[[ch07]]
[[adv_transactions]]
== Advanced Transactions and Scripting

[[ch07_intro]]
=== Introduction

In the previous chapter, we introduced the basic elements of bitcoin transactions and looked at the most common type of transaction script, the P2PKH script. In this chapter we will look at more advanced scripting and how we can use it to build transactions with complex conditions.

First, we will look at _multisignature_ scripts. Next, we will examine the second most common transaction script, _Pay-to-Script-Hash_, which opens up a whole world of complex scripts. Then, we will examine new script operators that add a time dimension to bitcoin, through _timelocks_. Finally, we will look at _Segregated Witness_, an architectural change to the structure of transactions.

[[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.

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>>.

The general form of a locking script setting an M-of-N multisignature condition is:

----
M <Public Key 1> <Public Key 2> ... <Public Key N> N CHECKMULTISIG
----

where N is the total number of listed public keys and M is the threshold of required signatures to spend the output.

A locking script setting a 2-of-3 multisignature condition looks like this:

----
2 <Public Key A> <Public Key B> <Public Key C> 3 CHECKMULTISIG
----

The preceding locking script can be satisfied with an unlocking script containing pairs of signatures and public keys:

----
<Signature B> <Signature C>
----
or any combination of two signatures from the private keys corresponding to the three listed public keys.

The two scripts together would form the combined validation script:

----
<Signature B> <Signature C> 2 <Public Key A> <Public Key B> <Public Key C> 3 CHECKMULTISIG
----

When executed, this combined script will evaluate to TRUE if, and only if, the unlocking script matches the conditions set by the locking script. In this case, the condition is whether the unlocking script has a valid signature from the two private keys that correspond to two of the three public keys set as an encumbrance.

[[multisig_bug]]
===== A bug in CHECKMULTISIG execution

((("scripting", "multisignature scripts", "CHECKMULTISIG bug")))((("CHECKMULTISIG bug workaround")))There is a bug in ++CHECKMULTISIG++'s execution that requires a slight workaround. When +CHECKMULTISIG+ executes, it should consume M+N+2 items on the stack as parameters. However, due to the bug, +CHECKMULTISIG+ will pop an extra value or one value more than expected.

Let's look at this in greater detail using the previous validation example:

----
<Signature B> <Signature C> 2 <Public Key A> <Public Key B> <Public Key C> 3 CHECKMULTISIG
----

First, +CHECKMULTISIG+ pops the top item, which is +N+ (in this example "3"). Then it pops +N+ items, which are the public keys that can sign. In this example, public keys A, B, and C. Then, it pops one item, which is +M+, the quorum (how many signatures are needed). Here M = 2. At this point, +CHECKMULTISIG+ should pop the final +M+ items, which are the signatures, and see if they are valid. However, unfortunately, a bug in the implementation causes +CHECKMULTISIG+ to pop one more item (M+1 total) than it should. The extra item is disregarded when checking the signatures so it has no direct effect on +CHECKMULTISIG+ itself. However, an extra value must be present because if it is not present, when +CHECKMULTISIG+ attempts to pop on an empty stack, it will cause a stack error and script failure (marking the transaction as invalid). Because the extra item is disregarded it can be anything, but customarily +0+ is used.

Because this bug became part of the consensus rules, it must now be replicated forever. Therefore the correct script validation would look like this:

----
0 <Signature B> <Signature C> 2 <Public Key A> <Public Key B> <Public Key C> 3 CHECKMULTISIG
----

Thus the unlocking script actually used in multisig is not:

----
<Signature B> <Signature C>
----

but instead it is:

----
0 <Signature B> <Signature C>
----

From now on, if you see a multisig unlocking script, you should expect to see an extra +0+ in the beginning, whose only purpose is as a workaround to a bug that accidentally became a consensus rule.((("", startref="Smulti07")))

[[p2sh]]
=== Pay-to-Script-Hash (P2SH)

((("transactions", "advanced", "Pay-to-Script-Hash")))((("scripting", "Pay-to-Script-Hash", id="Spay07")))Pay-to-Script-Hash (P2SH) was introduced in 2012 as a powerful new type of transaction that greatly simplifies the use of complex transaction scripts. To explain the need for P2SH, let's look at a practical example.

((("use cases", "import/export", id="mohamseven")))((("scripting", "Pay-to-Script-Hash", "import/export example")))((("Pay-to-Script-Hash (P2SH)", "import/export example")))In <<ch01_intro_what_is_bitcoin>> we introduced Mohammed, an electronics importer based in Dubai. Mohammed's company uses bitcoin's multisignature feature extensively for its corporate accounts. Multisignature scripts are one of the most common uses of bitcoin's advanced scripting capabilities and are a very powerful feature. ((("accounts receivable (AR)")))Mohammed's company uses a multisignature script for all customer payments, known in accounting terms as "accounts receivable," or AR. With the multisignature scheme, any payments made by customers are locked in such a way that they require at least two signatures to release, from Mohammed and one of his partners or from his attorney who has a backup key. A multisignature scheme like that offers corporate governance controls and protects against theft, embezzlement, or loss.

The resulting script is quite long and looks like this:

----
2 <Mohammed's Public Key> <Partner1 Public Key> <Partner2 Public Key> <Partner3 Public Key> <Attorney Public Key> 5 CHECKMULTISIG
----

Although multisignature scripts are a powerful feature, they are cumbersome to use. Given the preceding script, Mohammed would have to communicate this script to every customer prior to payment. Each customer would have to use special bitcoin wallet software with the ability to create custom transaction scripts, and each customer would have to understand how to create a transaction using custom scripts. Furthermore, the resulting transaction would be about five times larger than a simple payment transaction, because this script contains very long public keys. The burden of that extra-large transaction would be borne by the customer in the form of fees. Finally, a large transaction script like this would be carried in the UTXO set in RAM in every full node, until it was spent. All of these issues make using complex locking scripts difficult in practice.

P2SH was developed to resolve these practical difficulties and to make the use of complex scripts as easy as a payment to a bitcoin address. With P2SH payments, the complex locking script is replaced with its digital fingerprint, a cryptographic hash. When a transaction attempting to spend the UTXO is presented later, it must contain the script that matches the hash, in addition to the unlocking script. In simple terms, P2SH means "pay to a script matching this hash, a script that will be presented later when this output is spent."

((("redeem scripts")))((("scripting", "redeem scripts")))In P2SH transactions, the locking script that is replaced by a hash is referred to as the _redeem script_ because it is presented to the system at redemption time rather than as a locking script. <<without_p2sh>> shows the script without P2SH and <<with_p2sh>> shows the same script encoded with P2SH.

[[without_p2sh]]
.Complex script without P2SH
|=======
| Locking Script | 2 PubKey1 PubKey2 PubKey3 PubKey4 PubKey5 5 CHECKMULTISIG
| Unlocking Script | Sig1 Sig2
|=======

[[with_p2sh]]
.Complex script as P2SH
|=======
| Redeem Script | 2 PubKey1 PubKey2 PubKey3 PubKey4 PubKey5 5 CHECKMULTISIG
| Locking Script | HASH160 <20-byte hash of redeem script> EQUAL
| Unlocking Script | Sig1 Sig2 <redeem script>
|=======

As you can see from the tables, with P2SH the complex script that details the conditions for spending the output (redeem script) is not presented in the locking script. Instead, only a hash of it is in the locking script and the redeem script itself is presented later, as part of the unlocking script when the output is spent. This shifts the burden in fees and complexity from the sender to the recipient (spender) of the transaction.

Let's look at Mohammed's company, the complex multisignature script, and the resulting P2SH scripts.

First, the multisignature script that Mohammed's company uses for all incoming payments from customers:

----
2 <Mohammed's Public Key> <Partner1 Public Key> <Partner2 Public Key> <Partner3 Public Key> <Attorney Public Key> 5 CHECKMULTISIG
----

If the placeholders are replaced by actual public keys (shown here as 520-bit numbers starting with 04) you can see that this script becomes very long:

----
2
  5 CHECKMULTISIG
----

This entire script can instead be represented by a 20-byte cryptographic hash, by first applying the SHA256 hashing algorithm and then applying the RIPEMD160 algorithm on the result.

We use +libbitcoin-explorer+ (+bx+) on the command-line to produce the script hash, as follows:

----
echo \
2 \
[04C16B8698A9ABF84250A7C3EA7EEDEF9897D1C8C6ADF47F06CF73370D74DCCA01CDCA79DCC5C395D7EEC6984D83F1F50C900A24DD47F569FD4193AF5DE762C587] \
[04A2192968D8655D6A935BEAF2CA23E3FB87A3495E7AF308EDF08DAC3C1FCBFC2C75B4B0F4D0B1B70CD2423657738C0C2B1D5CE65C97D78D0E34224858008E8B49] \
[047E63248B75DB7379BE9CDA8CE5751D16485F431E46117B9D0C1837C9D5737812F393DA7D4420D7E1A9162F0279CFC10F1E8E8F3020DECDBC3C0DD389D9977965] \
[0421D65CBD7149B255382ED7F78E946580657EE6FDA162A187543A9D85BAAA93A4AB3A8F044DADA618D087227440645ABE8A35DA8C5B73997AD343BE5C2AFD94A5] \
[043752580AFA1ECED3C68D446BCAB69AC0BA7DF50D56231BE0AABF1FDEEC78A6A45E394BA29A1EDF518C022DD618DA774D207D137AAB59E0B000EB7ED238F4D800] \
5 CHECKMULTISIG \
| bx script-encode | bx sha256 | bx ripemd160
54c557e07dde5bb6cb791c7a540e0a4796f5e97e
----

The series of commands above first encodes Mohammed's multisig redeem script as a serialized hex-encoded bitcoin Script. The next +bx+ command calculates the SHA256 hash of that. The next +bx+ command hashes again with RIPEMD160, producing the final script-hash:

