btcnodejs

developed with ❤️ by chainside

btcnodejs

btcnodejs is a Segwit-compliant bitcoin library which provides tools for managing bitcoin data structures. It is the NodeJS version of btcpy.

This library is a work in progress and its usage in a production environment is highly discouraged. Also, as long as the version is 0.*, API breaking changes might occur

Some of the functionalities are a wrapping around bitcore-lib and bitcoinjs-lib, and their development is still in progress.

It makes usage of bytebuffer.js for representing most of the data structures

Installation

To install the library, run npm install btcnodejs

Browserify

This library can be used in the browser with browserify. If you are familiar with browserify, you can skip this.

Assuming the entry point of the project is a file main.js like:

constbtcnodejs=require("btcnodejs");constnet=btcnodejs.network;net.setup("testnet");vark=newbtcnodejs.HDPrivateKey();console.log(k.privkey.toWIF());

Go into the main.js folder and run:

browserify main.js > browser_main.js

Now you can load the 'browserified' main.js into your html:

<!DOCTYPE html><html><head><title>Example Browserify</title></head><body><scriptsrc="browser_main.js"></script></body></html>

What it does

This library aims to manage bitcoin data structures. It offers functionalities for

Transactions and block headers deserialization
Scripts creation
Privatekeys, Publickeys and HDkeys management
Transactions signing

What it does not do

This library does not implement the following functionalities:

Validation : when transactions and scripts are parsed, only format errors are reported. No proof-of-work validation, script execution, transaction validation and signature verification is performed
Networking : this library does not provide functionalities to communicate with bitcoin nodes. Separates networking modules will be released soon.

Tests

In order to run tests, cd in the package directory and run

npm test

To run tests in the browser, you first need brfs installed. Then you can run browserify on the tests file, by doing (within the package directory):

browserify -t brfs test/test.js > test/browser_tests.js

Now you can create the .html file with the test script:

<!DOCTYPE html><html><head><title>Mocha Tests</title><linkrel="stylesheet" href="node_modules/mocha/mocha.css"></head><body><divid="mocha"></div><scriptsrc="node_modules/mocha/mocha.js"></script><script>mocha.setup('bdd')</script><scriptsrc="test/browser_tests.js"></script><script>mocha.run();</script></body></html>

Usage

On the first import, network setup must be executed. This is achieved by doing:

constnetwork=require('btcnodejs').networknetwork.setup('testnet')//network can be either 'testnet' or 'mainnet'

Once the network setup is executed, every subsequent setup will throw an exception.

The network module also exposes functionalities to get the current setup network

constnetwork=require('btcnodejs').networknetwork.setup('testnet')network.net_name()//outputs 'testnet'network.is_mainnet()//returns 'false'

API

Transactions

`btcnodejs.Transaction`

Transactions are immutable objects representing bitcoin transactions.

Attributes

version : Integer
inputs : list of Input objects
outputs : list of Output objects
locktime : Locktime object
segwit : Boolean
txid : String

new Transaction(version, inputs, outputs, locktime, segwit=false)

toJSON()

Returns the JSON representation of the transaction

hash()

Computes the double sha256 on the serialized transaction. Returns the hex string representing the hash

segwitId()

Computes the txid of a segwit transaction Returns the hex string representing the id of the transaction.

static fromHex(hex)

hex : Hexadecimal string

Returns a Transaction object

constbtcnodejs=require('btcnodejs')constTransaction=btcnodejs.Transactionbtcnodejs.network.setup('testnet')consttx=Transaction.fromHex("0100000001e4da173fbefe5e60ff63dfd38566ade407532294db655463b77a783f379ce605000000006b4"+"83045022100af246c27890c2bc07a0b7450d3d82509702a44a4defdff766355240b114ee2ac02207bb67b"+"468452fa1b325dd5583879f5c1412e0bb4dae1c2c96c7a408796ab76f1012102ab9e8575536a1e99604a1"+"58fc60fe2ebd1cb1839e919b4ca42b8d050cfad71b2ffffffff0100c2eb0b000000001976a914df76c017"+"354ac39bde796abe4294d31de8b5788a88ac00000000")console.log(tx.txid)//'e977c07090c2a1dcaefd3f3c4ebf4e231f4116cb272f805b0b22a85e7eece09c'

toHex()

