What is bitcoin public key

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Here is an example:. As you can see, this secret number is a bit unwieldy. One of the key functions of a Bitcoin wallet is to manage the private key. In fact, private keys are almost never handled directly by users. Bitcoin wallets provide a way to write down this private key in a much more human readable format, referred to as a recovery phrase, secret passphrase, or seed phrase. A recovery phrase is a list of words, usually between 12 and 24, that allow you to reconstruct your Bitcoin wallet and gain access to your funds even if your Bitcoin wallet is destroyed.

Here is an example of a recovery phrase consisting of 12 words:. Because the recovery phrase is equivalent to a private key, you should never share the words with anyone, or store the plain text on your computer or online. While the recovery phrase is an improvement upon the private key, it still leaves a lot to be desired. This presents problems because safely storing a piece of paper can be hard.

Storing all those recovery phrases on paper quickly becomes onerous. For this reason, the Bitcoin. Here you can create a single custom password and use it to unlock all of your private keys, which are stored in encrypted form in your Google or iCloud account. To set up Cloud Backup in the Bitcoin.

Read more: Make sure your cryptoassets are safe with these simple tips. There are two main types of wallets: hardware wallets and software wallets. Hardware wallets are the most secure type of Bitcoin wallet because their private keys are stored on a physical device and theoretically cannot be accessed by a computer or from the internet. When a person wishes to make a transaction, they plug in the hardware wallet usually via USB.

The hardware wallet will sign transactions without compromising the private key. The downside to hardware wallets is the cost and availability of the devices. Ledger and Trezor are well known hardware wallets. Software wallets exist on computing devices, like a desktop computer, a smartphone, or in a web browser. Since computing devices run many programs or applications, they are susceptible to viruses, malware, and phishing schemes, making all software wallets vulnerable to some degree.

That being said, hacking incidents are extremely rare and software wallets are generally considered safe for everyday use. There are many software wallet choices, which can make choosing overwhelming. We welcome you to try the Bitcoin. Начните брать на сумму от 30 долларов! Выберите из Bitcoin, Bitcoin Cash, Ethereum и остальных криптовалют.

Что такое биткоин? Как приобрести биткоины. Как сделать биткоин-кошелек. How to choose the best Bitcoin wallet. Как выслать биткоины. Как мне получить биткоин? Что такое некастодиальный кошелек? Биткоин основан на идеях, изложенных в документе года, озаглавленном Bitcoin: A Peer-to-Peer Electronic Cash System «Биткоин: одноранговая система электронных денег». CСоздайте биткоин-кошелек, установив приложение Bitcoin. Нетрудно узреть, что в этом случае отсутствует третье пересечение с кривой , которое мы называли.

Для того, чтоб избежать этого казуса, введем так именуемую точку в бесконечности point of infinity , обозначаемую традиционно либо просто , как на картинке. И будем говорить, что в случае отсутствия пересечения. Особенный энтузиазм для нас представляет вариант, когда мы желаем сложить точку саму с собой 2 кадр, точка. В этом случае просто проведем касательную к точке и отразим полученную точку пересечения относительно. Сейчас, легким движением руки, можно ввести операцию умножения точки на какое-то число.

В итоге получим новейшую точку , то есть раз. С картинкой все обязано стать вообщем понятно: Elliptic curve over a finite field В ECC употребляется точно таковая же кривая, лишь рассматриваемая над неким конечным полем — обычное число. То есть. Теги: bitcoin blockchain cryptography ecdsa private key public key. Хабы: Криптография Python Программирование Биллинговые системы.

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Могу где принимают к оплате биткоин аццкий

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Blockchain is touted as the most revolutionary technology to hit the financial services industry, banking the unbanked and returning power to the people. Bitcoin addresses are represented by an alphanumeric string of between 26 and 35 characters, usually beginning with 1, 3, or bc1.

Bitcoin uses a hash in addition to the public key for security reasons. Read Bitcoin Hash Rate to learn more. This salt is usually added in the form of a few random numbers, characters, or symbols into the seed phrase. This key pair is created using a mathematical curve and consists of your private key, derived from your seed phrase, and a public key derived from your private key.

Exposing your address to receive payments is much more secure as you can always generate new addresses from the public key. Information can also be encrypted to your public key, and only your private key can decrypt it, allowing people to send you messages that can only you can read.

This is useful for signing documents to prove the identity of the person sending it without giving away too much information. Your public key, private key, and address are three different parts of a single structure, and they all play critical roles in the functioning of the decentralized system. The private key is the most important component of them, with the other two being derived from it. Banks are secure on a broader level, but a single point of failure creates a single attack point.

Decentralized systems by nature are more complex than centralized ones, especially in their current state. Blockchain is still a new technology, and while there are some disadvantages to using blockchain over traditional financial systems today, this may not be the case for too much longer. For example, public keys are generated using co-ordinates on an elliptic curve, which implies knowing one co-ordinate is enough to derive the second co-ordinate.

This can be hard to distinguish as the hash of the compressed and uncompressed public keys give different addresses of the same length. Addresses are indeed shorter than public keys, but they also bring protection against various cryptographic attack vectors. Private keys are generated using a pneumonic phrase — a set of words that act as a seed to the function that generates the private key.

This seed phrase is generally a list of 12 to 24 randomly generated words used to recover all information regarding a wallet. The private key generation function takes five inputs, including a password, the number of iterations, salt, key length, and a pseudorandom function. The password is the pneumonic phrase, and the function returns a private key from which both your public key and payment addresses can be derived.