The 20-byte hash of Mohammed's redeem script is:

----
54c557e07dde5bb6cb791c7a540e0a4796f5e97e
----

A P2SH transaction locks the output to this hash instead of the longer redeem script, using the locking script:

----
HASH160 54c557e07dde5bb6cb791c7a540e0a4796f5e97e EQUAL
----

which, as you can see, is much shorter. Instead of "pay to this 5-key multisignature script," the P2SH equivalent transaction is "pay to a script with this hash." A customer making a payment to Mohammed's company need only include this much shorter locking script in his payment. When Mohammed and his partners want to spend this UTXO, they must present the original redeem script (the one whose hash locked the UTXO) and the signatures necessary to unlock it, like this:

----
<Sig1> <Sig2> <2 PK1 PK2 PK3 PK4 PK5 5 CHECKMULTISIG>
----

The two scripts are combined in two stages. First, the redeem script is checked against the locking script to make sure the hash matches:

----
<2 PK1 PK2 PK3 PK4 PK5 5 CHECKMULTISIG> HASH160 <redeem scriptHash> EQUAL
----
If the redeem script hash matches, the unlocking script is executed on its own, to unlock the redeem script:

----
<Sig1> <Sig2> 2 PK1 PK2 PK3 PK4 PK5 5 CHECKMULTISIG
----

Almost all the scripts described in this chapter can only be implemented as P2SH scripts. They cannot be used directly in the locking script of an UTXO.((("", startref="mohamseven")))

==== P2SH Addresses

((("scripting", "Pay-to-Script-Hash", "addresses")))((("Pay-to-Script-Hash (P2SH)", "addresses")))((("bitcoin improvement proposals", "Address Format for P2SH (BIP-13)")))Another important part of the P2SH feature is the ability to encode a script hash as an address, as defined in BIP-13. P2SH addresses are Base58Check encodings of the 20-byte hash of a script, just like bitcoin addresses are Base58Check encodings of the 20-byte hash of a public key. P2SH addresses use the version prefix "5," which results in Base58Check-encoded addresses that start with a "3."

For example, Mohammed's complex script, hashed and Base58Check-encoded as a P2SH address, becomes +39RF6JqABiHdYHkfChV6USGMe6Nsr66Gzw+. We can confirm that with the +bx+ command:

----
echo \
'54c557e07dde5bb6cb791c7a540e0a4796f5e97e'\
 | bx address-encode -v 5
39RF6JqABiHdYHkfChV6USGMe6Nsr66Gzw
----


Now, Mohammed can give this "address" to his customers and they can use almost any bitcoin wallet to make a simple payment, as if it were a bitcoin address. The 3 prefix gives them a hint that this is a special type of address, one corresponding to a script instead of a public key, but otherwise it works in exactly the same way as a payment to a bitcoin address.

P2SH addresses hide all of the complexity, so that the person making a payment does not see the script.

==== Benefits of P2SH

((("scripting", "Pay-to-Script-Hash", "benefits of")))((("Pay-to-Script-Hash (P2SH)", "benefits of")))The P2SH feature offers the following benefits compared to the direct use of complex scripts in locking outputs:

* Complex scripts are replaced by shorter fingerprints in the transaction output, making the transaction smaller.
* Scripts can be coded as an address, so the sender and the sender's wallet don't need complex engineering to implement P2SH.
* P2SH shifts the burden of constructing the script to the recipient, not the sender.
* P2SH shifts the burden in data storage for the long script from the output (which additionally to being stored on the blockchain is in the UTXO set) to the input (only stored on the blockchain).
* P2SH shifts the burden in data storage for the long script from the present time (payment) to a future time (when it is spent).
* P2SH shifts the transaction fee cost of a long script from the sender to the recipient, who has to include the long redeem script to spend it.

==== 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.

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.

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")))

[WARNING]
====
((("warnings and cautions", "accidental bitcoin locking")))P2SH locking scripts contain the hash of a redeem script, which gives no clues as to the content of the redeem script itself. The P2SH transaction will be considered valid and accepted even if the redeem script is invalid. You might accidentally lock bitcoin in such a way that it cannot later be spent.
====



[[op_return]]
=== Data Recording Output (RETURN)

((("transactions", "advanced", "data recording output")))((("scripting", "data recording output")))((("RETURN operator")))((("data recording (nonpayment data)")))((("nonpayment data")))((("blockchain (the)", "nonpayment data recording")))((("digital notary services")))Bitcoin's distributed and timestamped ledger, the blockchain, has potential uses far beyond payments. Many developers have tried to use the transaction scripting language to take advantage of the security and resilience of the system for applications such as digital notary services, stock certificates, and smart contracts. Early attempts to use bitcoin's script language for these purposes involved creating transaction outputs that recorded data on the blockchain; for example, to record a digital fingerprint of a file in such a way that anyone could establish proof-of-existence of that file on a specific date by reference to that transaction.

((("blockchain bloat")))((("bloat")))((("unspent transaction outputs (UTXO)")))((("UTXO sets")))The use of bitcoin's blockchain to store data unrelated to bitcoin payments is a controversial subject. Many developers consider such use abusive and want to discourage it. Others view it as a demonstration of the powerful capabilities of blockchain technology and want to encourage such experimentation. Those who object to the inclusion of nonpayment data argue that it causes "blockchain bloat," burdening those running full bitcoin nodes with carrying the cost of disk storage for data that the blockchain was not intended to carry. Moreover, such transactions create UTXO that cannot be spent, using the destination bitcoin address as a freeform 20-byte field. Because the address is used for data, it doesn't correspond to a private key and the resulting UTXO can _never_ be spent; it's a fake payment. These transactions that can never be spent are therefore never removed from the UTXO set and cause the size of the UTXO database to forever increase, or "bloat."

In version 0.9 of the Bitcoin Core client, a compromise was reached with the introduction of the +RETURN+ operator. +RETURN+ allows developers to add 80 bytes of nonpayment data to a transaction output. However, unlike the use of "fake" UTXO, the +RETURN+ operator creates an explicitly _provably unspendable_ output, which does not need to be stored in the UTXO set. +RETURN+ outputs are recorded on the blockchain, so they consume disk space and contribute to the increase in the blockchain's size, but they are not stored in the UTXO set and therefore do not bloat the UTXO memory pool and burden full nodes with the cost of more expensive RAM.

+RETURN+ scripts look like this:

----
RETURN <data>
----

((("Proof of Existence")))((("DOCPROOF prefix")))The data portion is limited to 80 bytes and most often represents a hash, such as the output from the SHA256 algorithm (32 bytes). Many applications put a prefix in front of the data to help identify the application. For example, the http://proofofexistence.com[Proof of Existence] digital notarization service uses the 8-byte prefix +DOCPROOF+, which is ASCII encoded as +44 4f 43 50 52 4f 4f 46+ in hexadecimal.

Keep in mind that there is no "unlocking script" that corresponds to +RETURN+ that could possibly be used to "spend" a +RETURN+ output. The whole point of +RETURN+ is that you can't spend the money locked in that output, and therefore it does not need to be held in the UTXO set as potentially spendable—+RETURN+ is _provably unspendable_. +RETURN+ is usually an output with a zero bitcoin amount, because any bitcoin assigned to such an output is effectively lost forever. If a +RETURN+ is referenced as an input in a transaction, the script validation engine will halt the execution of the validation script and mark the transaction as invalid. The execution of +RETURN+ essentially causes the script to "RETURN" with a +FALSE+ and halt. Thus, if you accidentally reference a +RETURN+ output as an input in a transaction, that transaction is invalid.

A standard transaction (one that conforms to the +IsStandard()+ checks) can have only one +RETURN+ output. However, a single +RETURN+ output can be combined in a transaction with outputs of any other type.

Two new command-line options have been added in Bitcoin Core as of version 0.10. The option +datacarrier+ controls relay and mining of +RETURN+ transactions, with the default set to "1" to allow them. The option +datacarriersize+ takes a numeric argument specifying the maximum size in bytes of the +RETURN+ script, 83 bytes by default, which, allows for a maximum of 80 bytes of +RETURN+ data plus one byte of +RETURN+ opcode and two bytes of +PUSHDATA+ opcode.

[NOTE]
====
+RETURN+ was initially proposed with a limit of 80 bytes, but the limit was reduced to 40 bytes when the feature was released. In February 2015, in version 0.10 of Bitcoin Core, the limit was raised back to 80 bytes. Nodes may choose not to relay or mine +RETURN+, or only relay and mine +RETURN+ containing less than 80 bytes of data.
====

=== Timelocks

((("transactions", "advanced", "timelocks")))((("scripting", "timelocks", id="Stimelock07")))((("nLocktime field")))((("scripting", "timelocks", "uses for")))((("timelocks", "uses for")))Timelocks are restrictions on transactions or outputs that only allow spending after a point in time. Bitcoin has had a transaction-level timelock feature from the beginning. It is implemented by the +nLocktime+ field in a transaction. Two new timelock features were introduced in late 2015 and mid-2016 that offer UTXO-level timelocks. These are +CHECKLOCKTIMEVERIFY+ and +CHECKSEQUENCEVERIFY+.

Timelocks are useful for postdating transactions and locking funds to a date in the future. More importantly, timelocks extend bitcoin scripting into the dimension of time, opening the door for complex multistep smart contracts.

[[transaction_locktime_nlocktime]]
==== Transaction Locktime (nLocktime)

((("scripting", "timelocks", "nLocktime")))((("timelocks", "nLocktime")))From the beginning, bitcoin has had a transaction-level timelock feature. Transaction locktime is a transaction-level setting (a field in the transaction data structure) that defines the earliest time that a transaction is valid and can be relayed on the network or added to the blockchain. Locktime is also known as +nLocktime+ from the variable name used in the Bitcoin Core codebase. It is set to zero in most transactions to indicate immediate propagation and execution. If +nLocktime+ is nonzero and below 500 million, it is interpreted as a block height, meaning the transaction is not valid and is not relayed or included in the blockchain prior to the specified block height. If it is greater than or equal to 500 million, it is interpreted as a Unix Epoch timestamp (seconds since Jan-1-1970) and the transaction is not valid prior to the specified time. Transactions with +nLocktime+ specifying a future block or time must be held by the originating system and transmitted to the bitcoin network only after they become valid. If a transaction is transmitted to the network before the specified +nLocktime+, the transaction will be rejected by the first node as invalid and will not be relayed to other nodes. The use of +nLocktime+ is equivalent to postdating a paper check.

