoin improvement proposals", "Encrypted Private Keys (BIP-38)")))((("keys and addresses", "advanced forms", "encrypted private keys")))((("public and private keys", "encrypted private keys")))((("passwords", "encrypted private keys")))((("security", "passwords")))Private keys must remain secret. The need for _confidentiality_ of the private keys is a truism that is quite difficult to achieve in practice, because it conflicts with the equally important security objective of _availability_. Keeping the private key private is much harder when you need to store backups of the private key to avoid losing it. A private key stored in a wallet that is encrypted by a password might be secure, but that wallet needs to be backed up. At times, users need to move keys from one wallet to another—to upgrade or replace the wallet software, for example. Private key backups might also be stored on paper (see <<paper_wallets>>) or on external storage media, such as a USB flash drive. But what if the backup itself is stolen or lost? These conflicting security goals led to the introduction of a portable and convenient standard for encrypting private keys in a way that can be understood by many different wallets and bitcoin clients, standardized by BIP-38 (see <<appdxbitcoinimpproposals>>).
A BIP-38 encryption scheme takes as input a bitcoin private key, usually encoded in the WIF, as a Base58Check string with the prefix of "5." Additionally, the BIP-38 encryption scheme takes a passphrase—a long password—usually composed of several words or a complex string of alphanumeric characters. The result of the BIP-38 encryption scheme is a Base58Check-encoded encrypted private key that begins with the prefix +6P+. If you see a key that starts with +6P+, it is encrypted and requires a passphrase in order to convert (decrypt) it back into a WIF-formatted private key (prefix +5+) that can be used in any wallet. Many wallet applications now recognize BIP-38-encrypted private keys and will prompt the user for a passphrase to decrypt and import the key. Third-party applications, such as the incredibly useful browser-based http://bitaddress.org[Bit Address] (Wallet Details tab), can be used to decrypt BIP-38 keys.
BIP-38 proposes a common standard for encrypting private keys with a passphrase and encoding them with Base58Check so that they can be stored securely on backup media, transported securely between wallets, or kept in any other conditions where the key might be exposed. The standard for encryption uses the Advanced Encryption Standard (AES), a standard established by the NIST and used broadly in data encryption implementations for commercial and military applications.
A BIP-38 encryption scheme takes as input a bitcoin private key, usually encoded in the WIF, as a Base58Check string with the prefix of "5." Additionally, the BIP-38 encryption scheme takes a passphrase—a long password—usually composed of several words or a complex string of alphanumeric characters. The result of the BIP-38 encryption scheme is a Base58Check-encoded encrypted private key that begins with the prefix +6P+. If you see a key that starts with +6P+, it is encrypted and requires a passphrase in order to convert (decrypt) it back into a WIF-formatted private key (prefix +5+) that can be used in any wallet. Many wallet applications now recognize BIP-38-encrypted private keys and will prompt the user for a passphrase to decrypt and import the key. Third-party applications, such as the incredibly useful browser-based http://bitaddress.org[Bit Address] (Wallet Details tab), can be used to decrypt BIP-38 keys.
The most common use case for BIP-38 encrypted keys is for paper wallets that can be used to back up private keys on a piece of paper. As long as the user selects a strong passphrase, a paper wallet with BIP-38 encrypted private keys is incredibly secure and a great way to create offline bitcoin storage (also known as "cold storage").
Test the encrypted keys in <<table_4-10>> using bitaddress.org to see how you can get the decrypted key by entering the passphrase.
[[table_4-10]]
.Example of BIP-38 encrypted private key
.Example of BIP-38 encrypted private key
|=======
| *Private Key (WIF)* | 5J3mBbAH58CpQ3Y5RNJpUKPE62SQ5tfcvU2JpbnkeyhfsYB1Jcn
| *Passphrase* | MyTestPassphrase
@ -636,44 +642,46 @@ Test the encrypted keys in <<table_4-10>> using bitaddress.org to see how you ca
[[p2sh_addresses]]
==== Pay-to-Script Hash (P2SH) and Multisig Addresses
==== Pay-to-Script Hash (P2SH) and Multisig Addresses
((("keys and addresses", "advanced forms", "pay-to-script hash and multisig addresses")))((("Pay-to-Script-Hash (P2SH)", "multisig addresses and")))((("multisig addresses")))((("addresses", "multisig addresses")))As we know, traditional bitcoin addresses begin with the number “1” and are derived from the public key, which is derived from the private key. Although anyone can send bitcoin to a “1” address, that bitcoin can only be spent by presenting the corresponding private key signature and public key hash.
((("keys and addresses", "advanced forms", "pay-to-script hash and multisig addresses")))((("Pay-to-Script-Hash (P2SH)", "multisig addresses and")))((("multisig addresses")))((("addresses", "multisig addresses")))As we know, traditional bitcoin addresses begin with the number “1” and are derived from the public key, which is derived from the private key. Although anyone can send bitcoin to a “1” address, that bitcoin can only be spent by presenting the corresponding private key signature and public key hash.
((("bitcoin improvement proposals", "Pay to Script Hash (BIP-16)")))Bitcoin addresses that begin with the number “3” are pay-to-script hash (P2SH) addresses, sometimes erroneously called multisignature or multisig addresses. They designate the beneficiary of a bitcoin transaction as the hash of a script, instead of the owner of a public key. The feature was introduced in January 2012 with BIP-16 (see <<appdxbitcoinimpproposals>>), and is being widely adopted because it provides the opportunity to add functionality to the address itself. Unlike transactions that "send" funds to traditional “1” bitcoin addresses, also known as a pay-to-public-key-hash (P2PKH), funds sent to “3” addresses require something more than the presentation of one public key hash and one private key signature as proof of ownership. The requirements are designated at the time the address is created, within the script, and all inputs to this address will be encumbered with the same requirements.
A P2SH address is created from a transaction script, which defines who can spend a transaction output (for more details, see <<p2sh>>). Encoding a P2SH address involves using the same double-hash function as used during creation of a bitcoin address, only applied on the script instead of the public key:
----
script hash = RIPEMD160(SHA256(script))
----
The resulting "script hash" is encoded with Base58Check with a version prefix of 5, which results in an encoded address starting with a +3+. An example of a P2SH address is +3F6i6kwkevjR7AsAd4te2YB2zZyASEm1HM+, which can be derived using the Bitcoin Explorer commands +script-encode+, +sha256+, +ripemd160+, and +base58check-encode+ (see <<appdx_bx>>) as follows:
----
$ echo dup hash160 [89abcdefabbaabbaabbaabbaabbaabbaabbaabba] equalverify checksig > script
$ bx script-encode < script | bx sha256 | bx ripemd160 | bx base58check-encode --version 5
$ echo \
'DUP HASH160 [89abcdefabbaabbaabbaabbaabbaabbaabbaabba] EQUALVERIFY CHECKSIG' > script
$ bx script-encode < script | bx sha256 | bx ripemd160 \
| bx base58check-encode --version 5
3F6i6kwkevjR7AsAd4te2YB2zZyASEm1HM
----
[TIP]
====
P2SH is not necessarily the same as a multisignature standard transaction. A P2SH address _most often_ represents a multi-signature script, but it might also represent a script encoding other types of transactions.
P2SH is not necessarily the same as a multisignature standard transaction. A P2SH address _most often_ represents a multi-signature script, but it might also represent a script encoding other types of transactions.
====
===== Multisignature addresses and P2SH
Currently, the most common implementation of the P2SH function is the multi-signature address script. As the name implies, the underlying script requires more than one signature to prove ownership and therefore spend funds. The bitcoin multi-signature feature is designed to require M signatures (also known as the “threshold”) from a total of N keys, known as an M-of-N multisig, where M is equal to or less than N. For example, Bob the coffee shop owner from <<ch01_intro_what_is_bitcoin>> could use a multisignature address requiring 1-of-2 signatures from a key belonging to him and a key belonging to his spouse, ensuring either of them could sign to spend a transaction output locked to this address. This would be similar to a “joint account” as implemented in traditional banking where either spouse can spend with a single signature. Or Gopesh,((("use cases", "offshore contract services"))) the web designer paid by Bob to create a website, might have a 2-of-3 multisignature address for his business that ensures that no funds can be spent unless at least two of the business partners sign a transaction.
Currently, the most common implementation of the P2SH function is the multi-signature address script. As the name implies, the underlying script requires more than one signature to prove ownership and therefore spend funds. The bitcoin multi-signature feature is designed to require M signatures (also known as the “threshold”) from a total of N keys, known as an M-of-N multisig, where M is equal to or less than N. For example, Bob the coffee shop owner from <<ch01_intro_what_is_bitcoin>> could use a multisignature address requiring 1-of-2 signatures from a key belonging to him and a key belonging to his spouse, ensuring either of them could sign to spend a transaction output locked to this address. This would be similar to a “joint account” as implemented in traditional banking where either spouse can spend with a single signature. Or Gopesh,((("use cases", "offshore contract services"))) the web designer paid by Bob to create a website, might have a 2-of-3 multisignature address for his business that ensures that no funds can be spent unless at least two of the business partners sign a transaction.
We will explore how to create transactions that spend funds from P2SH (and multi-signature) addresses in <<transactions>>.
==== Vanity Addresses
((("keys and addresses", "advanced forms", "vanity addresses")))((("vanity addresses", id="vanity04")))((("addresses", "vanity addresses", id="Avanity04")))Vanity addresses are valid bitcoin addresses that contain human-readable messages. For example, +1LoveBPzzD72PUXLzCkYAtGFYmK5vYNR33+ is a valid address that contains the letters forming the word "Love" as the first four Base-58 letters. Vanity addresses require generating and testing billions of candidate private keys, until a bitcoin address with the desired pattern is found. Although there are some optimizations in the vanity generation algorithm, the process essentially involves picking a private key at random, deriving the public key, deriving the bitcoin address, and checking to see if it matches the desired vanity pattern, repeating billions of times until a match is found.