Returns the hexadecimal representation of the transactions

serialize(segwit = this.segwit)

segwit : Boolean

Returns a ByteBuffer containing the serialized transaction. If called with no parameter, the serialization is performed based on the transaction type. To perform a non-segwit serialization of a segwit transaction(i.e. to compute the segwit txid), false can be passed to the function.

static deserialize(bytebuffer)

bytebuffer : ByteBuffer object

Returns a Transaction object from a ByteBuffer object representing the serialized transaction

toMutable()

Returns a MutableTransaction object

`btcnodejs.MutableTransaction`

Mutable Transaction objects

Attributes

version : Integer
inputs : list of Input objects
outputs : list of Output objects
locktime : Locktime object
segwit : Boolean
txid : String

new MutableTransaction(version, inputs, outputs, locktime, segwit=false)

Returns a MutableTransaction object

toImmutable()

Returns an immutable Transaction object

spend(txouts, solvers)

txouts : List of Output objects
solvers : List of Solver objects

Returns a Transaction object where the scriptSigs of its inputs are computed.

constbtcnodejs=require('./lib/index')btcnodejs.network.setup(network)vart=newbtcnodejs.Transaction(...)vartospend=btcnodejs.Transaction.fromHex('...')varkey=btcnodejs.Privatekey.fromWIF(wif_key)varsolver=newbtcnodejs.P2pkhSolver(key)varunsigned=t.toMutable()varspent=unsigned.spend([tospend.outputs[1]],[solver])

`btcnodejs.Sighash`

Sighash object

Attributes

sighash : String
- **values : 'ALL' | 'NONE' | 'SINGLE'
anyonecanpay : Boolean

new Sighash(sighash, anyonecanpay = false)

Returns a Sighash object

`btcnodejs.Input`

Transaction Input object

Attributes

txid : String
out : Integer
scriptSig : ScriptSig object
sequence : Sequence object
witness : Witness object

new Input(txid, out, scriptSig, sequence, witness = undefined)

Returns an Input object

toJSON()

Returns the JSON representation of the Input

`btcnodejs.Output`

Transaction Output object

Attributes

amount : Integer
scriptPubKey : scriptPubKey object

new Output(amount, scriptPubKey)

Returns an Output object

toJSON()

Returns the JSON representation of the Output

`btcnodejs.Witness`

Input Witness Object

Attributes

data : List of ByteBuffers

new Witness(data)

Returns a Witness Object where data represents the required data to sign a transaction Input

serialize()

Returns a ByteBuffer representing the Witness serialization as it appears in a bitcoin transaction

toScriptSig()

Returns a ScriptSig object

toHex()

Returns the hexadecimal representation of the Witness object

`btcnodejs.Sequence`

Sequence object representing the sequence number of a transaction Input

Attributes

n : Integer

new Sequence(n)

Returns a Sequence object

isTime()

Returns a Boolean which tells if the Sequence is measured in time

isBlocks()

Returns a Boolean which tells if the Sequence is measured in blocks

isActive()

Returns a Boolean which tells if a Sequence restriction is active

`btcnodejs.Locktime`

Locktime object representing the locktime on a transaction

Attributes

n : Integer

new Locktime(n)

Returns a Locktime object

isTime()

Returns a Boolean which tells if the Locktime is measured in time

isBlocks()

Returns a Boolean which tells if the Locktime is measured in blocks

isActive()

Returns a Boolean which tells if a Locktime restriction is active

Scripts

`btcnodejs.Script`

Base Script object representing a general script as a ByteBuffer. Every Script class extends Script.

Attributes

body : ByteBuffer

new Script(body)

Returns a Script object initialized from a bytebuffer representing the script

serialize()

Returns the body of the script_code

`btcnodejs.ScriptSig`

ScriptSig object

toAsm()

Returns a string representing the ASM of the script

static fromAsm(asm)

Returns a ScriptSig from an ASM string

toHex()

Returns the hexadecimal representation of the ScriptSig

static fromHex(hex)

Returns a ScriptSig object from an hexadecimal string representing the body of the script

toWitness()