[[locktime_limitations]]
===== Transaction locktime limitations

+nLocktime+ has the limitation that while it makes it possible to spend some outputs in the future, it does not make it impossible to spend them until that time. Let's explain that with the following example.

((("use cases", "buying coffee", id="alicesseven")))Alice signs a transaction spending one of her outputs to Bob's address, and sets the transaction +nLocktime+ to 3 months in the future. Alice sends that transaction to Bob to hold. With this transaction Alice and Bob know that:

* Bob cannot transmit the transaction to redeem the funds until 3 months have elapsed.
* Bob may transmit the transaction after 3 months.

However:

* Alice can create another transaction, double-spending the same inputs without a locktime. Thus, Alice can spend the same UTXO before the 3 months have elapsed.
* Bob has no guarantee that Alice won't do that.

It is important to understand the limitations of transaction +nLocktime+. The only guarantee is that Bob will not be able to redeem it before 3 months have elapsed. There is no guarantee that Bob will get the funds. To achieve such a guarantee, the timelock restriction must be placed on the UTXO itself and be part of the locking script, rather than on the transaction. This is achieved by the next form of timelock, called Check Lock Time Verify.

==== Check Lock Time Verify (CLTV)

((("Check Lock Time Verify (CLTV)", id="cltv07")))((("timelocks", "Check Lock Time Verify (CLTV)")))((("scripting", "timelocks", "Check Lock Time Verify (CLTV)")))((("bitcoin improvement proposals", "CHECKLOCKTIMEVERIFY (BIP-65)")))In December 2015, a new form of timelock was introduced to bitcoin as a soft fork upgrade. Based on a specification in BIP-65, a new script operator called _CHECKLOCKTIMEVERIFY_ (_CLTV_) was added to the scripting language. +CLTV+ is a per-output timelock, rather than a per-transaction timelock as is the case with +nLocktime+. This allows for much greater flexibility in the way timelocks are applied.

In simple terms, by adding the +CLTV+ opcode in the redeem script of an output it restricts the output, so that it can only be spent after the specified time has elapsed.

[TIP]
====
While +nLocktime+ is a transaction-level timelock, +CLTV+ is an output-based timelock.
====

+CLTV+ doesn't replace +nLocktime+, but rather restricts specific UTXO such that they can only be spent in a future transaction with +nLocktime+ set to a greater or equal value.

The +CLTV+ opcode takes one parameter as input, expressed as a number in the same format as +nLocktime+ (either a block height or Unix epoch time). As indicated by the +VERIFY+ suffix, +CLTV+ is the type of opcode that halts execution of the script if the outcome is +FALSE+. If it results in TRUE, execution continues.

In order to lock an output with +CLTV+, you insert it into the redeem script of the output in the transaction that creates the output. For example, if Alice is paying Bob's address, the output would normally contain a P2PKH script like this:

----
DUP HASH160 <Bob's Public Key Hash> EQUALVERIFY CHECKSIG
----

To lock it to a time, say 3 months from now, the transaction would be a P2SH transaction with a redeem script like this:

----
<now + 3 months> CHECKLOCKTIMEVERIFY DROP DUP HASH160 <Bob's Public Key Hash> EQUALVERIFY CHECKSIG
----

where +<now {plus} 3 months>+ is a block height or time value estimated 3 months from the time the transaction is mined: current block height {plus} 12,960 (blocks) or current Unix epoch time {plus} 7,760,000 (seconds). For now, don't worry about the +DROP+ opcode that follows +CHECKLOCKTIMEVERIFY+; it will be explained shortly.

When Bob tries to spend this UTXO, he constructs a transaction that references the UTXO as an input. He uses his signature and public key in the unlocking script of that input and sets the transaction +nLocktime+ to be equal or greater to the timelock in the +CHECKLOCKTIMEVERIFY+ Alice set. Bob then broadcasts the transaction on the bitcoin network.

Bob's transaction is evaluated as follows. If the +CHECKLOCKTIMEVERIFY+ parameter Alice set is less than or equal the spending transaction's +nLocktime+, script execution continues (acts as if a &#x201c;no operation&#x201d; or NOP opcode was executed). Otherwise, script execution halts and the transaction is deemed invalid.

More precisely, +CHECKLOCKTIMEVERIFY+ fails and halts execution, marking the transaction invalid if (source: BIP-65):

1. the stack is empty; or
1. the top item on the stack is less than 0; or
1. the lock-time type (height versus timestamp) of the top stack item and the +nLocktime+ field are not the same; or
1. the top stack item is greater than the transaction's +nLocktime+ field; or
1. the +nSequence+ field of the input is 0xffffffff.

[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 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. 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")))

The standard is defined in https://github.com/bitcoin/bips/blob/master/bip-0065.mediawiki[BIP-65 (CHECKLOCKTIMEVERIFY)].

==== Relative Timelocks

+nLocktime+ and +CLTV+ are ((("timelocks", "relative timelocks", id="Trelative07")))((("scripting", "timelocks", "relative timelocks")))((("relative timelocks", id="relativetime07")))both _absolute timelocks_ in that they specify an absolute point in time. The next two timelock features we will examine are _relative timelocks_ in that they specify, as a condition of spending an output, an elapsed time from the confirmation of the output in the blockchain.

Relative timelocks are useful because they allow a chain of two or more interdependent transactions to be held off chain, while imposing a time constraint on one transaction that is dependent on the elapsed time from the confirmation of a previous transaction. In other words, the clock doesn't start counting until the UTXO is recorded on the blockchain. This functionality is especially useful in bidirectional state channels and Lightning Networks, as we will see in <<state_channels>>.

Relative timelocks, like absolute timelocks, are implemented with both a transaction-level feature and a script-level opcode. The transaction-level relative timelock is implemented as a consensus rule on the value of +nSequence+, a transaction field that is set in every transaction input. Script-level relative timelocks are implemented with the +CHECKSEQUENCEVERIFY+ (CSV) opcode.

((("bitcoin improvement proposals", "Relative lock-time using consensus-enforced sequence numbers (BIP-68)")))((("bitcoin improvement proposals", "CHECKSEQUENCEVERIFY (BIP-112)")))Relative timelocks are implemented according to the specifications in https://github.com/bitcoin/bips/blob/master/bip-0068.mediawiki[BIP-68, Relative lock-time using consensus-enforced sequence numbers] and https://github.com/bitcoin/bips/blob/master/bip-0112.mediawiki[BIP-112, CHECKSEQUENCEVERIFY].

BIP-68 and BIP-112 were activated in May 2016 as a soft fork upgrade to the consensus rules.

==== Relative Timelocks with nSequence

((("nSequence field")))((("scripting", "timelocks", "relative timelocks with nSequence")))Relative timelocks can be set on each input of a transaction, by setting the +nSequence+ field in each input.

===== Original meaning of nSequence

The +nSequence+ field was originally intended (but never properly implemented) to allow modification of transactions in the mempool. In that use, a transaction containing inputs with +nSequence+ value below 2^32^ - 1 (0xFFFFFFFF) indicated a transaction that was not yet "finalized." Such a transaction would be held in the mempool until it was replaced by another transaction spending the same inputs with a higher +nSequence+ value. Once a transaction was received whose inputs had an +nSequence+ value of 0xFFFFFFFF it would be considered "finalized" and mined.

The original meaning of +nSequence+ was never properly implemented and the value of +nSequence+ is customarily set to 0xFFFFFFFF in transactions that do not utilize timelocks. For transactions with nLocktime or +CHECKLOCKTIMEVERIFY+, the +nSequence+ value must be set to less than 2^31^ for the timelock guards to have an effect, as explained below.

===== nSequence as a consensus-enforced relative timelock

Since the activation of BIP-68, new consensus rules apply for any transaction containing an input whose +nSequence+ value is less than 2^31^ (bit 1<<31 is not set). Programmatically, that means that if the most significant (bit 1<<31) is not set, it is a flag that means "relative locktime." Otherwise (bit 1<<31 set), the +nSequence+ value is reserved for other uses such as enabling +CHECKLOCKTIMEVERIFY+, +nLocktime+, Opt-In-Replace-By-Fee, and other future developments.

Transaction inputs with +nSequence+ values less than 2^31^ are interpreted as having a relative timelock. Such a transaction is only valid once the input has aged by the relative timelock amount. For example, a transaction with one input with an +nSequence+ relative timelock of 30 blocks is only valid when at least 30 blocks have elapsed from the time the UTXO referenced in the input was mined. Since +nSequence+ is a per-input field, a transaction may contain any number of timelocked inputs, all of which must have sufficiently aged for the transaction to be valid. A transaction can include both timelocked inputs (+nSequence+ < 2^31^) and inputs without a relative timelock (+nSequence+ >= 2^31^).

The +nSequence+ value is specified in either blocks or seconds, but in a slightly different format than we saw used in +nLocktime+. A type-flag is used to differentiate between values counting blocks and values counting time in seconds. The type-flag is set in the 23rd least-significant bit (i.e., value 1<<22). If the type-flag is set, then the +nSequence+ value is interpreted as a multiple of 512 seconds. If the type-flag is not set, the +nSequence+ value is interpreted as a number of blocks.

When interpreting +nSequence+ as a relative timelock, only the 16 least significant bits are considered. Once the flags (bits 32 and 23) are evaluated, the +nSequence+ value is usually "masked" with a 16-bit mask (e.g., +nSequence+ & 0x0000FFFF).