((("keys and addresses", "advanced forms", "vanity addresses")))((("vanity addresses", id="vanity04")))((("addresses", "vanity addresses", id="Avanity04")))Vanity addresses are valid bitcoin addresses that contain human-readable messages. For example, +1LoveBPzzD72PUXLzCkYAtGFYmK5vYNR33+ is a valid address that contains the letters forming the word "Love" as the first four Base-58 letters. Vanity addresses require generating and testing billions of candidate private keys, until a bitcoin address with the desired pattern is found. Although there are some optimizations in the vanity generation algorithm, the process essentially involves picking a private key at random, deriving the public key, deriving the bitcoin address, and checking to see if it matches the desired vanity pattern, repeating billions of times until a match is found.
Once a vanity address matching the desired pattern is found, the private key from which it was derived can be used by the owner to spend bitcoin in exactly the same way as any other address. Vanity addresses are no less or more secure than any other address. They depend on the same Elliptic Curve Cryptography (ECC) and SHA as any other address. You can no more easily find the private key of an address starting with a vanity pattern than you can any other address.
In <<ch01_intro_what_is_bitcoin>>, we introduced Eugenia, a children's charity director operating in the Philippines. Let's say that Eugenia is organizing a bitcoin fundraising drive and wants to use a vanity bitcoin address to publicize the fundraising. Eugenia will create a vanity address that starts with "1Kids" to promote the children's charity fundraiser. Let's see how this vanity address will be created and what it means for the security of Eugenia's charity.((("use cases", "charitable donations", startref="eugeniafour")))
In <<ch01_intro_what_is_bitcoin>>, we introduced Eugenia, a children's charity director operating in the Philippines. Let's say that Eugenia is organizing a bitcoin fundraising drive and wants to use a vanity bitcoin address to publicize the fundraising. Eugenia will create a vanity address that starts with "1Kids" to promote the children's charity fundraiser. Let's see how this vanity address will be created and what it means for the security of Eugenia's charity.((("use cases", "charitable donations", startref="eugeniafour")))
===== Generating vanity addresses
@ -697,7 +705,7 @@ Let's look at the pattern "1Kids" as a number and see how frequently we might fi
|=======
| Length | Pattern | Frequency | Average search time
| 1 | 1K | 1 in 58 keys | < 1 milliseconds
| 2 | 1Ki| 1 in 3,364 | 50 milliseconds
| 2 | 1Ki| 1 in 3,364 | 50 milliseconds
| 3 | 1Kid | 1 in 195,000 | < 2 seconds
| 4 | 1Kids | 1 in 11 million | 1 minute
| 5 | 1KidsC | 1 in 656 million | 1 hour
@ -710,9 +718,9 @@ Let's look at the pattern "1Kids" as a number and see how frequently we might fi
|=======
As you can see, Eugenia won't be creating the vanity address "1KidsCharity" anytime soon, even if she had access to several thousand computers. Each additional character increases the difficulty by a factor of 58. Patterns with more than seven characters are usually found by specialized hardware, such as custom-built desktops with multiple GPUs. These are often repurposed bitcoin mining "rigs" that are no longer profitable for bitcoin mining but can be used to find vanity addresses. Vanity searches on GPU systems are many orders of magnitude faster than on a general-purpose CPU.
As you can see, Eugenia won't be creating the vanity address "1KidsCharity" anytime soon, even if she had access to several thousand computers. Each additional character increases the difficulty by a factor of 58. Patterns with more than seven characters are usually found by specialized hardware, such as custom-built desktops with multiple GPUs. These are often repurposed bitcoin mining "rigs" that are no longer profitable for bitcoin mining but can be used to find vanity addresses. Vanity searches on GPU systems are many orders of magnitude faster than on a general-purpose CPU.
Another way to find a vanity address is to outsource the work to a pool of vanity miners, such as the pool at http://vanitypool.appspot.com[Vanity Pool]. A pool is a service that allows those with GPU hardware to earn bitcoin searching for vanity addresses for others. For a small payment (0.01 bitcoin or approximately $5 at the time of this writing), Eugenia can outsource the search for a seven-character pattern vanity address and get results in a few hours instead of having to run a CPU search for months.
Another way to find a vanity address is to outsource the work to a pool of vanity miners, such as the pool at http://vanitypool.appspot.com[Vanity Pool]. A pool is a service that allows those with GPU hardware to earn bitcoin searching for vanity addresses for others. For a small payment (0.01 bitcoin or approximately $5 at the time of this writing), Eugenia can outsource the search for a seven-character pattern vanity address and get results in a few hours instead of having to run a CPU search for months.
Generating a vanity address is a brute-force exercise: try a random key, check the resulting address to see if it matches the desired pattern, repeat until successful. <<vanity_miner_code>> shows an example of a "vanity miner," a program designed to find vanity addresses, written in C++. The example uses the libbitcoin library, which we introduced in <<alt_libraries>>.
@ -762,9 +770,9 @@ The example code will take a few seconds to find a match for the three-character
===== Vanity address security
((("security", "vanity addresses")))Vanity addresses can be used to enhance _and_ to defeat security measures; they are truly a double-edged sword. Used to improve security, a distinctive address makes it harder for adversaries to substitute their own address and fool your customers into paying them instead of you. Unfortunately, vanity addresses also make it possible for anyone to create an address that _resembles_ any random address, or even another vanity address, thereby fooling your customers.
((("security", "vanity addresses")))Vanity addresses can be used to enhance _and_ to defeat security measures; they are truly a double-edged sword. Used to improve security, a distinctive address makes it harder for adversaries to substitute their own address and fool your customers into paying them instead of you. Unfortunately, vanity addresses also make it possible for anyone to create an address that _resembles_ any random address, or even another vanity address, thereby fooling your customers.
Eugenia could advertise a randomly generated address (e.g., +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy+) to which people can send their donations. Or, she could generate a vanity address that starts with 1Kids, to make it more distinctive.
Eugenia could advertise a randomly generated address (e.g., +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy+) to which people can send their donations. Or, she could generate a vanity address that starts with 1Kids, to make it more distinctive.
In both cases, one of the risks of using a single fixed address (rather than a separate dynamic address per donor) is that a thief might be able to infiltrate your website and replace it with his own address, thereby diverting donations to himself. If you have advertised your donation address in a number of different places, your users may visually inspect the address before making a payment to ensure it is the same one they saw on your website, on your email, and on your flyer. In the case of a random address like +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy+, the average user will perhaps inspect the first few characters "1J7mdg" and be satisfied that the address matches. Using a vanity address generator, someone with the intent to steal by substituting a similar-looking address can quickly generate addresses that match the first few characters, as shown in <<table_4-13>>.
@ -777,12 +785,12 @@ In both cases, one of the risks of using a single fixed address (rather than a s
| *Vanity (6-character match)* | 1J7mdg5WxGENmwyJP9xuGhG5KRzu99BBCX
|=======
So does a vanity address increase security? If Eugenia generates the vanity address +1Kids33q44erFfpeXrmDSz7zEqG2FesZEN+, users are likely to look at the vanity pattern word _and a few characters beyond_, for example noticing the "1Kids33" part of the address. That would force an attacker to generate a vanity address matching at least six characters (two more), expending an effort that is 3,364 times (58 &#x00D7; 58) higher than the effort Eugenia expended for her 4-character vanity. Essentially, the effort Eugenia expends (or pays a vanity pool for) "pushes" the attacker into having to produce a longer pattern vanity. If Eugenia pays a pool to generate an 8-character vanity address, the attacker would be pushed into the realm of 10 characters, which is infeasible on a personal computer and expensive even with a custom vanity-mining rig or vanity pool. What is affordable for Eugenia becomes unaffordable for the attacker, especially if the potential reward of fraud is not high enough to cover the cost of the vanity address generation.((("", startref="Avanity04")))((("", startref="vanity04")))((("", startref="eugeniafour")))
So does a vanity address increase security? If Eugenia generates the vanity address +1Kids33q44erFfpeXrmDSz7zEqG2FesZEN+, users are likely to look at the vanity pattern word _and a few characters beyond_, for example noticing the "1Kids33" part of the address. That would force an attacker to generate a vanity address matching at least six characters (two more), expending an effort that is 3,364 times (58 &#x00D7; 58) higher than the effort Eugenia expended for her 4-character vanity. Essentially, the effort Eugenia expends (or pays a vanity pool for) "pushes" the attacker into having to produce a longer pattern vanity. If Eugenia pays a pool to generate an 8-character vanity address, the attacker would be pushed into the realm of 10 characters, which is infeasible on a personal computer and expensive even with a custom vanity-mining rig or vanity pool. What is affordable for Eugenia becomes unaffordable for the attacker, especially if the potential reward of fraud is not high enough to cover the cost of the vanity address generation.((("", startref="Avanity04")))((("", startref="vanity04")))((("", startref="eugeniafour")))
[[paper_wallets]]
==== Paper Wallets
((("keys and addresses", "advanced forms", "paper wallets")))((("paper wallets", id="paperw04")))((("wallets", "types of", "paper wallets", id="Wpaper04")))Paper wallets are bitcoin private keys printed on paper. Often the paper wallet also includes the corresponding bitcoin address for convenience, but this is not necessary because it can be derived from the private key. Paper wallets are a very effective way to create backups or offline bitcoin storage, also known as "cold storage." As a backup mechanism, a paper wallet can provide security against the loss of key due to a computer mishap such as a hard-drive failure, theft, or accidental deletion. As a "cold storage" mechanism, if the paper wallet keys are generated offline and never stored on a computer system, they are much more secure against hackers, keyloggers, and other online computer threats.