Returns a Witness object where its data is retrieved from the ScriptSig body removing the push operations

constbtcnodejs=require('btcnodejs')constScriptSig=btcnodejs.ScriptSigbtcnodejs.network.setup('testnet')constsig=ScriptSig.fromHex("483045022100b7bf286e5f6ac6fa308e8876a8a59b289094851a26cf62c20abd174917eb7762022069b5269e584e4c7"+"6f207d1b789bff7171a663d795e49751c12cf07dceb2a94c70121024a0dcb0527c2751ea4dda3aa98f6eface16e978d"+"ba8062bcbed623f158c07691")sig.toWitness().toHex()// "02483045022100b7bf286e5f6ac6fa308e8876a8a59b289094851a26cf62c20abd174917eb7762022069b5269e584e4c76f207d1b789bff7171a663d795e49751c12c f07dceb2a94c70121024a0dcb0527c2751ea4dda3aa98f6eface16e978dba8062bcbed623f158c07691"

`btcnodejs.ScriptPubKey`

ScriptPubkey object representing a general script pubkey. It extends Script and is extended by specific ScriptPubkey types.

toHex()

Returns the hexadecimal representation of the ScriptPubKey

static fromHex(hex)

Returns a ScriptPubKey object from an hexadecimal string representing the body of the script. If the hex is representing an identifiable script, the fromHex() will return an instance of the specific ScriptPubKey. At the moment, identifiables scripts are P2pkh, P2sh, P2wpkhV0, P2wshV0, MultiSig

constbtcnodejs=require('btcnodejs')constScriptPubKey=btcnodejs.ScriptPubKeybtcnodejs.network.setup('testnet')constspk=ScriptPubKey.fromHex('76a9148b4912ec0496b5f759f3af5ab24d6f4779a52f9e88ac')spkinstanceofbtcnodejs.P2pkhScript//true

toAddress(network = undefined, segwitV = undefined)

network : String
segwitV : Integer

Returns the p2sh/p2wsh address of the Script.

If network is not specified, the initial setup network will be considered as the address network.
If segwitV is specified, the address will be of type 'p2wsh', with segwitV value as the segwit version

constbtcnodejs=require('btcnodejs')constScriptPubKey=btcnodejs.ScriptPubKeybtcnodejs.network.setup('testnet')constspk=ScriptPubKey.fromHex('76a9148b4912ec0496b5f759f3af5ab24d6f4779a52f9e88ac')constp2pkh_address=spk.toAddress()p2pkh_address.hash// "029c09b86e1e4c3822bc71859af3300520d577c2"p2pkh_address.toBase58()// "2MsV2GNkfjxPjsp9ux2vwxW5HYaZh1HDtXJ

`btcnodejs.P2pkhScript`

P2pkhScript object

new P2pkhScript(source)

source : Address object | Publickey object | ByteBuffer

Returns a P2pkhScript object. This can be obtained from an Address, a Publickey or a ByteBuffer representing a pubkeyhash

Attributes

type : String
pubkeyhash : ByteBuffer

getAddress()

Returns an Address object representing the script Address

`btcnodejs.P2wpkhV0Script`

Segwit version of P2pkhScript. It has the same interface of P2pkhScript but the source Address must be a Segwit Address object

getScriptCode()

Returns the ScriptCode of the P2wpkhV0Script

`btcnodejs.P2shScript`

P2shScript object

Attributes

type : String
scripthash : ByteBuffer

new P2shScript(source)

source : Address object | ScriptPubKey object | ByteBuffer

Returns a P2pkhScript object. This can be obtained from an Address, a ScriptPubKey or a ByteBuffer representing a scripthash

getAddress()

Returns an Address object representing the script Address

`btcnodejs.P2wshV0Script`

Segwit version of P2shScript. It has the same interface of P2shScript but the source Address must be a Segwit Address object

`btcnodejs.IfElseScript`

IfElseScript object

new IfElseScript(source)

source : Array of ScriptPubKey objects

Attributes

type : String
if_script : ScriptPubKey object
else_script : ScriptPubKey object

constbtcnodejs=require('btcnodejs')btcnodejs.network.setup('testnet')constp2pkh=newbtcnodejs.P2pkhScript(btcnodejs.Publickey.fromHex("026263992eda6538202047f1514e0f6155a229c3d61b066807664e9ef73d406d95"))constmultisig=newbtcnodejs.MultiSigScript([2,btcnodejs.Publickey.fromHex("02c08786d63f78bd0a6777ffe9c978cf5899756cfc32bfad09a89e211aeb926242"),btcnodejs.Publickey.fromHex("033e81519ecf373ea3a5c7e1c051b71a898fb3438c9550e274d980f147eb4d069d"),btcnodejs.Publickey.fromHex("036d568125a969dc78b963b494fa7ed5f20ee9c2f2fc2c57f86c5df63089f2ed3a"),3])constie_script=newbtcnodejs.IfElseScript([p2pkh,multisig])