<<bip_68_def_of_nseq>> shows the binary layout of the +nSequence+ value, as defined by BIP-68.

[[bip_68_def_of_nseq]]
.BIP-68 definition of nSequence encoding (Source: BIP-68)
image::images/mbc2_0701.png["BIP-68 definition of nSequence encoding"]


Relative timelocks based on consensus enforcement of the +nSequence+ value are defined in BIP-68.

The standard is defined in https://github.com/bitcoin/bips/blob/master/bip-0068.mediawiki[BIP-68, Relative lock-time using consensus-enforced sequence numbers].

==== Relative Timelocks with CSV

((("scripting", "timelocks", "relative timelocks with CHECKSEQUENCEVERIFY")))((("CHECKSEQUENCEVERIFY (CSV)")))Just like CLTV and +nLocktime+, there is a script opcode for relative timelocks that leverages the +nSequence+ value in scripts. That opcode is +CHECKSEQUENCEVERIFY+, commonly referred to as +CSV+ for short.

The +CSV+ opcode when evaluated in an UTXO's redeem script allows spending only in a transaction whose input +nSequence+ value is greater than or equal to the +CSV+ parameter. Essentially, this restricts spending the UTXO until a certain number of blocks or seconds have elapsed relative to the time the UTXO was mined.

As with CLTV, the value in +CSV+ must match the format in the corresponding +nSequence+ value. If +CSV+ is specified in terms of blocks, then so must +nSequence+. If +CSV+ is specified in terms of seconds, then so must +nSequence+.

Relative timelocks with +CSV+ are especially useful when several (chained) transactions are created and signed, but not propagated, when they're kept "off-chain." A child transaction cannot be used until the parent transaction has been propagated, mined, and aged by the time specified in the relative timelock. One application of this use case can be seen in <<state_channels>> and <<lightning_network>>.((("", startref="relativetime07")))((("", startref="Trelative07")))

+CSV+ is defined in detail in https://github.com/bitcoin/bips/blob/master/bip-0112.mediawiki[BIP-112, CHECKSEQUENCEVERIFY].


==== Median-Time-Past

((("scripting", "timelocks", "Median-Tme-Past")))((("Median-Tme-Past")))((("timelocks", "Median-Tme-Past")))As part of the activation of relative timelocks, there was also a change in the way "time" is calculated for timelocks (both absolute and relative). In bitcoin there is a subtle, but very significant, difference between wall time and consensus time. Bitcoin is a decentralized network, which means that each participant has his or her own perspective of time. Events on the network do not occur instantaneously everywhere. Network latency must be factored into the perspective of each node. Eventually everything is synchronized to create a common ledger. Bitcoin reaches consensus every 10 minutes about the state of the ledger as it existed in the _past_.

The timestamps set in block headers are set by the miners. There is a certain degree of latitude allowed by the consensus rules to account for differences in clock accuracy between decentralized nodes. However, this creates an unfortunate incentive for miners to lie about the time in a block so as to earn extra fees by including timelocked transactions that are not yet mature. See the following section for more information.

To remove the incentive to lie and strengthen the security of timelocks, a BIP was proposed and activated at the same time as the BIPs for relative timelocks. This is BIP-113, which defines a new consensus measurement of time called _Median-Time-Past_.

Median-Time-Past is calculated by taking the timestamps of the last 11 blocks and finding the median. That median time then becomes consensus time and is used for all timelock calculations. By taking the midpoint from approximately two hours in the past, the influence of any one block's timestamp is reduced. By incorporating 11 blocks, no single miner can influence the timestamps in order to gain fees from transactions with a timelock that hasn't yet matured.

Median-Time-Past changes the implementation of time calculations for +nLocktime+, +CLTV+, +nSequence+, and +CSV+. The consensus time calculated by Median-Time-Past is always approximately one hour behind wall clock time. If you create timelock transactions, you should account for it when estimating the desired value to encode in +nLocktime+, +nSequence+, +CLTV+, and +CSV+.

Median-Time-Past is specified in https://github.com/bitcoin/bips/blob/master/bip-0113.mediawiki[BIP-113].

[[fee_sniping]]
==== Timelock Defense Against Fee Sniping

((("scripting", "timelocks", "defense against fee-sniping")))((("timelocks", "defense against fee-sniping")))((("fees", "fee sniping")))((("security", "defense against fee-sniping")))((("sniping")))Fee-sniping is a theoretical attack scenario, where miners attempting to rewrite past blocks "snipe" higher-fee transactions from future blocks to maximize their profitability.

For example, let's say the highest block in existence is block  #100,000. If instead of attempting to mine block #100,001 to extend the chain, some miners attempt to remine  #100,000. These miners can choose to include any valid transaction (that hasn't been mined yet) in their candidate block  #100,000. They don't have to remine the block with the same transactions. In fact, they have the incentive to select the most profitable (highest fee per kB) transactions to include in their block. They can include any transactions that were in the "old" block  #100,000, as well as any transactions from the current mempool. Essentially they have the option to pull transactions from the "present" into the rewritten "past" when they re-create block  #100,000.

Today, this attack is not very lucrative, because block reward is much higher than total fees per block. But at some point in the future, transaction fees will be the majority of the reward (or even the entirety of the reward). At that time, this scenario becomes inevitable.

To prevent "fee sniping," when Bitcoin Core creates transactions, it uses +nLocktime+ to limit them to the "next block," by default. In our scenario, Bitcoin Core would set +nLocktime+ to 100,001 on any transaction it created. Under normal circumstances, this +nLocktime+ has no effect&#x2014;the transactions could only be included in block #100,001 anyway; it's the next block.

But under a blockchain fork attack, the miners would not be able to pull high-fee transactions from the mempool, because all those transactions would be timelocked to block #100,001. They can only remine  #100,000 with whatever transactions were valid at that time, essentially gaining no new fees.

To achieve this, Bitcoin Core sets the +nLocktime+ on all new transactions to <current block # + 1> and sets the +nSequence+ on all the inputs to 0xFFFFFFFE to enable +nLocktime+.((("", startref="Stimelock07")))

=== Scripts with Flow Control (Conditional Clauses)

((("transactions", "advanced", "flow control scripts")))((("scripting", "flow control scripts", id="Sflow07")))((("conditional clauses", id="condition07")))((("flow control", id="flow07")))One of the more powerful features of Bitcoin Script is flow control, also known as conditional clauses. You are probably familiar with flow control in various programming languages that use the construct +IF...THEN...ELSE+. Bitcoin conditional clauses look a bit different, but are essentially the same construct.

At a basic level, bitcoin conditional opcodes allow us to construct a redeem script that has two ways of being unlocked, depending on a +TRUE+/+FALSE+ outcome of evaluating a logical condition. For example, if x is +TRUE+, the redeem script is A and the ELSE redeem script is B.

Additionally, bitcoin conditional expressions can be "nested" indefinitely, meaning that a conditional clause can contain another within it, which contains another, etc. Bitcoin Script flow control can be used to construct very complex scripts with hundreds or even thousands of possible execution paths. There is no limit to nesting, but consensus rules impose a limit on the maximum size, in bytes, of a script.

Bitcoin implements flow control using the +IF+, +ELSE+, +ENDIF+, and +NOTIF+ opcodes. Additionally, conditional expressions can contain boolean operators such as +BOOLAND+, pass:[<span class="keep-together"><code>BOOLOR</code></span>], and +NOT+.

At first glance, you may find the bitcoin's flow control scripts confusing. That is because Bitcoin Script is a stack language. The same way that +1 {plus} 1+ looks "backward" when expressed as +1 1 ADD+, flow control clauses in bitcoin also look "backward."

In most traditional (procedural) programming languages, flow control looks like this:

.Pseudocode of flow control in most programming languages
----
if (condition):
  code to run when condition is true
else:
  code to run when condition is false
code to run in either case
----

In a stack-based language like Bitcoin Script, the logical condition comes before the +IF+, which makes it look "backward," like this:

.Bitcoin Script flow control
----
condition
IF
  code to run when condition is true
ELSE
  code to run when condition is false
ENDIF
code to run in either case
----

When reading Bitcoin Script, remember that the condition being evaluated comes _before_ the +IF+ opcode.

==== Conditional Clauses with VERIFY Opcodes

((("VERIFY opcodes")))((("IF clauses")))((("opcodes", "VERIFY")))Another form of conditional in Bitcoin Script is any opcode that ends in +VERIFY+. The +VERIFY+ suffix means that if the condition evaluated is not +TRUE+, execution of the script terminates immediately and the transaction is deemed invalid.

((("guard clauses")))Unlike an +IF+ clause, which offers alternative execution paths, the +VERIFY+ suffix acts as a _guard clause_, continuing only if a precondition is met.

For example, the following script requires Bob's signature and a pre-image (secret) that produces a specific hash. Both conditions must be satisfied to unlock:

.A redeem script with an +EQUALVERIFY+  guard clause.
----
HASH160 <expected hash> EQUALVERIFY <Bob's Pubkey> CHECKSIG
----

To redeem this, Bob must construct an unlocking script that presents a valid pre-image and a signature:

.An unlocking script to satisfy the above redeem script
----
<Bob's Sig> <hash pre-image>
----

Without presenting the pre-image, Bob can't get to the part of the script that checks for his signature.

[role="pagebreak-after"]
This script can be written with an +IF+ instead:

.A redeem script with an +IF+ guard clause
----
HASH160 <expected hash> EQUAL
IF
   <Bob's Pubkey> CHECKSIG
ENDIF
----

Bob's unlocking script is identical:

.An unlocking script to satisfy the above redeem script
----
<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 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.