((("keys and addresses", "advanced forms", "paper wallets")))((("paper wallets", id="paperw04")))((("wallets", "types of", "paper wallets", id="Wpaper04")))Paper wallets are bitcoin private keys printed on paper. Often the paper wallet also includes the corresponding bitcoin address for convenience, but this is not necessary because it can be derived from the private key. Paper wallets are a very effective way to create backups or offline bitcoin storage, also known as "cold storage." As a backup mechanism, a paper wallet can provide security against the loss of key due to a computer mishap such as a hard-drive failure, theft, or accidental deletion. As a "cold storage" mechanism, if the paper wallet keys are generated offline and never stored on a computer system, they are much more secure against hackers, keyloggers, and other online computer threats.
Paper wallets come in many shapes, sizes, and designs, but at a very basic level are just a key and an address printed on paper. <<table_4-14>> shows the simplest form of a paper wallet.
@ -801,7 +809,7 @@ Paper wallets can be generated easily using a tool such as the client-side JavaS
.An example of a simple paper wallet from bitaddress.org
image::images/mbc2_0408.png[]
((("bitcoin improvement proposals", "Encrypted Private Keys (BIP-38)")))The disadvantage of a simple paper wallet system is that the printed keys are vulnerable to theft. A thief who is able to gain access to the paper can either steal it or photograph the keys and take control of the bitcoin locked with those keys. A more sophisticated paper wallet storage system uses BIP-38 encrypted private keys. The keys printed on the paper wallet are protected by a passphrase that the owner has memorized. Without the passphrase, the encrypted keys are useless. Yet, they still are superior to a passphrase-protected wallet because the keys have never been online and must be physically retrieved from a safe or other physically secured storage. <<paper_wallet_encrypted>> shows a paper wallet with an encrypted private key (BIP-38) created on the bitaddress.org site.
((("bitcoin improvement proposals", "Encrypted Private Keys (BIP-38)")))The disadvantage of a simple paper wallet system is that the printed keys are vulnerable to theft. A thief who is able to gain access to the paper can either steal it or photograph the keys and take control of the bitcoin locked with those keys. A more sophisticated paper wallet storage system uses BIP-38 encrypted private keys. The keys printed on the paper wallet are protected by a passphrase that the owner has memorized. Without the passphrase, the encrypted keys are useless. Yet, they still are superior to a passphrase-protected wallet because the keys have never been online and must be physically retrieved from a safe or other physically secured storage. <<paper_wallet_encrypted>> shows a paper wallet with an encrypted private key (BIP-38) created on the bitaddress.org site.
[[paper_wallet_encrypted]]
.An example of an encrypted paper wallet from bitaddress.org. The passphrase is "test."
@ -822,12 +830,8 @@ image::images/mbc2_0410.png[]
.The bitcoinpaperwallet.com paper wallet with the private key concealed
image::images/mbc2_0411.png[]
Other designs feature additional copies of the key and address, in the form of detachable stubs similar to ticket stubs, allowing you to store multiple copies to protect against fire, flood, or other natural disasters.((("", startref="KAadvanced04")))((("", startref="Wpaper04")))((("", startref="paperw04")))
Other designs feature additional copies of the key and address, in the form of detachable stubs similar to ticket stubs, allowing you to store multiple copies to protect against fire, flood, or other natural disasters.((("", startref="KAadvanced04")))((("", startref="Wpaper04")))((("", startref="paperw04")))
[[paper_wallet_spw]]
.An example of a paper wallet with additional copies of the keys on a backup "stub"
image::images/mbc2_0412.png[]

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@ -66,13 +66,13 @@ You may also notice a lot of strange and indecipherable fields and hexadecimal s
((("balances")))When we say that a user's wallet has "received" bitcoin, what we mean is that the wallet has detected a UTXO that can be spent with one of the keys controlled by that wallet. Thus, a user's bitcoin "balance" is the sum of all UTXO that user's wallet can spend and which may be scattered among hundreds of transactions and hundreds of blocks. The concept of a balance is created by the wallet application. The wallet calculates the user's balance by scanning the blockchain and aggregating the value of any UTXO the wallet can spend with the keys it controls. Most wallets maintain a database or use a database service to store a quick reference set of all the UTXO they can spend with the keys they control.
((("satoshis")))A transaction output can have an arbitrary (integer) value denominated as a multiple of satoshis. Just like dollars can be divided down to two decimal places as cents, bitcoin can be divided down to eight decimal places as satoshis. Although an output can have any arbitrary value, once created it is indivisible. This is an important characteristic of outputs that needs to be emphasized: outputs are _discrete_ and _indivisible_ units of value, denominated in integer satoshis. An unspent output can only be consumed in its entirety by a transaction.
((("satoshis")))A transaction output can have an arbitrary (integer) value denominated as a multiple of satoshis. Just as dollars can be divided down to two decimal places as cents, bitcoin can be divided down to eight decimal places as satoshis. Although an output can have any arbitrary value, once created it is indivisible. This is an important characteristic of outputs that needs to be emphasized: outputs are _discrete_ and _indivisible_ units of value, denominated in integer satoshis. An unspent output can only be consumed in its entirety by a transaction.
((("change, making")))If an UTXO is larger than the desired value of a transaction, it must still be consumed in its entirety and change must be generated in the transaction. In other words, if you have a UTXO worth 20 bitcoin and want to pay only 1 bitcoin, your transaction must consume the entire 20-bitcoin UTXO and produce two outputs: one paying 1 bitcoin to your desired recipient and another paying 19 bitcoin in change back to your wallet. As a result of the indivisible nature of transaction outputs, most bitcoin transactions will have to generate change.
((("change, making")))If a UTXO is larger than the desired value of a transaction, it must still be consumed in its entirety and change must be generated in the transaction. In other words, if you have a UTXO worth 20 bitcoin and want to pay only 1 bitcoin, your transaction must consume the entire 20-bitcoin UTXO and produce two outputs: one paying 1 bitcoin to your desired recipient and another paying 19 bitcoin in change back to your wallet. As a result of the indivisible nature of transaction outputs, most bitcoin transactions will have to generate change.
Imagine a shopper buying a $1.50 beverage, reaching into her wallet and trying to find a combination of coins and bank notes to cover the $1.50 cost. The shopper will choose exact change if available e.g. a dollar bill and two quarters (a quarter is $0.25), or a combination of smaller denominations (six quarters), or if necessary, a larger unit such as a $5 note. If she hands too much money, say $5, to the shop owner, she will expect $3.50 change, which she will return to her wallet and have available for future transactions.
Similarly, a bitcoin transaction must be created from a user's UTXO in whatever denominations that user has available. Users cannot cut an UTXO in half any more than they can cut a dollar bill in half and use it as currency. The user's wallet application will typically select from the user's available UTXO to compose an amount greater than or equal to the desired transaction amount.
Similarly, a bitcoin transaction must be created from a user's UTXO in whatever denominations that user has available. Users cannot cut a UTXO in half any more than they can cut a dollar bill in half and use it as currency. The user's wallet application will typically select from the user's available UTXO to compose an amount greater than or equal to the desired transaction amount.
As with real life, the bitcoin application can use several strategies to satisfy the purchase amount: combining several smaller units, finding exact change, or using a single unit larger than the transaction value and making change. All of this complex assembly of spendable UTXO is done by the user's wallet automatically and is invisible to users. It is only relevant if you are programmatically constructing raw transactions from UTXO.
@ -171,7 +171,7 @@ Here are some hints:
To build a transaction, a wallet selects from the UTXO it controls, UTXO with enough value to make the requested payment. Sometimes one UTXO is enough, other times more than one is needed. For each UTXO that will be consumed to make this payment, the wallet creates one input pointing to the UTXO and unlocks it with an unlocking script.
Let's look at the components of an input in greater detail. The first part of an input is a pointer to an UTXO by reference to the transaction hash and an output index, which identifies the specific UTXO in that transaction. The second part is an unlocking script, which the wallet constructs in order to satisfy the spending conditions set in the UTXO. Most often, the unlocking script is a digital signature and public key proving ownership of the bitcoin. However, not all unlocking scripts contain signatures. The third part is a sequence number, which will be discussed later.
Let's look at the components of an input in greater detail. The first part of an input is a pointer to a UTXO by reference to the transaction hash and an output index, which identifies the specific UTXO in that transaction. The second part is an unlocking script, which the wallet constructs in order to satisfy the spending conditions set in the UTXO. Most often, the unlocking script is a digital signature and public key proving ownership of the bitcoin. However, not all unlocking scripts contain signatures. The third part is a sequence number, which will be discussed later.
Consider our example in <<transactions_behind_the_scenes>>. The transaction inputs are an array (list) called +vin+:
@ -298,7 +298,7 @@ Transaction fees are calculated based on the size of the transaction in kilobyte
Over time, the way transaction fees are calculated and the effect they have on transaction prioritization has evolved. At first, transaction fees were fixed and constant across the network. Gradually, the fee structure relaxed and may be influenced by market forces, based on network capacity and transaction volume. Since at least the beginning of 2016, capacity limits in bitcoin have created competition between transactions, resulting in higher fees and effectively making free transactions a thing of the past. Zero fee or very low fee transactions rarely get mined and sometimes will not even be propagated across the network.
((("fees", "fee relay policies")))((("minrelaytxfee option")))In Bitcoin Core, fee relay policies are set by the +minrelaytxfee+ option. The current default +minrelaytxfee+ is 0.00001 bitcoin or a hundredth of a millibitcoin per kilobyte. Therefore, by default, transactions with a fee less than 0.0001 bitcoin are treated as free and are only relayed if there is space in the mempool; otherwise, they are dropped. Bitcoin nodes can override the default fee relay policy by adjusting the value of +minrelaytxfee+.