`btcnodejs.RelativeTimelockScript`

RelativeTimelockScript object

new RelativeTimelockScript(source)

source : Array[ScriptPubKey object, Sequence object]

Returns a RelativeTimelockScript object

Attributes

sequence : Sequence object
locked_script : ScriptPubKey object
type : String

`btcnodejs.MultiSigScript`

MultisigScript object

new MultiSigScript(source)

source : [m, Publickey_1, Publickey_2, ... , Publickey_n, n]

Returns a MultiSigScript object

Attributes

type : String
m : Integer
n : Integer
pubkeys : Array of Publickey objects

constbtcnodejs=require('btcnodejs')btcnodejs.network.setup('testnet')//Creating a 2-of-3 Multisig Scriptconstmultisig=newbtcnodejs.MultiSigScript([2,btcnodejs.Publickey.fromHex("02c08786d63f78bd0a6777ffe9c978cf5899756cfc32bfad09a89e211aeb926242"),btcnodejs.Publickey.fromHex("033e81519ecf373ea3a5c7e1c051b71a898fb3438c9550e274d980f147eb4d069d"),btcnodejs.Publickey.fromHex("036d568125a969dc78b963b494fa7ed5f20ee9c2f2fc2c57f86c5df63089f2ed3a"),3])

Solvers

Solvers are objects which are able to compute the scriptSig and Witness from a given array of digests. They are an easy way to compute transaction input's signatures.

They all provide the method:

solve(digests)

digests : Array of digests

which returns an object :

{scriptSig : ScriptSig object , witness: Witness object}

constbtcnodejs=require('btcnodejs')btcnodejs.network.setup('testnet')constprivate_key=btcnodejs.Privatekey.fromHex('9b1b400e3b1211c6a56695cf1742f0a94ea38b995c1e1fb910458baa8a0874c4')constp2pkh_solver=newbtcnodejs.P2pkhSolver(private_key)p2pkh_solver.solve(["0e12bda8a692aefa29651e87af9f47127ab098be1c189284e41d8e17a0516add"]).scriptSig.toHex()//'47304402202409f1f966c382f02e023ac828d7653e9268777bd1030e7101338f36a383fde302207ced2d14ff131d3b349bb00d3010a16f08831548e68750223cb8117cab553cab01210330e8ca46b7e5aa07d975ee152214431e419fac34e50becaf7e46db9a9c97d244'

`btcnodejs.P2pkhSolver`

Solver for P2pkh Scripts

Attributes

privkey : Privatekey object
sighash : Sighash object

new P2pkhSolver(privkey, sighash = new Sighash('ALL'))

Returns a P2pkhSolver object

constbtcnodejs=require('btcnodejs')btcnodejs.network.setup('testnet')constprivate_key=btcnodejs.Privatekey.fromHex('9b1b400e3b1211c6a56695cf1742f0a94ea38b995c1e1fb910458baa8a0874c4')constp2pkh_solver=newbtcnodejs.P2pkhSolver(private_key)

`btcnodejs.P2wpkhV0Solver`

Solver for P2wpkh version 0 scripts. It extends P2pkhSolver

`btcnodejs.P2shSolver`

Solver for P2sh scripts

Attributes

redeemScript : ScriptPubKey object
redeemScriptSolver : Solver object

new P2shSolver(redeemScript, redeemScriptSolver)

`btcnodejs.P2wshV0Solver`

Solver for P2wsh version 0 Scripts

Attributes

witnessScript : ScriptPubKey object
witnessScriptSolver : Solver object

new P2wshV0Solver(witnessScript, witnessScriptSolver)

`btcnodejs.MultiSigSolver`

Solver for MultiSig Scripts

Attributes

privkeys : Array of Privatekey objects
sighashes : Array of Sighash objects

new MultiSigSolver(privkeys, sighashes = [new Sighash('ALL')])

The number of sigashes must be equal to the number of privatekeys.