[TIP]
====
((("EQUAL opcode")))((("opcodes", "EQUAL")))((("EQUALVERIFY opcode")))((("opcodes", "EQUALVERIFY")))An opcode such as +EQUAL+ will push the result (+TRUE+/+FALSE+) onto the stack, leaving it there for evaluation by subsequent opcodes. In contrast, the opcode +EQUALVERIFY+ suffix does not leave anything on the stack. Opcodes that end in +VERIFY+ do not leave the result on the stack.
====

==== Using Flow Control in Scripts

A very common use for flow control in Bitcoin Script is to construct a redeem script that offers multiple execution paths, each a different way of redeeming the UTXO.

((("use cases", "buying coffee")))Let's look at a simple example, where we have two signers, Alice and Bob, and either one is able to redeem. With multisig, this would be expressed as a 1-of-2 multisig script. For the sake of demonstration, we will do the same thing with an +IF+ clause:

----
IF
 <Alice's Pubkey> CHECKSIG
ELSE
 <Bob's Pubkey> CHECKSIG
ENDIF
----

Looking at this redeem script, you may be wondering: "Where is the condition? There is nothing preceding the +IF+ clause!"

The condition is not part of the redeem script. Instead, the condition will be offered in the unlocking script, allowing Alice and Bob to "choose" which execution path they want.

Alice redeems this with the unlocking script:
----
<Alice's Sig> 1
----

The +1+ at the end serves as the condition (+TRUE+) that will make the +IF+ clause execute the first redemption path for which Alice has a signature.

For Bob to redeem this, he would have to choose the second execution path by giving a +FALSE+ value to the +IF+ clause:

----
<Bob's Sig> 0
----

Bob's unlocking script puts a +0+ on the stack, causing the +IF+ clause to execute the second (+ELSE+) script, which requires Bob's signature.

Since +IF+ clauses can be nested, we can create a "maze" of execution paths. The unlocking script can provide a "map" selecting which execution path is actually executed:

----
IF
  script A
ELSE
  IF
    script B
  ELSE
    script C
  ENDIF
ENDIF
----

In this scenario, there are three execution paths (+script A+, +script B+, and +script C+). The unlocking script provides a path in the form of a sequence of +TRUE+ or +FALSE+ values. To select path +script B+, for example, the unlocking script must end in +1 0+ (+TRUE+, +FALSE+). These values will be pushed onto the stack, so that the second value (+FALSE+) ends up at the top of the stack. The outer +IF+ clause pops the +FALSE+ value and executes the first +ELSE+ clause. Then the +TRUE+ value moves to the top of the stack and is evaluated by the inner (nested) +IF+, selecting the +B+ execution path.

Using this construct, we can build redeem scripts with tens or hundreds of execution paths, each offering a different way to redeem the UTXO. To spend, we construct an unlocking script that navigates the execution path by putting the appropriate +TRUE+ and +FALSE+ values on the stack at each flow control point.((("", startref="Sflow07")))((("", startref="flow07")))((("", startref="condition07")))

=== Complex Script Example

((("transactions", "advanced", "example")))((("scripting", "complex script example", id="Scomplex07")))In this section we combine many of the concepts from this chapter into a single example.

((("use cases", "import/export", id="mohamseventwo")))Our example uses the story of Mohammed, the company owner in Dubai who is operating an import/export business.

((("transactions", "advanced", "multisignature scripts")))((("scripting", "multisignature scripts", "import/export example")))((("multisignature scripts")))In this example, Mohammed wishes to construct a company capital account with flexible rules. The scheme he creates requires different levels of authorization depending on timelocks. The participants in the multisig scheme are Mohammed, his two partners Saeed and Zaira, and their company lawyer Abdul. The three partners make decisions based on a majority rule, so two of the three must agree. However, in the case of a problem with their keys, they want their lawyer to be able to recover the funds with one of the three partner signatures. Finally, if all partners are unavailable or incapacitated for a while, they want the lawyer to be able to manage the account directly.

Here's the redeem script that Mohammed designs to achieve this (line number prefix as XX):

.Variable Multi-Signature with Timelock
----
01  IF
02    IF
03      2
04    ELSE
05      <30 days> CHECKSEQUENCEVERIFY DROP
06      <Abdul the Lawyer's Pubkey> CHECKSIGVERIFY
07      1
08    ENDIF
09    <Mohammed's Pubkey> <Saeed's Pubkey> <Zaira's Pubkey> 3 CHECKMULTISIG
10  ELSE
11    <90 days> CHECKSEQUENCEVERIFY DROP
12    <Abdul the Lawyer's Pubkey> CHECKSIG
13  ENDIF
----

Mohammed's script implements three execution paths using nested +IF...ELSE+ flow control clauses.

In the first execution path, this script operates as a simple 2-of-3 multisig with the three partners. This execution path consists of lines 3 and 9. Line 3 sets the quorum of the multisig to +2+ (2-of-3). This execution path can be selected by putting +TRUE TRUE+ at the end of the unlocking script:

.Unlocking script for the first execution path (2-of-3 multisig)
----
0 <Mohammed's Sig> <Zaira's Sig> TRUE TRUE
----


[TIP]
====
The +0+ at the beginning of this unlocking script is because of a bug in +CHECKMULTISIG+ that pops an extra value from the stack. The extra value is disregarded by the +CHECKMULTISIG+, but it must be present or the script fails. Pushing +0+ (customarily) is a workaround to the bug, as described in <<multisig_bug>>.
====

The second execution path can only be used after 30 days have elapsed from the creation of the UTXO. At that time, it requires the signature of Abdul the lawyer and one of the three partners (a 1-of-3 multisig). This is achieved by line 7, which sets the quorum for the multisig to +1+. To select this execution path, the unlocking script would end in +FALSE TRUE+:

.Unlocking script for the second execution path (Lawyer + 1-of-3)
----
0 <Saeed's Sig> <Abdul's Sig> FALSE TRUE
----

[TIP]
====
Why +FALSE TRUE+? Isn't that backward? Because the two values are pushed on to the stack, with +FALSE+ pushed first, then +TRUE+ pushed second. +TRUE+ is therefore popped _first_ by the first +IF+ opcode.
====

Finally, the third execution path allows Abdul the lawyer to spend the funds alone, but only after 90 days. To select this execution path, the unlocking script has to end in +FALSE+:

.Unlocking script for the third execution path (Lawyer only)
----
<Abdul's Sig> FALSE
----

Try running the script on paper to see how it behaves on the stack.

A few more things to consider when reading this example. See if you can find the answers:

* Why can't the lawyer redeem the third execution path at any time by selecting it with +FALSE+ on the unlocking script?

* How many execution paths can be used 5, 35, and 105 days, respectively, after the UTXO is mined?

* Are the funds lost if the lawyer loses his key? Does your answer change if 91 days have elapsed?

* How do the partners "reset" the clock every 29 or 89 days to prevent the lawyer from accessing the funds?

* Why do some +CHECKSIG+ opcodes in this script have the +VERIFY+ suffix while others don't?((("", startref="Scomplex07")))((("", startref="mohamseventwo")))

[[segwit]]
=== Segregated Witness

((("segwit (Segregated Witness)", id="Ssegwit07")))Segregated Witness (segwit) is an upgrade to the bitcoin consensus rules and network protocol, proposed and implemented as a BIP-9 soft-fork that was activated on bitcoin's mainnet on August 1st, 2017.

In cryptography, the term "witness" is used to describe a solution to a cryptographic puzzle. In bitcoin terms, the witness satisfies a cryptographic condition placed on a unspent transaction output (UTXO).

In the context of bitcoin, a digital signature is _one type of witness_, but a witness is more broadly any solution that can satisfy the conditions imposed on an UTXO and unlock that UTXO for spending. The term “witness” is a more general term for an “unlocking script” or “scriptSig.”

Before segwit’s introduction, every input in a transaction was followed by the witness data that unlocked it. The witness data was embedded in the transaction as part of each input. The term _segregated witness_, or _segwit_ for short, simply means separating the signature or unlocking script of a specific output. Think "separate scriptSig," or “separate signature” in the simplest form.

Segregated Witness therefore is an architectural change to bitcoin that aims to move the witness data from the +scriptSig+ (unlocking script) field of a transaction into a separate _witness_ data structure that accompanies a transaction. Clients may request transaction data with or without the accompanying witness data.

In this section we will look at some of the benefits of Segregated Witness, describe the mechanism used to deploy and implement this architecture change, and demonstrate the use of Segregated Witness in transactions and addresses.

Segregated Witness is defined by the following BIPs:

https://github.com/bitcoin/bips/blob/master/bip-0141.mediawiki[BIP-141] :: The main definition of Segregated Witness.

https://github.com/bitcoin/bips/blob/master/bip-0143.mediawiki[BIP-143] :: Transaction Signature Verification for Version 0 Witness Program

https://github.com/bitcoin/bips/blob/master/bip-0144.mediawiki[BIP-144] :: Peer Services&#x2014;New network messages and serialization formats

https://github.com/bitcoin/bips/blob/master/bip-0145.mediawiki[BIP-145] :: getblocktemplate Updates for Segregated Witness (for mining)

https://github.com/bitcoin/bips/blob/master/bip-0173.mediawiki[BIP-173]:: Base32 address format for native v0-16 witness outputs


==== Why Segregated Witness?

Segregated Witness is an architectural change that has several effects on the scalability, security, economic incentives, and performance of bitcoin:

Transaction Malleability :: By moving the witness outside the transaction, the transaction hash used as an identifier no longer includes the witness data. Since the witness data is the only part of the transaction that can be modified by a third party (see <<segwit_txid>>), removing it also removes the opportunity for transaction malleability attacks. With Segregated Witness, transaction hashes become immutable by anyone other than the creator of the transaction, which greatly improves the implementation of many other protocols that rely on advanced bitcoin transaction construction, such as payment channels, chained transactions, and lightning networks.