((("fees", "fee relay policies")))((("minrelaytxfee option")))In Bitcoin Core, fee relay policies are set by the +minrelaytxfee+ option. The current default +minrelaytxfee+ is 0.00001 bitcoin or a hundredth of a millibitcoin per kilobyte. Therefore, by default, transactions with a fee less than 0.00001 bitcoin are treated as free and are only relayed if there is space in the mempool; otherwise, they are dropped. Bitcoin nodes can override the default fee relay policy by adjusting the value of +minrelaytxfee+.
((("dynamic fees")))((("fees", "dynamic fees")))Any bitcoin service that creates transactions, including wallets, exchanges, retail applications, etc., _must_ implement dynamic fees. Dynamic fees can be implemented through a third-party fee estimation service or with a built-in fee estimation algorithm. If you're unsure, begin with a third-party service and as you gain experience design and implement your own algorithm if you wish to remove the third-party dependency.
@ -459,7 +459,7 @@ Try validating the preceding script yourself using pencil and paper. When the sc
((("security", "locking and unlocking scripts")))In the original bitcoin client, the unlocking and locking scripts were concatenated and executed in sequence. For security reasons, this was changed in 2010, because of a vulnerability that allowed a malformed unlocking script to push data onto the stack and corrupt the locking script. In the current implementation, the scripts are executed separately with the stack transferred between the two executions, as described next.
First, the unlocking script is executed, using the stack execution engine. If the unlocking script is executed without errors (e.g., it has no "dangling" operators left over), the main stack (not the alternate stack) is copied and the locking script is executed. If the result of executing the locking script with the stack data copied from the unlocking script is "TRUE," the unlocking script has succeeded in resolving the conditions imposed by the locking script and, therefore, the input is a valid authorization to spend the UTXO. If any result other than "TRUE" remains after execution of the combined script, the input is invalid because it has failed to satisfy the spending conditions placed on the UTXO.
First, the unlocking script is executed, using the stack execution engine. If the unlocking script is executed without errors (e.g., it has no "dangling" operators left over), the main stack is copied and the locking script is executed. If the result of executing the locking script with the stack data copied from the unlocking script is "TRUE," the unlocking script has succeeded in resolving the conditions imposed by the locking script and, therefore, the input is a valid authorization to spend the UTXO. If any result other than "TRUE" remains after execution of the combined script, the input is invalid because it has failed to satisfy the spending conditions placed on the UTXO.
[[p2pkh]]
@ -677,7 +677,7 @@ Note that in verifying the signature, the private key is neither known nor revea
[TIP]
====
The math of ECDSA is complex and difficult to understand. There are a number of great guides online that might help. Search for "ECDSA explained" or try this one: http://bit.ly/2r0HhGB[].
ECDSA is necessarily a fairly complicated piece of math; a full explanation is beyond the scope of this book. A number of great guides online take you through it step by step: search for "ECDSA explained" or try this one: http://bit.ly/2r0HhGB[].
====
==== The Importance of Randomness in Signatures

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@ -12,7 +12,7 @@ First, we will look at _multisignature_ scripts. Next, we will examine the secon
[[multisig]]
=== Multisignature
((("transactions", "advanced", "multisignature scripts")))((("transactions", "advanced", id="Tadv07")))((("scripting", "multisignature scripts", id="Smulti07")))((("multisignature scripts")))Multisignature scripts set a condition where N public keys are recorded in the script and at least M of those must provide signatures to unlock the funds. This is also known as an M-of-N scheme, where N is the total number of keys and M is the threshold of signatures required for validation. For example, a 2-of-3 multisignature is one where three public keys are listed as potential signers and at least two of those must be used to create signatures for a valid transaction to spend the funds.
((("transactions", "advanced", "multisignature scripts")))((("transactions", "advanced", id="Tadv07")))((("scripting", "multisignature scripts", id="Smulti07")))((("multisignature scripts")))Multisignature scripts set a condition where N public keys are recorded in the script and at least M of those must provide signatures to unlock the funds. This is also known as an M-of-N scheme, where N is the total number of keys and M is the threshold of signatures required for validation. For example, a 2-of-3 multisignature is one where three public keys are listed as potential signers and at least two of those must be used to create signatures for a valid transaction to spend the funds.
At this time, _standard_ multisignature scripts are limited to at most 3 listed public keys, meaning you can do anything from a 1-of-1 to a 3-of-3 multisignature or any combination within that range. The limitation to 3 listed keys might be lifted by the time this book is published, so check the +IsStandard()+ function to see what is currently accepted by the network. Note that the limit of 3 keys applies only to standard (also known as "bare") multisignature scripts, not to multisignature scripts wrapped in a Pay-to-Script-Hash (P2SH) script. P2SH multisignature scripts are limited to 15 keys, allowing for up to 15-of-15 multisignature. We will learn about P2SH in <<p2sh>>.
@ -211,11 +211,11 @@ P2SH addresses hide all of the complexity, so that the person making a payment d
==== Redeem Script and Validation
((("scripting", "Pay-to-Script-Hash", "redeem scripts and validation")))((("Pay-to-Script-Hash (P2SH)", "redeem scripts and validation")))((("redeem scripts")))((("validation")))Prior to version 0.9.2 of the Bitcoin Core client, Pay-to-Script-Hash was limited to the standard types of bitcoin transaction scripts, by the +IsStandard()+ function. That means that the redeem script presented in the spending transaction could only be one of the standard types: P2PK, P2PKH, or multisig, excluding +RETURN+ and P2SH itself.
((("scripting", "Pay-to-Script-Hash", "redeem scripts and validation")))((("Pay-to-Script-Hash (P2SH)", "redeem scripts and validation")))((("redeem scripts")))((("validation")))Prior to version 0.9.2 of the Bitcoin Core client, Pay-to-Script-Hash was limited to the standard types of bitcoin transaction scripts, by the +IsStandard()+ function. That means that the redeem script presented in the spending transaction could only be one of the standard types: P2PK, P2PKH, or multisig.
As of version 0.9.2 of the Bitcoin Core client, P2SH transactions can contain any valid script, making the P2SH standard much more flexible and allowing for experimentation with many novel and complex types of transactions.
Note that you are not able to put a P2SH inside a P2SH redeem script, because the P2SH specification is not recursive. While it is technically possible to include +RETURN+ in a redeem script, as nothing in the rules prevents you from doing so, it is of no practical use because executing +RETURN+ during validation will cause the transaction to be marked invalid.
You are not able to put a P2SH inside a P2SH redeem script, because the P2SH specification is not recursive. Also, while it is technically possible to include +RETURN+ (see <<op_return>>) in a redeem script, as nothing in the rules prevents you from doing so, it is of no practical use because executing +RETURN+ during validation will cause the transaction to be marked invalid.
Note that because the redeem script is not presented to the network until you attempt to spend a P2SH output, if you lock an output with the hash of an invalid redeem script it will be processed regardless. The UTXO will be successfully locked. However, you will not be able to spend it because the spending transaction, which includes the redeem script, will not be accepted because it is an invalid script. This creates a risk, because you can lock bitcoin in a P2SH that cannot be spent later. The network will accept the P2SH locking script even if it corresponds to an invalid redeem script, because the script hash gives no indication of the script it represents.((("", startref="Spay07")))
@ -325,12 +325,12 @@ More precisely, +CHECKLOCKTIMEVERIFY+ fails and halts execution, marking the tra
[NOTE]
====
+CLTV+ and +nLocktime+ use the same format to describe timelocks, either a block height or the time elapsed in seconds since Unix epoch. Critically, when used together, the format of +nLocktime+ must match that of +CLTV+ in the inputs&#x2014;they must both reference either block height or time in seconds.
+CLTV+ and +nLocktime+ use the same format to describe timelocks, either a block height or the time elapsed in seconds since Unix epoch. Critically, when used together, the format of +nLocktime+ must match that of +CLTV+ in the outputs&#x2014;they must both reference either block height or time in seconds.
====
After execution, if +CLTV+ is satisfied, the time parameter that preceded it remains as the top item on the stack and may need to be dropped, with +DROP+, for correct execution of subsequent script opcodes. You will often see +CHECKLOCKTIMEVERIFY+ followed by +DROP+ in scripts for this reason.
By using nLocktime in conjunction with +CLTV+, the scenario described in <<locktime_limitations>> changes. Because Alice locked the UTXO itself, it is now impossible for either Bob or Alice to spend it before the 3-month locktime has expired.((("", startref="alicesseven")))
By using nLocktime in conjunction with +CLTV+, the scenario described in <<locktime_limitations>> changes. Alice can no longer spend the money (because it's locked with Bob's key) and Bob cannot spend it before the 3-month locktime has expired.((("", startref="alicesseven")))
By introducing timelock functionality directly into the scripting language, +CLTV+ allows us to develop some very interesting complex scripts.((("", startref="cltv07")))
@ -498,7 +498,7 @@ Bob's unlocking script is identical:
<Bob's Sig> <hash pre-image>
----
The script with +IF+ does the same thing as using an opcode with a +VERIFY+ suffix; they both operate as guard clauses. However, the +VERIFY+ construction is more efficient, using one fewer opcode.
The script with +IF+ does the same thing as using an opcode with a +VERIFY+ suffix; they both operate as guard clauses. However, the +VERIFY+ construction is more efficient, using two fewer opcodes.
So, when do we use +VERIFY+ and when do we use +IF+? If all we are trying to do is to attach a precondition (guard clause), then +VERIFY+ is better. If, however, we want to have more than one execution path (flow control), then we need an +IF...ELSE+ flow control clause.