`btcnodejs.IfElseSolver`

Solver for If Else Scripts

Attributes

branch : Integer
innerSolver : Solver object

new IfElseSolver(branch, innerSolver)

`btcnodejs.RelativeTimelockSolver`

Attributes

innerSolver : Solver object

new RelativeTimelockSolver(innerSolver)

Crypto

The library provides structures and methods to handle Private and Public key objects

`btcnodejs.Privatekey`

Attributes

body : ByteBuffer

new Privatekey(bytebuffer)

Returns a Privatekey object where the body is a bytebuffer representing the private key

static fromHex(hex)

hex : Hexadecimal String

Returns a Privatekey object from an hexadecimal string representing a private key

toHex()

Returns the Hexadecimal representation of the Privatekey

serialize()

Returns the body of the Privatekey

getPublic(compressed = true)

compressed : Boolean

Returns a Publickey object representing the public key associated with this Privatekey. By passing compressed = false, the public key will be of uncompressed type.

sign(message)

message : String

Computes the signature of a message, using the elliptic nodejs library using the secp256k1 curve.

signDER(message)

Returns the signature of the message in DER encoding

toWIF(compressed = false)

Returns the Wallet import format string representing the private key. If true is passed in input, the WIF string will represent a private key associated with a compressed Publickey.

fromWIF(wif_string)

wif_string : String

Return a Privatekey object from its Wallet import format string.

fromBip32(bip32_string)

bip32_string : String

Returns a Privatekey object from its Bip32 format string.

`btcnodejs.Publickey`

Publickey object

Attributes

type: String
uncompressed : ByteBuffer
compressed : ByteBuffer

new Publickey(bytebuffer)

Returns a Publickey object. Its type will be odd, even, uncompressed based on the the input bytebuffer data. It will keep both the uncompressed and compressed versions as its body, but its type will decide which version to use for any operation.

hash()

Returns the hash of the Publickey body.

static fromHex(hex)

Returns a Publickey object from its hexadecimal representation

toHex(compressed = true)

Returns the hexadecimal representation of its body. If false is passed as input it will return the hexadecimal representing its uncompressed version.

toAddress(network = undefined, segwit = false)

network : String
segwit : Boolean

Returns an Address object created from the Publickey hash.

If network is undefined, the first network name setup will be used.
If segwit is true, the Address type will be p2wpkh, otherwise it will be p2pkh

serialize()

Returns the Publickey body

HD

This library exposes functionalities to manage Hierarchical deterministic keys. It makes usage of bitcore-lib for some functionalities

`btcnodejs.HDPrivateKey`

Hierarchical deterministic PrivateKey object

Attributes

privkey : Privatekey object
depth : Integer
fingerPrint : Integer
parentFingerPrint : Integer
childIndex : Integer
chainCode : String
checksum : Integer
xprivkey : String

new HDPrivateKey(source)

source : String | undefined

Returns an HDPrivateKey object. If no parameter is given as input, a random HDPrivateKey is returned. Otherwise, a bip32 representation of an hd key can be passed

derive(path)

path : String

Returns a child HDPrivateKey derived as specified in BIP32. The path must be a string starting with 'm/'. To derive an hardened child, its index in the path is followed by ' i.e derive('m/0'')

getPublic()

Returns the corresponding HDPublicKey

static fromSeed(seed)

seed : String

Returns a master HDPrivateKey generated from the hexadecimal string representing a seed

`btcnodejs.HDPublicKey`

Hierarchical deterministic Public key object

Attributes

pubkey : Privatekey object
depth : Integer
fingerPrint : Integer
parentFingerPrint : Integer
childIndex : Integer
chainCode : String
checksum : Integer
xpubkey : String

new HDPublicKey(source)

source : String | undefined

Returns an HDPublicKey object. If no parameter is given as input, a random HDPublicKey is returned. Otherwise, a bip32 representation of an hd key can be passed.

derive(path)

path : String

Returns a child HDPublicKey derived as specified in BIP32.

Address

This library exposes functionalities to manage bitcoin addresses. It wraps bitcoinjs-lib for addresses encodings.

