Complex Scripts

Site: Saylor Academy
Course: CS120: Bitcoin for Developers I
Book: Complex Scripts
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Date: Monday, March 4, 2024, 10:21 AM

Description

Let's finish by learning about conditional clauses and flow control, and taking a look at some examples of complex scripts.

Scripts with Flow Control (Conditional Clauses)

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, BOOLOR, 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 istrue
else:
 code to run when condition isfalse
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 istrue
ELSE
 code to run when condition isfalse
ENDIF
code to run in either case

 

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


Source: Andreas M. Antonopoulos, https://github.com/bitcoinbook/bitcoinbook/blob/develop/ch07.asciidoc
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 License.

Conditional Clauses with VERIFY Opcodes

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.

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 it:

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><hashpre-image>


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

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><hashpre-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: 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.

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.

Complex Script Example

In this section we combine many of the concepts from this chapter into a single example.

Our example uses the story of Mohammed, the company owner in Dubai who is operating an import/export business.

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 A bug in CHECKMULTISIG execution.

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 <Abdul the Lawyer's Sig> <Saeed'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 the Lawyer'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?

Segregated Witness

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 an 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:

BIP-141

The main definition of Segregated Witness.

BIP-143

Transaction Signature Verification for Version 0 Witness Program

BIP-144

Peer Services – New network messages and serialization formats

BIP-145

getblocktemplate Updates for Segregated Witness (for mining)

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 data, 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 Transaction identifiers), 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 data, 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(n2) 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 – 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 non-upgraded 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.

Pay-to-Witness-Public-Key-Hash (P2WPKH)

In [cup_of_coffee], 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 in the input part. Instead, Bob's transaction has an empty scriptSig in the transaction data (the first part of a transaction, which includes the input part) and includes his signature in the witness data (the second part of a transaction, which is separated from the transaction data):

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 receiver has no way of knowing if the sender'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.

Pay-to-Witness-Script-Hash (P2WSH)

The second type of witness program corresponds to a Pay-to-Script-Hash (P2SH) script. We saw this type of script in Pay-to-Script-Hash (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-5 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.

Mohammed's company can spend 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 data as part of the witness data. Within the transaction input, Mohammed's 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>"
[...]

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 provides stronger security to P2WSH (128 bits of security in P2WSH versus 80 bits of security in P2SH). It is also used to differentiate between the two types of witness programs (P2WPKH and P2WSH) by using the length of the hash (see below).

Differentiating between P2WPKH and P2WSH

In the previous two sections, we demonstrated two types of witness programs: Pay-to-Witness-Public-Key-Hash (P2WPKH) and Pay-to-Witness-Script-Hash (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 non-upgraded 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 Pay-to-Script-Hash (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.

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 Pay-to-Witness-Script-Hash (P2WSH), Mohammed's company is using Segregated Witness payments with 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:

 

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.

Bitcoin non-segwit (legacy) and segwit addresses shows bitcoin non-segwit (legacy) and segwit addresses.

 

Table 3. Bitcoin non-segwit (legacy) and segwit addresses

Type Encoding Prefix
Legacy P2PKH Address Base58 1
Legacy Testnet P2PKH Address Base58 m or n
Legacy P2SH Address Base58 3
Legacy Testnet P2SH Address Base58 2
Nested (embedded) Segwit P2SH(P2WPKH) Address Base58 3
Nested (embedded) Segwit P2SH(P2WSH) Address Base58 3
Native Segwit P2WPKH Address Bech32 bc1
Native Segwit Testnet P2WPKH Address Bech32 tb1
Native Segwit P2WSH Address Bech32 bc1
Native Segwit Testnet P2WSH Address Bech32 tb1

Transaction identifiers

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 a pure segwit transaction (a transaction that only contains segwit inputs) has empty scriptSigs in every input, there is no part of the transaction that can be modified by a third party. Therefore, in a pure 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 pure segwit transaction can be considered immutable by third parties.

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. Only pure segwit transactions (transactions that only contain segwit inputs) have a txid that 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(n2) 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” (deleting) 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 –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 feerate of 30 satoshi per byte and a 75% fee discount on witness data:

 

Without Segregated Witness

Transaction A fee: 28,590 satoshi

Transaction B fee: 20,760 satoshi

With Segregated Witness

Transaction A fee: 12,255 satoshi

Transaction B fee: 10,425 satoshi

 

Both transactions are less expensive when segregated witness is implemented. Comparing the costs between the two transactions, we see that before Segregated Witness, the transaction with the positive Net-new-UTXO has significant cost-savings. With Segregated Witness, the cost difference shrinks significantly in absolute as well as relative terms. While it would require inputs to become cheaper than outputs to incentivize UTXO set consolidation, this discount reduces the incentive to create new UTXO in order to avoid using more 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 partially mitigates a misalignment of incentives that may have inadvertently created more bloat in the UTXO set.