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@ -20,7 +20,7 @@ image::images/mbc2_0801.png["FullNodeReferenceClient_Small"]
All nodes include the routing function to participate in the network and might include other functionality. All nodes validate and propagate transactions and blocks, and discover and maintain connections to peers. In the full-node example in <<full_node_reference>>, the routing function is indicated by an orange circle named "Network Routing Node" or with the letter "N."
((("full-node clients")))Some nodes, called full nodes, also maintain a complete and up-to-date copy of the blockchain. Full nodes can autonomously and authoritatively verify any transaction without external reference. ((("simple-payment-verification (SPV)")))Some nodes maintain only a subset of the blockchain and verify transactions using a method called _simplified payment verification_, or SPV. ((("lightweight clients")))These nodes are known as SPV nodes or lightweight nodes. In the full-node example in the figure, the full-node blockchain database function is indicated by a blue circle called "Full Blockchain" or the letter "B." In <<bitcoin_network>>, SPV nodes are drawn without the blue circle, showing that they do not have a full copy of the blockchain.
((("full-node clients")))Some nodes, called full nodes, also maintain a complete and up-to-date copy of the blockchain. Full nodes can autonomously and authoritatively verify any transaction without external reference. ((("simple-payment-verification (SPV)")))Some nodes maintain only a subset of the blockchain and verify transactions using a method called _simplified payment verification_, or SPV. ((("lightweight clients")))These nodes are known as SPV nodes or lightweight nodes. In the full-node example in the figure, the full-node blockchain database function is indicated by a circle called "Full Blockchain" or the letter "B." In <<bitcoin_network>>, SPV nodes are drawn without the "B" circle, showing that they do not have a full copy of the blockchain.
((("bitcoin nodes", "mining nodes")))((("mining and consensus", "mining nodes")))((("Proof-of-Work algorithm")))((("mining and consensus", "Proof-of-Work algorithm")))Mining nodes compete to create new blocks by running specialized hardware to solve the Proof-of-Work algorithm. Some mining nodes are also full nodes, maintaining a full copy of the blockchain, while others are lightweight nodes participating in pool mining and depending on a pool server to maintain a full node. The mining function is shown in the full node as a black circle called "Miner" or the letter "M."
@ -175,7 +175,7 @@ image::images/mbc2_0806.png["InventorySynchronization"]
((("bitcoin network", "SPV nodes", id="BNspvnodes08")))((("bitcoin nodes", "SPV nodes", id="BNospv08")))((("simple-payment-verification (SPV)", id="simple08")))Not all nodes have the ability to store the full blockchain. Many bitcoin clients are designed to run on space- and power-constrained devices, such as smartphones, tablets, or embedded systems. For such devices, a _simplified payment verification_ (SPV) method is used to allow them to operate without storing the full blockchain. These types of clients are called SPV clients or lightweight clients. As bitcoin adoption surges, the SPV node is becoming the most common form of bitcoin node, especially for bitcoin wallets.
SPV nodes download only the block headers and do not download the transactions included in each block. The resulting chain of blocks, without transactions, is 1,000 times smaller than the full blockchain. SPV nodes cannot construct a full picture of all the UTXOs that are available for spending because they do not know about all the transactions on the network. SPV nodes verify transactions using a slightly different methodology that relies on peers to provide partial views of relevant parts of the blockchain on demand.
SPV nodes download only the block headers and do not download the transactions included in each block. The resulting chain of blocks, without transactions, is 1,000 times smaller than the full blockchain. SPV nodes cannot construct a full picture of all the UTXOs that are available for spending because they do not know about all the transactions on the network. SPV nodes verify transactions using a slightly different method that relies on peers to provide partial views of relevant parts of the blockchain on demand.
As an analogy, a full node is like a tourist in a strange city, equipped with a detailed map of every street and every address. By comparison, an SPV node is like a tourist in a strange city asking random strangers for turn-by-turn directions while knowing only one main avenue. Although both tourists can verify the existence of a street by visiting it, the tourist without a map doesn't know what lies down any of the side streets and doesn't know what other streets exist. Positioned in front of 23 Church Street, the tourist without a map cannot know if there are a dozen other "23 Church Street" addresses in the city and whether this is the right one. The mapless tourist's best chance is to ask enough people and hope some of them are not trying to mug him.

5
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@ -84,11 +84,8 @@ You can search for that block hash in any block explorer website, such as _block
https://blockchain.info/block/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
https://blockexplorer.com/block/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
Using the Bitcoin Core reference client on the command line:
----
$ bitcoin-cli getblock 000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
----
@ -285,7 +282,7 @@ Keep in mind that testnet3 is a large blockchain, in excess of 20 GB in early 20
===== Using testnet
Bitcoin Core, like almost all other bitcoin software, has full support for operation on testnet instead of mainnet, but also allows you to mine testnet coins and operate a full testnet node.
Bitcoin Core, like almost all other bitcoin software, has full support for operation on testnet instead of mainnet. All of Bitcoin Core's functions work on testnet, including the wallet, mining testnet coins, and syncing a full testnet node.
To start Bitcoin Core on testnet instead of mainnet you use the +testnet+ switch:

28
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@ -596,7 +596,7 @@ At the time of writing, the network is attempting to find a block whose header h
0000000000000000029AB9000000000000000000000000000000000000000000
----
As you can see, there are a lot of zeros at the beginning of that target, meaning that the acceptable range of hashes is much smaller, hence it's more difficult to find a valid hash. It will take on average more than 1.8 septa-hashes (thousand billion billion hashes) per second for the network to discover the next block. That seems like an impossible task, but fortunately the network is bringing 3 exa-hashes per second (EH/sec) of processing power to bear, which will be able to find a block in about 10 minutes on average.((("", startref="Cproof10")))((("", startref="proof10")))
As you can see, there are a lot of zeros at the beginning of that target, meaning that the acceptable range of hashes is much smaller, hence it's more difficult to find a valid hash. It will take on average more than 1.8 zeta-hashes (thousand billion billion hashes) per second for the network to discover the next block. That seems like an impossible task, but fortunately the network is bringing 3 exa-hashes per second (EH/sec) of processing power to bear, which will be able to find a block in about 10 minutes on average.((("", startref="Cproof10")))((("", startref="proof10")))
[[target_bits]]
==== Target Representation
@ -702,9 +702,11 @@ The difficulty of mining is closely related to the cost of electricity and the e
=== Successfully Mining the Block
((("mining and consensus", "mining the block", "successful completion")))((("use cases", "mining for bitcoin", id="jingtentwo")))As we saw earlier, Jing's node has constructed a candidate block and prepared it for mining. Jing has several hardware mining rigs with application-specific integrated circuits, where hundreds of thousands of integrated circuits run the SHA256 algorithm in parallel at incredible speeds. Many of these specialized machines are connected to his mining node over USB or a local area network. Next, the mining node running on Jing's desktop transmits the block header to his mining hardware, which starts testing trillions of nonces per second.
((("mining and consensus", "mining the block", "successful completion")))((("use cases", "mining for bitcoin", id="jingtentwo")))As we saw earlier, Jing's node has constructed a candidate block and prepared it for mining. Jing has several hardware mining rigs with application-specific integrated circuits, where hundreds of thousands of integrated circuits run the SHA256 algorithm in parallel at incredible speeds. Many of these specialized machines are connected to his mining node over USB or a local area network. Next, the mining node running on Jing's desktop transmits the block header to his mining hardware, which starts testing trillions of nonces per second. Because the nonce is only 32 bits, after exhausting all the nonce possibilities (about 4 billion), the mining hardware changes the block header (adjusting the coinbase extra nonce space or timestamp) and resets the nonce counter, testing new combinations.
Almost 11 minutes after starting to mine block 277,316, one of the hardware mining machines finds a solution and sends it back to the mining node. When inserted into the block header, the nonce 924,591,752 produces a block hash of:
Almost 11 minutes after starting to mine block 277,316, one of the hardware mining machines finds a solution and sends it back to the mining node.
When inserted into the block header, the nonce 924,591,752 produces a block hash of:
----
0000000000000001b6b9a13b095e96db41c4a928b97ef2d944a9b31b2cc7bdc4
@ -805,7 +807,7 @@ Any mining node whose perspective resembles Node Y will start building a candida
Forks are almost always resolved within one block. While part of the network's hashing power is dedicated to building on top of "triangle" as the parent, another part of the hashing power is focused on building on top of "upside-down triangle." Even if the hashing power is almost evenly split, it is likely that one set of miners will find a solution and propagate it before the other set of miners have found any solutions. Let's say, for example, that the miners building on top of "triangle" find a new block "rhombus" that extends the chain (e.g., star-triangle-rhombus). They immediately propagate this new block and the entire network sees it as a valid solution as shown in <<fork4>>.
All nodes that had chosen "triangle" as the winner in the previous round will simply extend the chain one more block. The nodes that chose "upside-down triangle" as the winner, however, will now see two chains: star-triangle-rhombus and star-upside-down-triangle. The chain star-triangle-rhombus is now longer (more cumulative work) than the other chain. As a result, those nodes will set the chain star-triangle-rhombus as the main chain and change the star-upside-down-triangle chain to a secondary chain, as shown in <<fork5>>. This is a chain reconvergence, because those nodes are forced to revise their view of the blockchain to incorporate the new evidence of a longer chain. Any miners working on extending the chain star-upside-down-triangle will now stop that work because their candidate block is an "orphan," as its parent "upside-down-triangle" is no longer on the longest chain. The transactions within "upside-down-triangle" are re-inserted in the mempool for inclusion in the next block, because the block they were in is no longer in the main chain. The entire network reconverges on a single blockchain star-triangle-rhombus, with "rhombus" as the last block in the chain. All miners immediately start working on candidate blocks that reference "rhombus" as their parent to extend the star-triangle-rhombus chain.
