[[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
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
----

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.
====

[[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 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")))

==== 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 <<spending_bitcoin>>, ((("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 segit-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 addesses 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.

==== 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.