Script Versioning :: With the introduction of Segregated Witness scripts, every locking script is preceded by a _script version_ number, similar to how transactions and blocks have version numbers. The addition of a script version number allows the scripting language to be upgraded in a backward-compatible way (i.e., using soft fork upgrades) to introduce new script operands, syntax, or semantics. The ability to upgrade the scripting language in a nondisruptive way will greatly accelerate the rate of innovation in bitcoin.

Network and Storage Scaling :: The witness data is often a big contributor to the total size of a transaction. More complex scripts such as those used for multisig or payment channels are very large. In some cases these scripts account for the majority (more than 75%) of the data in a transaction. By moving the witness data outside the transaction, Segregated Witness improves bitcoin’s scalability. Nodes can prune the witness data after validating the signatures, or ignore it altogether when doing simplified payment verification. The witness data doesn’t need to be transmitted to all nodes and does not need to be stored on disk by all nodes.

Signature Verification Optimization :: Segregated Witness upgrades the signature functions (+CHECKSIG+, +CHECKMULTISIG+, etc.) to reduce the algorithm's computational complexity. Before segwit, the algorithm used to produce a signature required a number of hash operations that was proportional to the size of the transaction. Data-hashing computations increased in O(n^2^) with respect to the number of signature operations, introducing a substantial computational burden on all nodes verifying the signature. With segwit, the algorithm is changed to reduce the complexity to O(n).

Offline Signing Improvement :: Segregated Witness signatures incorporate the value (amount) referenced by each input in the hash that is signed. Previously, an offline signing device, such as a hardware wallet, would have to verify the amount of each input before signing a transaction. This was usually accomplished by streaming a large amount of data about the previous transactions referenced as inputs. Since the amount is now part of the commitment hash that is signed, an offline device does not need the previous transactions. If the amounts do not match (are misrepresented by a compromised online system), the signature will be invalid.

==== How Segregated Witness Works

At first glance, Segregated Witness appears to be a change to how transactions are constructed and therefore a transaction-level feature, but it is not. Rather, Segregated Witness is a change to how individual UTXO are spent and therefore is a per-output feature.

A transaction can spend Segregated Witness outputs or traditional (inline-witness) outputs or both. Therefore, it does not make much sense to refer to a transaction as a “Segregated Witness transaction.” Rather we should refer to specific transaction outputs as “Segregated Witness outputs."

When a transaction spends an UTXO, it must provide a witness. In a traditional UTXO, the locking script requires that witness data be provided _inline_ in the input part of the transaction that spends the UTXO. A Segregated Witness UTXO, however, specifies a locking script that can be satisfied with witness data outside of the input (segregated).

==== Soft Fork (Backward Compatibility)

Segregated Witness is a significant change to the way outputs and transactions are architected. Such a change would normally require a simultaneous change in every bitcoin node and wallet to change the consensus rules&#x2014;what is known as a hard fork. Instead, segregated witness is introduced with a much less disruptive change, which is backward compatible, known as a soft fork. This type of upgrade allows nonupgraded software to ignore the changes and continue to operate without any disruption.

Segregated Witness outputs are constructed so that older systems that are not segwit-aware can still validate them. To an old wallet or node, a Segregated Witness output looks like an output that _anyone can spend_. Such outputs can be spent with an empty signature, therefore the fact that there is no signature inside the transaction (it is segregated) does not invalidate the transaction. Newer wallets and mining nodes, however, see the Segregated Witness output and expect to find a valid witness for it in the transaction’s witness data.

==== Segregated Witness Output and Transaction Examples

Let’s look at some of our example transactions and see how they would change with Segregated Witness. We’ll first look at how a Pay-to-Public-Key-Hash (P2PKH) payment is transformed with the Segregated Witness program. Then, we’ll look at the Segregated Witness equivalent for Pay-to-Script-Hash (P2SH) scripts. Finally, we’ll look at how both of the preceding Segregated Witness programs can be embedded inside a P2SH script.

[[p2wpkh]]
===== Pay-to-Witness-Public-Key-Hash (P2WPKH)

In <<cup_of_coffee>>, ((("use cases", "buying coffee", id="aliced")))Alice created a transaction to pay Bob for a cup of coffee. That transaction created a P2PKH output with a value of 0.015 BTC that was spendable by Bob. The output’s script looks like this:

.Example P2PKH output script
----
DUP HASH160 ab68025513c3dbd2f7b92a94e0581f5d50f654e7 EQUALVERIFY CHECKSIG
----

With Segregated Witness, Alice would create a Pay-to-Witness-Public-Key-Hash (P2WPKH) script, which looks like this:

.Example P2WPKH output script
----
0 ab68025513c3dbd2f7b92a94e0581f5d50f654e7
----

As you can see, a Segregated Witness output’s locking script is much simpler than a traditional output. It consists of two values that are pushed on to the script evaluation stack. To an old (nonsegwit-aware) bitcoin client, the two pushes would look like an output that anyone can spend and does not require a signature (or rather, can be spent with an empty signature). To a newer, segwit-aware client, the first number (0) is interpreted as a version number (the _witness version_) and the second part (20 bytes) is the equivalent of a locking script known as a _witness program_. The 20-byte witness program is simply the hash of the public key, as in a P2PKH script.

Now, let’s look at the corresponding transaction that Bob uses to spend this output. For the original script (nonsegwit), Bob’s transaction would have to include a signature within the transaction input:

.Decoded transaction showing a P2PKH output being spent with a signature
----
[...]
“Vin” : [
"txid": "0627052b6f28912f2703066a912ea577f2ce4da4caa5a5fbd8a57286c345c2f2",
"vout": 0,
     	 "scriptSig": “<Bob’s scriptSig>”,
]
[...]
----

However, to spend the Segregated Witness output, the transaction has no signature on that input. Instead, Bob’s transaction has an empty +scriptSig+ and includes a Segregated Witness, outside the transaction itself:

.Decoded transaction showing a P2WPKH output being spent with separate witness data
----
[...]
“Vin” : [
"txid": "0627052b6f28912f2703066a912ea577f2ce4da4caa5a5fbd8a57286c345c2f2",
"vout": 0,
     	 "scriptSig": “”,
]
[...]
“witness”: “<Bob’s witness data>”
[...]
----

===== Wallet construction of P2WPKH

It is extremely important to note that P2WPKH should only be created by the payee (recipient) and not converted by the sender from a known public key, P2PKH script, or address. The sender has no way of knowing if the recipient's wallet has the ability to construct segwit transactions and spend P2WPKH outputs.

Additionally, P2WPKH outputs must be constructed from the hash of a _compressed_ public key. Uncompressed public keys are nonstandard in segwit and may be explicitly disabled by a future soft fork. If the hash used in the P2WPKH came from an uncompressed public key, it may be unspendable and you may lose funds. P2WPKH outputs should be created by the payee's wallet by deriving a compressed public key from their private key.

[WARNING]
====
P2WPKH should be constructed by the payee (recipient) by converting a compressed public key to a P2WPKH hash. You should never transform a P2PKH script, bitcoin address, or uncompressed public key to a P2WPKH witness script.
====

[[p2wsh]]
===== Pay-to-Witness-Script-Hash (P2WSH)

The ((("use cases", "import/export", id="mohamappd")))second type of witness program corresponds to a Pay-to-Script-Hash (P2SH) script. We saw this type of script in <<p2sh>>. In that example, P2SH was used by Mohammed's company to express a multisignature script. Payments to Mohammed's company were encoded with a locking script like this:

.Example P2SH output script
----
HASH160 54c557e07dde5bb6cb791c7a540e0a4796f5e97e EQUAL
----

This P2SH script references the hash of a _redeem script_ that defines a 2-of-3 multisignature requirement to spend funds. To spend this output, Mohammed's company would present the redeem script (whose hash matches the script hash in the P2SH output) and the signatures necessary to satisfy that redeem script, all inside the transaction input:

.Decoded transaction showing a P2SH output being spent
----
[...]
“Vin” : [
"txid": "abcdef12345...",
"vout": 0,
     	 "scriptSig": “<SigA> <SigB> <2 PubA PubB PubC PubD PubE 5 CHECKMULTISIG>”,
]
----

Now, let's look at how this entire example would be upgraded to segwit. If Mohammed's customers were using a segwit-compatible wallet, they would make a payment, creating a Pay-to-Witness-Script-Hash (P2WSH) output that would look like this:

.Example P2WSH output script
----
0 a9b7b38d972cabc7961dbfbcb841ad4508d133c47ba87457b4a0e8aae86dbb89
----

Again, as with the example of P2WPKH, you can see that the Segregated Witness equivalent script is a lot simpler and omits the various script operands that you see in P2SH scripts. Instead, the Segregated Witness program consists of two values pushed to the stack: a witness version (0) and the 32-byte SHA256 hash of the redeem script.

[TIP]
====
While P2SH uses the 20-byte +RIPEMD160(SHA256(script))+ hash, the P2WSH witness program uses a 32-byte +SHA256(script)+ hash. This difference in the selection of the hashing algorithm is deliberate and is used to differentiate between the two types of witness programs (P2WPKH and P2WSH) by the length of the hash and to provide stronger security to P2WSH (128 bits of security in P2WSH versus 80 bits of security in P2SH).

====

Mohammed's company can spend outputs the P2WSH output by presenting the correct redeem script and sufficient signatures to satisfy it. Both the redeem script and the signatures would be segregated _outside_ the spending transaction as part of the witness data. Within the transaction input, Mohammed's ((("", startref="mohamappd")))wallet would put an empty +scriptSig+:

.Decoded transaction showing a P2WSH output being spent with separate witness data
----
[...]
“Vin” : [
"txid": "abcdef12345...",
"vout": 0,
     	 "scriptSig": “”,
]
[...]
“witness”: “<SigA> <SigB> <2 PubA PubB PubC PubD PubE 5 CHECKMULTISIG>”
[...]
----

===== Differentiating between P2WPKH and P2WSH

In the previous two sections, we demonstrated two types of witness programs: <<p2wpkh>> and <<p2wsh>>. Both types of witness programs consist of a single byte version number followed by a longer hash. They look very similar, but are interpreted very differently: one is interpreted as a public key hash, which is satisfied by a signature and the other as a script hash, which is satisfied by a redeem script. The critical difference between them is the length of the hash:

* The public key hash in P2WPKH is 20 bytes
* The script hash in P2WSH is 32 bytes

This is the one difference that allows a wallet to differentiate between the two types of witness programs. By looking at the length of the hash, a wallet can determine what type of witness program it is, P2WPKH or P2WSH.