All nodes that had chosen "triangle" as the winner in the previous round will simply extend the chain one more block. The nodes that chose "upside-down triangle" as the winner, however, will now see two chains: star-triangle-rhombus and star-upside-down-triangle. The chain star-triangle-rhombus is now longer (more cumulative work) than the other chain. As a result, those nodes will set the chain star-triangle-rhombus as the main chain and change the star-upside-down-triangle chain to a secondary chain, as shown in <<fork5>>. This is a chain reconvergence, because those nodes are forced to revise their view of the blockchain to incorporate the new evidence of a longer chain. Any miners working on extending the chain star-upside-down-triangle will now stop that work because their candidate block is an "orphan," as its parent "upside-down-triangle" is no longer on the longest chain. The transactions within "upside-down-triangle" that are not within "triangle" are re-inserted in the mempool for inclusion in the next block to become a part of the main chain. The entire network reconverges on a single blockchain star-triangle-rhombus, with "rhombus" as the last block in the chain. All miners immediately start working on candidate blocks that reference "rhombus" as their parent to extend the star-triangle-rhombus chain.
[[fork4]]
[role="smallereighty"]
@ -829,12 +831,12 @@ The following list shows the total hashing power of the bitcoin network, over th
2009:: 0.5 MH/sec–8 MH/sec (16&#x00D7; growth)
2010:: 8 MH/sec–116 GH/sec (14,500&#x00D7; growth)
2011:: 16 GH/sec–9 TH/sec (562&#x00D7; growth)
2011:: 116 GH/sec–9 TH/sec (78&#x00D7; growth)
2012:: 9 TH/sec–23 TH/sec (2.5&#x00D7; growth)
2013:: 23 TH/sec–10 PH/sec (450&#x00D7; growth)
2014:: 10 PH/sec–300 PH/sec (3000&#x00D7; growth)
2015:: 300 PH/sec-800 PH/sec (266&#x00D7; growth)
2016:: 800 PH/sec-2.5 EH/sec (312&#x00D7; growth))
2014:: 10 PH/sec–300 PH/sec (30&#x00D7; growth)
2015:: 300 PH/sec-800 PH/sec (2.66&#x00D7; growth)
2016:: 800 PH/sec-2.5 EH/sec (3.12&#x00D7; growth)
In the chart in <<network_hashing_power>>, we can see that bitcoin network's hashing power increased over the past two years. As you can see, the competition between miners and the growth of bitcoin has resulted in an exponential increase in the hashing power (total hashes per second across the network).
@ -916,7 +918,7 @@ The massive increase of total hashing power has arguably made bitcoin impervious
Not all attackers will be motivated by profit, however. One potential attack scenario is where an attacker intends to disrupt the bitcoin network without the possibility of profiting from such disruption. A malicious attack aimed at crippling bitcoin would require enormous investment and covert planning, but could conceivably be launched by a well-funded, most likely state-sponsored, attacker. Alternatively, a well-funded attacker could attack bitcoin's consensus by simultaneously amassing mining hardware, compromising pool operators, and attacking other pools with denial-of-service. All of these scenarios are theoretically possible, but increasingly impractical as the bitcoin network's overall hashing power continues to grow exponentially.
Undoubtedly, a serious consensus attack would erode confidence in bitcoin in the short term, possibly causing a significant price decline. However, the bitcoin network and software are constantly evolving, so consensus attacks would be met with immediate countermeasures by the bitcoin community, making bitcoin hardier, stealthier, and more robust than ever.((("", startref="Cattack10")))((("", startref="MACattack10")))((("", startref="Sconsens10")))
Undoubtedly, a serious consensus attack would erode confidence in bitcoin in the short term, possibly causing a significant price decline. However, the bitcoin network and software are constantly evolving, so consensus attacks would be met with immediate countermeasures by the bitcoin community, making bitcoin more robust.((("", startref="Cattack10")))((("", startref="MACattack10")))((("", startref="Sconsens10")))
[[consensus_changes]]
=== Changing the Consensus Rules
@ -994,7 +996,7 @@ The term _soft fork_ was introduced to distinguish this upgrade method from a "h
One aspect of soft forks that is not immediately obvious is that soft fork upgrades can only be used to constrain the consensus rules, not to expand them. In order to be forward compatible, transactions and blocks created under the new rules must be valid under the old rules too, but not vice versa. The new rules can only limit what is valid; otherwise, they will trigger a hard fork when rejected under the old rules.
Soft forks can be implemented in a number of ways&#x2014;the term does not define a single method, rather a set of methods that all have one thing in common: they don't require all nodes to upgrade or force nonupgraded nodes out of consensus.
Soft forks can be implemented in a number of ways&#x2014;the term does not specify a particular method, rather a set of methods that all have one thing in common: they don't require all nodes to upgrade or force nonupgraded nodes out of consensus.
===== Soft forks redefining NOP opcodes
@ -1018,7 +1020,7 @@ Technical debt:: Because soft forks are more technically complex than a hard for
Validation relaxation:: Unmodified clients see transactions as valid, without evaluating the modified consensus rules. In effect, the unmodified clients are not validating using the full range of consensus rules, as they are blind to the new rules. This applies to NOP-based upgrades, as well as other soft fork upgrades.
Irreversible upgrades:: Because soft forks create transactions with additional consensus constraints, they become irreversible upgrades in practice. If a soft fork upgrade were to be reversed after being activated, any transactions created under the new rules could result in a loss of funds under the old rules. For example, if a CLTV transaction is evaluated under the old rules, there is no timelock constraint and it can be spent whenever. Therefore, critics contend that a failed soft fork that had to be reversed because of a bug would almost certainly lead to loss of funds.((("", startref="Crule10")))
Irreversible upgrades:: Because soft forks create transactions with additional consensus constraints, they become irreversible upgrades in practice. If a soft fork upgrade were to be reversed after beings activated, any transactions created under the new rules could result in a loss of funds under the old rules. For example, if a CLTV transaction is evaluated under the old rules, there is no timelock constraint and it can be spent at any time. Therefore, critics contend that a failed soft fork that had to be reversed because of a bug would almost certainly lead to loss of funds.((("", startref="Crule10")))
[[softforksignaling]]
=== Soft Fork Signaling with Block Version
@ -1086,7 +1088,7 @@ Unlike BIP-34, BIP-9 counts activation signaling in whole intervals based on the
BIP-9 offers a proposal state diagram to illustrate the various stages and transitions for a proposal, as shown in <<bip9states>>.
Proposals start in the +DEFINED+ state, once their parameters are known (defined) in the bitcoin software. For blocks with MTP after the start time, the proposal state transitions to +STARTED+. If the voting threshold is exceeded within a retarget period and the timeout has not been exceeded, the proposal state transitions to +LOCKED_IN+. One retarget period later, the proposal becomes +ACTIVE+. Proposals remain in the +ACTIVE+ state perpetually once they reach that state. If the timeout is elapsed before the voting threshold has been reached, the proposal state changes to +FAILED+, indicating a rejected proposal. +REJECTED+ proposals remain in that state perpetually.
Proposals start in the +DEFINED+ state, once their parameters are known (defined) in the bitcoin software. For blocks with MTP after the start time, the proposal state transitions to +STARTED+. If the voting threshold is exceeded within a retarget period and the timeout has not been exceeded, the proposal state transitions to +LOCKED_IN+. One retarget period later, the proposal becomes +ACTIVE+. Proposals remain in the +ACTIVE+ state perpetually once they reach that state. If the timeout elapses before the voting threshold has been reached, the proposal state changes to +FAILED+, indicating a rejected proposal. +FAILED+ proposals remain in that state perpetually.
[[bip9states]]
.BIP-9 state transition diagram
@ -1098,7 +1100,7 @@ The standard is defined in https://github.com/bitcoin/bips/blob/master/bip-0009.
=== Consensus Software Development
((("mining and consensus", "consensus software development")))((("development environment", "consensus software development")))Consensus software development continues to evolve and there is much discussion on the various mechanisms for changing the consensus rules. By its very nature, bitcoin sets a very high bar on coordination and consensus for changes. As a decentralized system, it has no "authority" that can impose its will on the participants of the network. Power is diffused between multiple constituencies such as miners, core developers, wallet developers, exchanges, merchants, and end users. Decisions cannot be made unilaterally by any of these constituencies. For example, while miners can theoretically change the rules by simple majority (51%), they are constrained by the consent of the other constituencies. If they act unilaterally, the rest of the participants may simply refuse to follow them, keeping the economic activity on a minority chain. Without economic activity (transactions, merchants, wallets, exchanges), the miners will be mining a worthless coin with empty blocks. This diffusion of power means that all the participants must coordinate, or no changes can be made. Status quo is the stable state of this system with only a few changes possible if there is strong consensus by a very large majority. The 95% threshold for soft forks is reflective of this reality.
((("mining and consensus", "consensus software development")))((("development environment", "consensus software development")))Consensus software continues to evolve and there is much discussion on the various mechanisms for changing the consensus rules. By its very nature, bitcoin sets a very high bar on coordination and consensus for changes. As a decentralized system, it has no "authority" that can impose its will on the participants of the network. Power is diffused between multiple constituencies such as miners, core developers, wallet developers, exchanges, merchants, and end users. Decisions cannot be made unilaterally by any of these constituencies. For example, while miners can theoretically change the rules by simple majority (51%), they are constrained by the consent of the other constituencies. If they act unilaterally, the rest of the participants may simply refuse to follow them, keeping the economic activity on a minority chain. Without economic activity (transactions, merchants, wallets, exchanges), the miners will be mining a worthless coin with empty blocks. This diffusion of power means that all the participants must coordinate, or no changes can be made. Status quo is the stable state of this system with only a few changes possible if there is strong consensus by a very large majority. The 95% threshold for soft forks is reflective of this reality.