`btcnodejs.Address`

Attributes

network : String
type : String
hash : ByteBuffer

new Address(type, hash, network = undefined)

Returns an Address object. If network is not specified, the first setup network name will be used.

static fromBase58(base58string)

Returns an Address object from its base58 encoding

toBase58()

Returns a Base58 encoded string representing the bitcoin address

`btcnodejs.SegwitAddress`

SegwitAddress object extending Address. It has an extra version attribute specifying the segwit version.

Attributes

version : Integer

static fromBech32(bech32string)

Returns a Segwit Address object from its bech32 encoding

toBech32()

Returns a Bech32 encoded string representing the bitcoin Segwit address

Block

`btcnodejs.BlockHeader`

BlockHeader object

Attributes

version : Integer
prev_block : String
merkle_root : String
timestamp : Integer
bits : Integer
nonce : Integer

new BlockHeader(version, prev_block, merkle_root, timestamp, bits, nonce)

Returns a BlockHeader objects

static fromHex(hex)

Returns a BlockHeader object from an hexadecimal string representing the associated BlockHeader

serialize()

Returns a ByteBuffer representing the serialized BlockHeader

blockHash()

Returns an hexadecimal string representing the hash of the associated Block

TODO

Expand the test vectors
Add docstrings to code
Manage Block and MerkleBlock structures
Add caching in segwit digests computation
Add further helpers for creating transactions
Implement the functionalities which are now wrappings around external libraries
Manage OP_CODESEPARATOR in transaction signatures

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test		test
tools		tools
.gitignore		.gitignore
LICENSE.md		LICENSE.md
README.md		README.md
package.json		package.json

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btcnodejs

Table of Contents

Installation

Browserify

What it does

What it does not do

Tests

Usage

API

Transactions

btcnodejs.Transaction

Attributes

new Transaction(version, inputs, outputs, locktime, segwit=false)

toJSON()

hash()

segwitId()

static fromHex(hex)

toHex()

serialize(segwit = this.segwit)

static deserialize(bytebuffer)

toMutable()

btcnodejs.MutableTransaction

Attributes

new MutableTransaction(version, inputs, outputs, locktime, segwit=false)

toImmutable()

spend(txouts, solvers)

btcnodejs.Sighash

Attributes

new Sighash(sighash, anyonecanpay = false)

btcnodejs.Input

Attributes

new Input(txid, out, scriptSig, sequence, witness = undefined)

toJSON()

btcnodejs.Output

Attributes

new Output(amount, scriptPubKey)

toJSON()

btcnodejs.Witness

Attributes

new Witness(data)

serialize()

toScriptSig()

toHex()

btcnodejs.Sequence

Attributes

new Sequence(n)

isTime()

isBlocks()

isActive()

btcnodejs.Locktime

Attributes

new Locktime(n)

isTime()

isBlocks()

isActive()

Scripts

btcnodejs.Script

Attributes

new Script(body)

serialize()

btcnodejs.ScriptSig

toAsm()

static fromAsm(asm)

toHex()

static fromHex(hex)

toWitness()

btcnodejs.ScriptPubKey

toHex()

static fromHex(hex)

toAddress(network = undefined, segwitV = undefined)

btcnodejs.P2pkhScript

new P2pkhScript(source)

Attributes

getAddress()

btcnodejs.P2wpkhV0Script

`btcnodejs.Transaction`

`btcnodejs.MutableTransaction`

`btcnodejs.Sighash`

`btcnodejs.Input`

`btcnodejs.Output`

`btcnodejs.Witness`

`btcnodejs.Sequence`

`btcnodejs.Locktime`

`btcnodejs.Script`

`btcnodejs.ScriptSig`

`btcnodejs.ScriptPubKey`

`btcnodejs.P2pkhScript`

`btcnodejs.P2wpkhV0Script`

`btcnodejs.P2shScript`

`btcnodejs.P2wshV0Script`

`btcnodejs.IfElseScript`

`btcnodejs.RelativeTimelockScript`

`btcnodejs.MultiSigScript`

`btcnodejs.P2pkhSolver`

`btcnodejs.P2wpkhV0Solver`

`btcnodejs.P2shSolver`

`btcnodejs.P2wshV0Solver`

`btcnodejs.MultiSigSolver`

`btcnodejs.IfElseSolver`

`btcnodejs.RelativeTimelockSolver`

`btcnodejs.Privatekey`

`btcnodejs.Publickey`

`btcnodejs.HDPrivateKey`

`btcnodejs.HDPublicKey`