==== Upgrading to Segregated Witness

As we can see from the previous examples, upgrading to Segregated Witness is a two-step process. First, wallets must create special segwit type outputs. Then, these outputs can be spent by wallets that know how to construct Segregated Witness transactions. In the examples, Alice's wallet was segwit-aware and able to create special outputs with Segregated Witness scripts. Bob's wallet is also segwit-aware and able to spend those outputs. What may not be obvious from the example is that in practice, Alice's wallet needs to _know_ that Bob uses a segwit-aware wallet and can spend these outputs. Otherwise, if Bob's wallet is not upgraded and Alice tries to make segwit payments to Bob, Bob's wallet will not be able to detect these payments.

[TIP]
====
For P2WPKH and P2WSH payment types, both the sender and the recipient wallets need to be upgraded to be able to use segwit. Furthermore, the sender's wallet needs to know that the recipient's wallet is segwit-aware.
====

Segregated Witness will not be implemented simultaneously across the entire network. Rather, Segregated Witness is implemented as a backward-compatible upgrade, where _old and new clients can coexist_. Wallet developers will independently upgrade wallet software to add segwit capabilities. The P2WPKH and P2WSH payment types are used when both sender and recipient are segwit-aware. The traditional P2PKH and P2SH will continue to work for nonupgraded wallets. That leaves two important scenarios, which are addressed in the next section:

* Ability of a sender's wallet that is not segwit-aware to make a payment to a recipient's wallet that can process segwit transactions

* Ability of a sender's wallet that is segwit-aware to recognize and distinguish between recipients that are segwit-aware and ones that are not, by their _addresses_.

===== Embedding Segregated Witness inside P2SH

Let's assume, for example, that Alice's wallet is not upgraded to segwit, but Bob's wallet is upgraded and can handle segwit transactions. Alice and Bob can use "old" non-segwit transactions. But Bob would likely want to use segwit to reduce transaction fees, taking advantage of the discount that applies to witness data.

In this case Bob's wallet can construct a P2SH address that contains a segwit script inside it. Alice's wallet sees this as a "normal" P2SH address and can make payments to it without any knowledge of segwit. Bob's wallet can then spend this payment with a segwit transaction, taking full advantage of segwit and reducing transaction fees.

Both forms of witness scripts, P2WPKH and P2WSH, can be embedded in a P2SH address. The first is noted as P2SH(P2WPKH) and the second is noted as P2SH(P2WSH).

===== Pay-to-Witness-Public-Key-Hash inside Pay-to-Script-Hash

The first form of witness script we will examine is P2SH(P2WPKH). This is a Pay-to-Witness-Public-Key-Hash witness program, embedded inside a Pay-to-Script-Hash script, so that it can be used by a wallet that is not aware of segwit.

Bob's wallet constructs a P2WPKH witness program with Bob's public key. This witness program is then hashed and the resulting hash is encoded as a P2SH script. The P2SH script is converted to a bitcoin address, one that starts with a "3," as we saw in the <<p2sh>> section.

Bob's wallet starts with the P2WPKH witness program we saw earlier:

.Bob's P2WPKH witness program
----
0 ab68025513c3dbd2f7b92a94e0581f5d50f654e7
----

The P2WPKH witness program consists of the witness version and Bob's 20-byte public key hash.

Bob's wallet then hashes the preceding witness program, first with SHA256, then with RIPEMD160, producing another 20-byte hash.

Let's use +bx+ on the command-line to replicate that:

.HASH160 of the P2WPKH witness program
----
echo \
'0 [ab68025513c3dbd2f7b92a94e0581f5d50f654e7]'\
 | bx script-encode | bx sha256 | bx ripemd160
3e0547268b3b19288b3adef9719ec8659f4b2b0b
----


Next, the redeem script hash is converted to a bitcoin address. Let's use +bx+ on the command-line again:

.P2SH address
----
echo \
'3e0547268b3b19288b3adef9719ec8659f4b2b0b' \
| bx address-encode -v 5
37Lx99uaGn5avKBxiW26HjedQE3LrDCZru
----

Now, Bob can display this address for customers to pay for their coffee. Alice's wallet can make a payment to +37Lx99uaGn5avKBxiW26HjedQE3LrDCZru+, just as it would to any other bitcoin address.

To pay Bob, Alice's wallet would lock the output with a P2SH script:
----
HASH160 3e0547268b3b19288b3adef9719ec8659f4b2b0b EQUAL
----

Even though Alice's wallet has no support for segwit, the payment it creates can be spent by Bob with a segwit transaction.((("", startref="aliced")))

===== Pay-to-Witness-Script-Hash inside Pay-to-Script-Hash

Similarly, a P2WSH witness program for a multisig script or other complicated script can be embedded inside a P2SH script and address, making it possible for any wallet to make payments that are segwit compatible.

As we saw in <<p2wsh>>, Mohammed's ((("use cases", "import/export")))company is using Segregated Witness payments to multisignature scripts. To make it possible for any client to pay his company, regardless of whether their wallets are upgraded for segwit, Mohammed's wallet can embed the P2WSH witness program inside a P2SH script.

First, Mohammed's wallet hashes the redeem script with SHA256 (just once). Let's use +bx+ to do that on the command-line:

.Mohammed's wallet creates a P2WSH witness program
----
echo \
2 \ [04C16B8698A9ABF84250A7C3EA7EEDEF9897D1C8C6ADF47F06CF73370D74DCCA01CDCA79DCC5C395D7EEC6984D83F1F50C900A24DD47F569FD4193AF5DE762C587] \
[04A2192968D8655D6A935BEAF2CA23E3FB87A3495E7AF308EDF08DAC3C1FCBFC2C75B4B0F4D0B1B70CD2423657738C0C2B1D5CE65C97D78D0E34224858008E8B49] \
[047E63248B75DB7379BE9CDA8CE5751D16485F431E46117B9D0C1837C9D5737812F393DA7D4420D7E1A9162F0279CFC10F1E8E8F3020DECDBC3C0DD389D9977965] \
[0421D65CBD7149B255382ED7F78E946580657EE6FDA162A187543A9D85BAAA93A4AB3A8F044DADA618D087227440645ABE8A35DA8C5B73997AD343BE5C2AFD94A5] \
[043752580AFA1ECED3C68D446BCAB69AC0BA7DF50D56231BE0AABF1FDEEC78A6A45E394BA29A1EDF518C022DD618DA774D207D137AAB59E0B000EB7ED238F4D800] \
5 CHECKMULTISIG \
| bx script-encode | bx sha256
9592d601848d04b172905e0ddb0adde59f1590f1e553ffc81ddc4b0ed927dd73
----

Next, the hashed redeem script is turned into a P2WSH witness program:

----
0 9592d601848d04b172905e0ddb0adde59f1590f1e553ffc81ddc4b0ed927dd73
----

Then, the witness program itself is hashed with SHA256 and RIPEMD160, producing a new 20-byte hash, as used in traditional P2SH. Let's use +bx+ on the command-line to do that:

.The HASH160 of the P2WSH witness program
----
 echo \
'0 [9592d601848d04b172905e0ddb0adde59f1590f1e553ffc81ddc4b0ed927dd73]'\
 | bx script-encode | bx sha256 | bx ripemd160
86762607e8fe87c0c37740cddee880988b9455b2
----

Next, the wallet constructs a P2SH bitcoin address from this hash. Again, we use +bx+ to calculate on the command-line:

.P2SH bitcoin address
----
echo \
'86762607e8fe87c0c37740cddee880988b9455b2'\
 | bx address-encode -v 5
3Dwz1MXhM6EfFoJChHCxh1jWHb8GQqRenG
----

Now, Mohammed's clients can make payments to this address without any need to support segwit. To send a payment to Mohammed, a wallet would lock the output with the following P2SH script:

.P2SH script used to lock payments to Mohammed's multisig
----
HASH160 86762607e8fe87c0c37740cddee880988b9455b2 EQUAL
----

Mohammed's company can then construct segwit transactions to spend these payments, taking advantage of segwit features including lower transaction fees.

===== Segregated Witness addresses

Even after segwit activation, it will take some time until most wallets are upgraded. At first, segwit will be embedded in P2SH, as we saw in the previous section, to ease compatibility between segwit-aware and unaware wallets.

However, once wallets are broadly supporting segwit, it makes sense to encode witness scripts directly in a native address format designed for segwit, rather than embed it in P2SH.

The native segwit address format is defined in BIP-173:

https://github.com/bitcoin/bips/blob/master/bip-0173.mediawiki[BIP-173]:: Base32 address format for native v0-16 witness outputs

BIP-173 only encodes witness (P2WPKH and P2WSH) scripts. It is not compatible with non-segwit P2PKH or P2SH scripts. BIP-173 is a checksummed Base32 encoding, as compared to the Base58 encoding of a "traditional" bitcoin address. BIP-173 addresses are also called _bech32_ addresses, pronounced "beh-ch thirty two", alluding to the use of a "BCH" error detection algorithm and 32-character encoding set.

BIP-173 addresses use 32 lower-case-only alphanumeric character set, carefully selected to reduce errors from misreading or mistyping. By choosing a lower-case-only character set, bech32 is easier to read, speak, and 45% more efficient to encode in QR codes.