((("hard forks")))It is important to recognize that there is no perfect solution for consensus development. Both hard forks and soft forks involve tradeoffs. For some types of changes, soft forks may be a better choice; for others, hard forks may be a better choice. There is no perfect choice; both carry risks. The one constant characteristic of consensus software development is that change is difficult and consensus forces compromise.

28
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@ -7,7 +7,7 @@ In this chapter we will look at the features offered by the bitcoin blockchain,
=== Introduction
((("blockchain applications", "benefits of bitcoin system")))The bitcoin system was designed as a decentralized currency and payment system. However, most of its functionality is derived from much lower-level constructs that can be used for much broader applications. Bitcoin wasn't built with components such as accounts, users, balances, and payments. Instead, it uses a transactional scripting language with low-level cryptographic functions, as we saw in <<transactions>>. Just like the higher-level concepts of accounts, balances, and payments can be derived from these basic primitives, so can many other complex applications. Thus, the bitcoin blockchain can become an application platform offering trust services to applications, such as smart contracts, far surpassing the original purpose of digital currency and payments.
((("blockchain applications", "benefits of bitcoin system")))The bitcoin system was designed as a decentralized currency and payment system. However, most of its functionality is derived from much lower-level constructs that can be used for much broader applications. Bitcoin wasn't built with components such as accounts, users, balances, and payments. Instead, it uses a transactional scripting language with low-level cryptographic functions, as we saw in <<transactions>>. Just as the higher-level concepts of accounts, balances, and payments can be derived from these basic primitives, so can many other complex applications. Thus, the bitcoin blockchain can become an application platform offering trust services to applications, such as smart contracts, far surpassing the original purpose of digital currency and payments.
=== Building Blocks (Primitives)
@ -17,7 +17,7 @@ No Double-Spend:: The most fundamental guarantee of bitcoin's decentralized cons
Immutability:: Once a transaction is recorded in the blockchain and sufficient work has been added with subsequent blocks, the transaction's data becomes immutable. Immutability is underwritten by energy, as rewriting the blockchain requires the expenditure of energy to produce Proof-of-Work. The energy required and therefore the degree of immutability increases with the amount of work committed on top of the block containing a transaction.
Neutrality:: The decentralized bitcoin network propagates valid transactions regardless of the origin or content of those transactions. This means that anyone can create a valid transaction with sufficient fees and trust they will be able to transmit that transaction and have it included in the blockchain at anytime.
Neutrality:: The decentralized bitcoin network propagates valid transactions regardless of the origin or content of those transactions. This means that anyone can create a valid transaction with sufficient fees and trust they will be able to transmit that transaction and have it included in the blockchain at any time.
Secure Timestamping:: The consensus rules reject any block whose timestamp is too far in the past or future. This ensures that timestamps on blocks can be trusted. The timestamp on a block implies an unspent-before guarantee for the inputs of all included transactions.
@ -59,7 +59,7 @@ Proof-of-Existence (Digital Notary):: ((("digital notary services")))((("Proof o
Kickstarter (Lighthouse):: Consistency + Atomicity + Integrity. If you sign one input and the output (Integrity) of a fundraiser transaction, others can contribute to the fundraiser but it cannot be spent (Atomicity) until the goal (output value) is funded (Consistency).
Payment Channels:: ((("payment (state) channels", "building blocks (primitives) used in")))Quorum of Control + Timelock + No Double Spend + Nonexpiration + Censorship Resistance + Authorization. A multisig 2-of-2 (Quorum) with a timelock (Timelock) used as the "settlement" transaction of a payment channel can be held (Nonexpiration) and spent whenever (Censorship Resistance) by either party (Authorization). The two parties can then create commitment transactions that double-spend (No Double-Spend) the settlement on a shorter timelock (Timelock).
Payment Channels:: ((("payment (state) channels", "building blocks (primitives) used in")))Quorum of Control + Timelock + No Double Spend + Nonexpiration + Censorship Resistance + Authorization. A multisig 2-of-2 (Quorum) with a timelock (Timelock) used as the "settlement" transaction of a payment channel can be held (Nonexpiration) and spent at any time (Censorship Resistance) by either party (Authorization). The two parties can then create commitment transactions that double-spend (No Double-Spend) the settlement on a shorter timelock (Timelock).
=== Colored Coins
@ -245,7 +245,7 @@ image::images/mbc2_1204.png["A payment channel between Bob and Alice, showing th
==== Simple Payment Channel Example
((("payment (state) channels", "example of", id="PSCexample12")))To explain state channels, we have to start with a very simple example. We demonstrate a one-way channel, meaning that value is flowing in one direction only. We will also start with the naive assumption that no one is trying to cheat, to keep things simple. Once we have the basic channel idea explained, we will then look at what it takes to make it trustless so that neither party _can_ cheat, even if they are trying to.
((("payment (state) channels", "example of", id="PSCexample12")))To explain state channels, we start with a very simple example. We demonstrate a one-way channel, meaning that value is flowing in one direction only. We will also start with the naive assumption that no one is trying to cheat, to keep things simple. Once we have the basic channel idea explained, we will then look at what it takes to make it trustless so that neither party _can_ cheat, even if they are trying to.
For this example we will assume two participants: Emma and Fabian. Fabian offers a video streaming service that is billed by the second using a micropayment channel. Fabian charges 0.01 millibit (0.00001 BTC) per second of video, equivalent to 36 millibits (0.036 BTC) per hour of video. Emma is a user who purchases this streaming video service from Fabian. <<emma_fabian_streaming_video>> shows Emma buying the video streaming service from Fabian using a payment channel.
@ -311,7 +311,7 @@ The first form of unidirectional payment channel was demonstrated as a prototype
Timelocks are not the only way to invalidate prior commitment transactions. In the next sections we will see how a revocation key can be used to achieve the same result. Timelocks are effective but they have two distinct disadvantages. By establishing a maximum timelock when the channel is first opened, they limit the lifetime of the channel. Worse, they force channel implementations to strike a balance between allowing long-lived channels and forcing one of the participants to wait a very long time for a refund in case of premature closure. For example, if you allow the channel to remain open for 30 days, by setting the refund timelock to 30 days, if one of the parties disappears immediately the other party must wait 30 days for a refund. The more distant the endpoint, the more distant the refund.
The second problem is that since each subsequent commitment transaction must decrement the timelock, there is an explicit limit on the number of commitment transactions that can be exchanged between the parties. For example, a 30-day channel, setting a timelock of 4320 blocks into the future, can only accommodate 4320 intermediate commitment transactions before it must be closed. There is a danger in setting the timelock commitment transaction interval at 1 block. By setting the timelock interval between commitment transactions to 1 block, a developer is creating a very high burden for the channel participants who have to be vigilant, remain online and watching, and be ready to transmit the right commitment transaction at anytime.
The second problem is that since each subsequent commitment transaction must decrement the timelock, there is an explicit limit on the number of commitment transactions that can be exchanged between the parties. For example, a 30-day channel, setting a timelock of 4320 blocks into the future, can only accommodate 4320 intermediate commitment transactions before it must be closed. There is a danger in setting the timelock commitment transaction interval at 1 block. By setting the timelock interval between commitment transactions to 1 block, a developer is creating a very high burden for the channel participants who have to be vigilant, remain online and watching, and be ready to transmit the right commitment transaction at any time.
Now that we understand how timelocks can be used to invalidate prior commitments, we can see the difference between closing the channel cooperatively and closing it unilaterally by broadcasting a commitment transaction. All commitment transactions are timelocked, therefore broadcasting a commitment transaction will always involve waiting until the timelock has expired. But if the two parties agree on what the final balance is and know they both hold commitment transactions that will eventually make that balance a reality, they can construct a settlement transaction without a timelock representing that same balance. In a cooperative close, either party takes the most recent commitment transaction and builds a settlement transaction that is identical in every way except that it omits the timelock. Both parties can sign this settlement transaction knowing there is no way to cheat and get a more favorable balance. By cooperatively signing and transmitting the settlement transaction they can close the channel and redeem their balance immediately. Worst case, one of the parties can be petty, refuse to cooperate, and force the other party to do a unilateral close with the most recent commitment transaction. But if they do that, they have to wait for their funds too.((("", startref="PSCtrust12")))
@ -368,9 +368,17 @@ This way, each party has a commitment transaction, spending the 2-of-2 funding o
.Two asymmetric commitment transactions with delayed payment for the party holding the transaction
image::images/mbc2_1208.png["Two asymmetric commitment transactions with delayed payment for the party holding the transaction"]
Now we introduce the final element of this scheme: a revocation key that allows a wronged party to punish a cheater by taking the entire balance of the channel.
Now we introduce the final element of this scheme: a revocation key that prevents a cheater from broadcasting an expired commitment. The revocation key allows the wronged party to punish the cheater by taking the entire balance of the channel.
Each of the commitment transactions has a "delayed" output. The redemption script for that output allows one party to redeem it after 1000 blocks _or_ the other party to redeem it if they have a revocation key. So when Hitesh creates a commitment transaction for Irene to sign, he makes the second output payable to himself after 1000 blocks, or to whoever can present a revocation key. Hitesh constructs this transaction and creates a revocation key that he keeps secret. He will only reveal it to Irene when he is ready to move to a new channel state and wants to revoke this commitment. The second output's script looks like this:
The revocation key is composed of two secrets, each half generated independently by each channel participant. It is similar to a 2-of-2 multisig, but constructed using elliptic curve arithmetic, so that both parties know the revocation public key but each party knows only half the revocation secret key.
In each round, both parties reveal their half of the revocation secret to the other party, thereby giving the other party (who now has both halves) the means to claim the penalty output if this revoked transaction is ever broadcast.
Each of the commitment transactions has a "delayed" output. The redemption script for that output allows one party to redeem it after 1000 blocks, _or_ the other party to redeem it if they have a revocation key, penalizing transmission of a revoked commitment.