The BCH error detection algorithm is a vast improvement over the previous checksum algorithm (from Base58Check), allowing not only detection but also _correction_ of errors. Address-input interfaces (such as text-fields in forms) can detect and highlight which character was most likely mistyped when they detect an error.

From the BIP-173 specification, here are some examples of bech32 addresses:

Mainnet P2WPKH:: bc1qw508d6qejxtdg4y5r3zarvary0c5xw7kv8f3t4
Testnet P2WPKH:: tb1qw508d6qejxtdg4y5r3zarvary0c5xw7kxpjzsx
Mainnet P2WSH:: bc1qrp33g0q5c5txsp9arysrx4k6zdkfs4nce4xj0gdcccefvpysxf3qccfmv3
Testnet P2WSH:: tb1qrp33g0q5c5txsp9arysrx4k6zdkfs4nce4xj0gdcccefvpysxf3q0sl5k7

As you can see in these examples, a segwit bech32 string is up to 90 characters long and consists of three parts:

The human readable part:: This prefix "bc" or "tb" identifying mainnet or testnet.

The separator:: The digit "1", which is not part of the 32-character encoding set and can only appear in this position as a separator

The data part:: A minimum of 6 alphanumeric characters, the checksum encoded witness script

At this time, only a few wallets accept or produce native segwit bech32 addresses, but as segwit adoption increases, you will see these more and more often.

[[segwit_txid]]
===== Transaction identifiers

((("transaction IDs (txid)")))One of the greatest benefits of Segregated Witness is that it eliminates third-party transaction malleability.

Before segwit, transactions could have their signatures subtly modified by third parties, changing their transaction ID (hash) without changing any fundamental properties (inputs, outputs, amounts). This created opportunities for denial-of-service attacks as well as attacks against poorly written wallet software that assumed unconfirmed transaction hashes were immutable.

With the introduction of Segregated Witness, transactions have two identifiers, +txid+ and +wtxid+. The traditional transaction ID +txid+ is the double-SHA256 hash of the serialized transaction, without the witness data. A transaction +wtxid+ is the double-SHA256 hash of the new serialization format of the transaction with witness data.

The traditional +txid+ is calculated in exactly the same way as with a nonsegwit transaction. However, since the segwit transaction has empty ++scriptSig++s in every input, there is no part of the transaction that can be modified by a third party. Therefore, in a segwit transaction, the +txid+ is immutable by a third party, even when the transaction is unconfirmed.

The +wtxid+ is like an "extended" ID, in that the hash also incorporates the witness data. If a transaction is transmitted without witness data, then the +wtxid+ and +txid+ are identical. Note that since the +wtxid+ includes witness data (signatures) and since witness data may be malleable, the +wtxid+ should be considered malleable until the transaction is confirmed. Only the +txid+ of a segwit transaction can be considered immutable by third parties and only if _all_ the inputs of the transaction are segwit inputs.

[TIP]
====
Segregated Witness transactions have two IDs: +txid+ and +wtxid+. The +txid+ is the hash of the transaction without the witness data and the +wtxid+ is the hash inclusive of witness data. The +txid+ of a transaction where all inputs are segwit inputs is not susceptible to third-party transaction malleability.
====

==== Segregated Witness' New Signing Algorithm

Segregated Witness modifies the semantics of the four signature verification functions (+CHECKSIG+, +CHECKSIGVERIFY+, +CHECKMULTISIG+, and +CHECKMULTISIGVERIFY+), changing the way a transaction commitment hash is calculated.

Signatures in bitcoin transactions are applied on a _commitment hash_, which is calculated from the transaction data, locking specific parts of the data indicating the signer's commitment to those values. For example, in a simple +SIGHASH_ALL+ type signature, the commitment hash includes all inputs and outputs.

Unfortunately, the way the commitment hash was calculated introduced the possibility that a node verifying the signature can be forced to perform a significant number of hash computations. Specifically, the hash operations increase in O(n^2^) with respect to the number of signature operations in the transaction. An attacker could therefore create a transaction with a very large number of signature operations, causing the entire bitcoin network to have to perform hundreds or thousands of hash operations to verify the transaction.

Segwit represented an opportunity to address this problem by changing the way the commitment hash is calculated. For segwit version 0 witness programs, signature verification occurs using an improved commitment hash algorithm as specified in BIP-143.

The new algorithm achieves two important goals. Firstly, the number of hash operations increases by a much more gradual O(n) to the number of signature operations, reducing the opportunity to create denial-of-service attacks with overly complex transactions. Secondly, the commitment hash now also includes the value (amounts) of each input as part of the commitment. This means that a signer can commit to a specific input value without needing to "fetch" and check the previous transaction referenced by the input. In the case of offline devices, such as hardware wallets, this greatly simplifies the communication between the host and the hardware wallet, removing the need to stream previous transactions for validation. A hardware wallet can accept the input value "as stated" by an untrusted host. Since the signature is invalid if that input value is not correct, the hardware wallet doesn't need to validate the value before signing the input.

==== Economic Incentives for Segregated Witness

Bitcoin mining nodes and full nodes incur costs for the resources used to support the bitcoin network and the blockchain. As the volume of bitcoin transactions increases, so does the cost of resources (CPU, network bandwidth, disk space, memory). Miners are compensated for these costs through fees that are proportional to the size (in bytes) of each transaction. Nonmining full nodes are not compensated, so they incur these costs because they have a need to run an authoritative fully validating full-index node, perhaps because they use the node to operate a bitcoin business.

Without transaction fees, the growth in bitcoin data would arguably increase dramatically. Fees are intended to align the needs of bitcoin users with the burden their transactions impose on the network, through a market-based price discovery mechanism.

The calculation of fees based on transaction size treats all the data in the transaction as equal in cost. But from the perspective of full nodes and miners, some parts of a transaction carry much higher costs. Every transaction added to the bitcoin network affects the consumption of four resources on nodes:

Disk Space :: Every transaction is stored in the blockchain, adding to the total size of the blockchain. The blockchain is stored on disk, but the storage can be optimized by “pruning” older transactions.

CPU :: Every transaction must be validated, which requires CPU time.

Bandwidth :: Every transaction is transmitted (through flood propagation) across the network at least once. Without any optimization in the block propagation protocol, transactions are transmitted again as part of a block, doubling the impact on network capacity.

Memory :: Nodes that validate transactions keep the UTXO index or the entire UTXO set in memory to speed up validation. Because memory is at least one order of magnitude more expensive than disk, growth of the UTXO set contributes disproportionately to the cost of running a node.

As you can see from the list, not every part of a transaction has an equal impact on the cost of running a node or on the ability of bitcoin to scale to support more transactions. The most expensive part of a transaction are the newly created outputs, as they are added to the in-memory UTXO set. By comparison, signatures (aka witness data) add the least burden to the network and the cost of running a node, because witness data are only validated once and then never used again. Furthermore, immediately after receiving a new transaction and validating witness data, nodes can discard that witness data. If fees are calculated on transaction size, without discriminating between these two types of data, then the market incentives of fees are not aligned with the actual costs imposed by a transaction. In fact, the current fee structure actually encourages the opposite behavior, because witness data is the largest part of a transaction.

The incentives created by fees matter because they affect the behavior of wallets. All wallets must implement some strategy for assembling transactions that takes into consideration a number of factors, such as privacy (reducing address reuse), fragmentation (making lots of loose change), and fees. If the fees are overwhelmingly motivating wallets to use as few inputs as possible in transactions, this can lead to UTXO picking and change address strategies that inadvertently bloat the UTXO set.

Transactions consume UTXO in their inputs and create new UTXO with their outputs. A transaction, therefore, that has more inputs than outputs will result in a decrease in the UTXO set, whereas a transaction that has more outputs than inputs will result in an increase in the UTXO set. Let’s consider the _difference_ between inputs and outputs and call that the “Net-new-UTXO.” That’s an important metric, as it tells us what impact a transaction will have on the most expensive network-wide resource, the in-memory UTXO set. A transaction with positive Net-new-UTXO adds to that burden. A transaction with a negative Net-new-UTXO reduces the burden. We would therefore want to encourage transactions that are either negative Net-new-UTXO or neutral with zero Net-new-UTXO.

Let’s look at an example of what incentives are created by the transaction fee calculation, with and without Segregated Witness. We will look at two different transactions. Transaction A is a 3-input, 2-output transaction, which has a Net-new-UTXO metric of &#x2013;1, meaning it consumes one more UTXO than it creates, reducing the UTXO set by one. Transaction B is a 2-input, 3-output transaction, which has a Net-new-UTXO metric of 1, meaning it adds one UTXO to the UTXO set, imposing additional cost on the entire bitcoin network. Both transactions use multisignature (2-of-3) scripts to demonstrate how complex scripts increase the impact of segregated witness on fees. Let’s assume a transaction fee of 30 satoshi per byte and a 75% fee discount on witness data:

++++
<dl>
<dt>Without Segregated Witness</dt>
<dd>
<p>Transaction A fee: 25,710 satoshi</p>
<p>Transaction B fee: 18,990 satoshi</p>
</dd>

<dt>With Segregated Witness</dt>
<dd>
<p>Transaction A fee: 8,130 satoshi</p>
<p>Transaction B fee: 12,045 satoshi</p>
</dd>
</dl>
++++


Both transactions are less expensive when segregated witness is implemented. But comparing the costs between the two transactions, we see that before Segregated Witness, the fee is higher for the transaction that has a negative Net-new-UTXO. After Segregated Witness, the transaction fees align with the incentive to minimize new UTXO creation by not inadvertently penalizing transactions with many inputs.

Segregated Witness therefore has two main effects on the fees paid by bitcoin users. Firstly, segwit reduces the overall cost of transactions by discounting witness data and increasing the capacity of the bitcoin blockchain. Secondly, segwit’s discount on witness data corrects a misalignment of incentives that may have inadvertently created more bloat in the UTXO set.((("", startref="Tadv07")))((("", startref="Ssegwit07")))