So when Hitesh creates a commitment transaction for Irene to sign, he makes the second output payable to himself after 1000 blocks, or to the revocation public key (of which he only knows half the secret). Hitesh constructs this transaction. He will only reveal his half of the revocation secret to Irene when he is ready to move to a new channel state and wants to revoke this commitment.
The second output's script looks like this:
----
Output 0 <5 bitcoin>:
@ -391,9 +399,9 @@ CHECKSIG
Irene can confidently sign this transaction, since if transmitted it will immediately pay her what she is owed. Hitesh holds the transaction, but knows that if he transmits it in a unilateral channel closing, he will have to wait 1000 blocks to get paid.
When the channel is advanced to the next state, Hitesh has to _revoke_ this commitment transaction before Irene agrees to sign the next commitment transaction. To do that, all he has to do is send the _revocation key_ to Irene. Once Irene has the revocation key for this commitment, she can sign the next commitment with confidence. She knows that if Hitesh tries to cheat by publishing the prior commitment, she can use the revocation key to redeem Hitesh's delayed output. _If Hitesh cheats, Irene gets BOTH outputs_.
When the channel is advanced to the next state, Hitesh has to _revoke_ this commitment transaction before Irene agrees to sign the next commitment transaction. To do that, all he has to do is send his half of the _revocation key_ to Irene. Once Irene has both halves of the revocation secret key for this commitment, she can sign the next commitment with confidence. She knows that if Hitesh tries to cheat by publishing the prior commitment, she can use the revocation key to redeem Hitesh's delayed output. _If Hitesh cheats, Irene gets BOTH outputs_. Meanwhile, Hitesh only has half the revocation secret for that revocation public key and can't redeem the output until 1000 blocks. Irene will be able to redeem the output and punish Hitesh before the 1000 blocks have elapsed.
The revocation protocol is bilateral, meaning that in each round, as the channel state is advanced, the two parties exchange new commitments, exchange revocation keys for the previous commitment, and sign each other's commitment transactions. As they accept a new state, they make the prior state impossible to use, by giving each other the necessary revocation keys to punish any cheating.
The revocation protocol is bilateral, meaning that in each round, as the channel state is advanced, the two parties exchange new commitments, exchange revocation secrets for the previous commitments, and sign each other's new commitment transactions. As they accept a new state, they make the prior state impossible to use, by giving each other the necessary revocation secrets to punish any cheating.
Let's look at an example of how it works. One of Irene's customers wants to send 2 bitcoin to one of Hitesh's customers. To transmit 2 bitcoin across the channel, Hitesh and Irene must advance the channel state to reflect the new balance. They will commit to a new state (state number 2) where the channel's 10 bitcoin are split, 7 bitcoin to Hitesh and 3 bitcoin to Irene. To advance the state of the channel, they will each create new commitment transactions reflecting the new channel balance.
@ -426,7 +434,7 @@ IF
ELSE
# Refund after timeout.
<locktime> CHECKLOCKTIMEVERIFY DROP
<Payee Public Key> CHECKSIG
<Payer Public Key> CHECKSIG
ENDIF
----

2
code/key-to-address-ecc-example.py
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@ -21,7 +21,7 @@ print("Private Key Compressed (hex) is: ", compressed_private_key)
# Generate a WIF format from the compressed private key (WIF-compressed)
wif_compressed_private_key = bitcoin.encode_privkey(
bitcoin.decode_privkey(compressed_private_key, 'hex'), 'wif')
bitcoin.decode_privkey(compressed_private_key, 'hex'), 'wif_compressed')
print("Private Key (WIF-Compressed) is: ", wif_compressed_private_key)
# Multiply the EC generator point G with the private key to get a public key point

19
glossary.asciidoc
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@ -4,7 +4,7 @@
This quick glossary contains many of the terms used in relation to bitcoin. These terms are used throughout the book, so bookmark this for a quick reference.
address::
A bitcoin address looks like +1DSrfJdB2AnWaFNgSbv3MZC2m74996JafV+. It consists of a string of letters and numbers. It's really an encoded base58check version of a public key 160-bit hash. Just like you ask others to send an email to your email address, you would ask others to send you bitcoin to one of your bitcoin addresses.
A bitcoin address looks like +1DSrfJdB2AnWaFNgSbv3MZC2m74996JafV+. It consists of a string of letters and numbers. It's really an encoded base58check version of a public key 160-bit hash. Just as you ask others to send an email to your email address, you would ask others to send you bitcoin to one of your bitcoin addresses.
bip::
Bitcoin Improvement Proposals. A set of proposals that members of the bitcoin community have submitted to improve bitcoin. For example, BIP-21 is a proposal to improve the bitcoin uniform resource identifier (URI) scheme.
@ -55,8 +55,8 @@ difficulty retargeting::
difficulty target::
A difficulty at which all the computation in the network will find blocks approximately every 10 minutes.
double spending::
Double spending is the result of successfully spending some money more than once. Bitcoin protects against double spending by verifying each transaction added to the block chain to ensure that the inputs for the transaction had not previously already been spent.
double-spending::
Double spending is the result of successfully spending some money more than once. Bitcoin protects against double-spending by verifying each transaction added to the block chain to ensure that the inputs for the transaction had not previously already been spent.
ECDSA::
Elliptic Curve Digital Signature Algorithm or ECDSA is a cryptographic algorithm used by Bitcoin to ensure that funds can only be spent by their rightful owners.
@ -195,7 +195,7 @@ satoshi::
A satoshi is the smallest denomination of bitcoin that can be recorded on the blockchain. It is the equivalent of 0.00000001 bitcoin and is named after the creator of Bitcoin, Satoshi Nakamoto. ((("satoshi")))
Satoshi Nakamoto::
Satoshi Nakamoto is the name used by the person or people who designed Bitcoin and created its original reference implementation, Bitcoin Core. As a part of the implementation, they also devised the first blockchain database. In the process they were the first to solve the double spending problem for digital currency. Their real identity remains unknown.
Satoshi Nakamoto is the name used by the person or people who designed Bitcoin and created its original reference implementation, Bitcoin Core. As a part of the implementation, they also devised the first blockchain database. In the process they were the first to solve the double-spending problem for digital currency. Their real identity remains unknown.
Script::
Bitcoin uses a scripting system for transactions. Forth-like, Script is simple, stack-based, and processed from left to right. It is purposefully not Turing-complete, with no loops.
@ -218,19 +218,16 @@ Segregated Witness::
SHA::
The Secure Hash Algorithm or SHA is a family of cryptographic hash functions published by the National Institute of Standards and Technology (NIST).
simplified payment verification (SPV)::
Simplified Payment Verification (SPV)::
SPV or simplified payment verification is a method for verifying particular transactions were included in a block without downloading the entire block. The method is used by some lightweight Bitcoin clients.
soft fork::
soft fork or Soft-Forking Change is a temporary fork in the blockchain which commonly occurs when miners using non-upgraded nodes don't follow a new consensus rule their nodes don’t know about.
Not to be confused with fork, hard fork, software fork or Git fork.
SPV (aka Simplified Payment Verification)::
SPV or Simplified Payment Verification is a method for verifying particular transactions were included in a block without downloading the entire block. The method is used by some lightweight Bitcoin clients.
Stale Block::
Block which were successfully mined but which isn’t included on the current best block chain, likely because some other block at the same height had its chain extended first. Not to be confused with orphan block.
Block which was successfully mined but which isn’t included on the current best block chain, likely because some other block at the same height had its chain extended first. Not to be confused with orphan block.
timelocks::
A timelock is a type of encumbrance that restricts the spending of some bitcoin until a specified future time or block height. Timelocks feature prominently in many Bitcoin contracts, including payment channels and hashed timelock contracts.
@ -253,4 +250,4 @@ wallet::
Wallet Import Format (WIF)::
WIF or Wallet Import Format is a data interchange format designed to allow exporting and importing a single private key with a flag indicating whether or not it uses a compressed public key.
Some contributed definitions have been sourced under a CC-BY license from the https://en.bitcoin.it/wiki/Main_Page[bitcoin Wiki] or from other open source documentation sources.
Some contributed definitions have been sourced under a CC-BY license from the https://en.bitcoin.it/wiki/Main_Page[bitcoin Wiki] or from other open source documentation sources.

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4
preface.asciidoc
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@ -184,6 +184,7 @@ Following is a list of notable GitHub contributors, including their GitHub ID in
* Craig Dodd (cdodd)
* dallyshalla
* Darius Kramer (dkrmr)
* David Huie (DavidHuie)
* Diego Viola (diegoviola)
* Dirk Jäckel (biafra23)
* Dimitris Tsapakidis (dimitris-t)
@ -220,6 +221,7 @@ Following is a list of notable GitHub contributors, including their GitHub ID in
* Jonathan Cross (jonathancross)
* Jorgeminator
* Kai Bakker (kaibakker)
* Lucas Betschart (lclc)
* Magomed Aliev (30mb1)
* Mai-Hsuan Chia (mhchia)
* marcofalke
@ -237,6 +239,7 @@ Following is a list of notable GitHub contributors, including their GitHub ID in
* Richard Kiss (richardkiss)
* Ruben Alexander (hizzvizz)
* Sam Ritchie (sritchie)
* Sebastian Falbesoner (theStack)
* Sergej Kotliar (ziggamon)
* Seiichi Uchida (topecongiro)
* Simon de la Rouviere (simondlr)
@ -249,4 +252,5 @@ Following is a list of notable GitHub contributors, including their GitHub ID in
* wintercooled
* wjx
* Wojciech Langiewicz (wlk)
* Yancy Ribbens (yancyribbens)
* yurigeorgiev4((("", startref="acknowledge0")))