Bitcoin is only as secure as it is decentralized, and as a function of its network participation, the security of decentralized networks should improve with adoption. Quantum computers can perform calculations that take traditional computers decades or even centuries in mere minutes.

In theory. Realistically, Bitcoin is perfectly safe, and even if quantum computers find an algorithm to crack encryption, quantum encryption algorithms will be quick to replace them. In fact, some modern security measures can combat quantum computing today — multi-sig wallets are used to store funds that a group of individuals controls. Multi-sig wallet addresses start with a three and use a script to define the rules for creating a transaction, including how many signatures are needed for a transaction to go through.

Base is most commonly used to add binary attachments to email. Base58 is a text-based binary-encoding format developed for use in bitcoin and used in many other cryptocurrencies. It offers a balance between compact representation, readability, and error detection and prevention. Base58 is a subset of Base64, using the upper- and lowercase letters and numbers, but omitting some characters that are frequently mistaken for one another and can appear identical when displayed in certain fonts.

Or, more simply, it is a set of lower and capital letters and numbers without the four 0, O, l, I just mentioned. To add extra security against typos or transcription errors, Base58Check is a Base58 encoding format, frequently used in bitcoin, which has a built-in error-checking code. The checksum is an additional four bytes added to the end of the data that is being encoded. The checksum is derived from the hash of the encoded data and can therefore be used to detect and prevent transcription and typing errors.

When presented with a Base58Check code, the decoding software will calculate the checksum of the data and compare it to the checksum included in the code. If the two do not match, that indicates that an error has been introduced and the Base58Check data is invalid. For example, this prevents a mistyped bitcoin address from being accepted by the wallet software as a valid destination, an error that would otherwise result in loss of funds.

For example, in the case of a bitcoin address the prefix is zero 0x00 in hex , whereas the prefix used when encoding a private key is 0x80 in hex. A list of common version prefixes is shown in Table From the resulting byte hash hash-of-a-hash , we take only the first four bytes.

These four bytes serve as the error-checking code, or checksum. The checksum is concatenated appended to the end. The result is composed of three items: a prefix, the data, and a checksum. This result is encoded using the Base58 alphabet described previously. Figure illustrates the Base58Check encoding process. In bitcoin, most of the data presented to the user is Base58Check-encoded to make it compact, easy to read, and easy to detect errors. The version prefix in Base58Check encoding is used to create easily distinguishable formats, which when encoded in Base58 contain specific characters at the beginning of the Base58Check-encoded payload.

These characters make it easy for humans to identify the type of data that is encoded and how to use it. This is what differentiates, for example, a Base58Check-encoded bitcoin address that starts with a 1 from a Base58Check-encoded private key WIF format that starts with a 5.

Some example version prefixes and the resulting Base58 characters are shown in Table The code example uses the libbitcoin library introduced in Alternative Clients, Libraries, and Toolkits for some helper functions. The code uses a predefined private key so that it produces the same bitcoin address every time it is run, as shown in Example Both private and public keys can be represented in a number of different formats.

These representations all encode the same number, even though they look different. These formats are primarily used to make it easy for people to read and transcribe keys without introducing errors. The private key can be represented in a number of different formats, all of which correspond to the same bit number. Table shows three common formats used to represent private keys. Table shows the private key generated in these three formats.

All of these representations are different ways of showing the same number, the same private key. They look different, but any one format can easily be converted to any other format. You can use sx tools to decode the Base58Check format on the command line. We use the base58check-decode command:. To encode into Base58Check the opposite of the previous command , we provide the hex private key, followed by the Wallet Import Format WIF version prefix Public keys are also presented in different ways, most importantly as either compressed or uncompressed public keys.

As we saw previously, the public key is a point on the elliptic curve consisting of a pair of coordinates x,y. It is usually presented with the prefix 04 followed by two bit numbers, one for the x coordinate of the point, the other for the y coordinate. The prefix 04 is used to distinguish uncompressed public keys from compressed public keys that begin with a 02 or a Compressed public keys were introduced to bitcoin to reduce the size of transactions and conserve disk space on nodes that store the bitcoin blockchain database.

As we saw in the section Public Keys , a public key is a point x,y on an elliptic curve. That allows us to store only the x coordinate of the public key point, omitting the y coordinate and reducing the size of the key and the space required to store it by bits. Whereas uncompressed public keys have a prefix of 04 , compressed public keys start with either a 02 or a 03 prefix. Visually, this means that the resulting y coordinate can be above the x-axis or below the x-axis.

As you can see from the graph of the elliptic curve in Figure , the curve is symmetric, meaning it is reflected like a mirror by the x-axis. So, while we can omit the y coordinate we have to store the sign of y positive or negative , or in other words, we have to remember if it was above or below the x-axis because each of those options represents a different point and a different public key.

Therefore, to distinguish between the two possible values of y, we store a compressed public key with the prefix 02 if the y is even, and 03 if it is odd, allowing the software to correctly deduce the y coordinate from the x coordinate and uncompress the public key to the full coordinates of the point. Public key compression is illustrated in Figure This compressed public key corresponds to the same private key, meaning that it is generated from the same private key.

However, it looks different from the uncompressed public key. This can be confusing, because it means that a single private key can produce a public key expressed in two different formats compressed and uncompressed that produce two different bitcoin addresses. However, the private key is identical for both bitcoin addresses. Compressed public keys are gradually becoming the default across bitcoin clients, which is having a significant impact on reducing the size of transactions and therefore the blockchain.

However, not all clients support compressed public keys yet. Newer clients that support compressed public keys have to account for transactions from older clients that do not support compressed public keys. This is especially important when a wallet application is importing private keys from another bitcoin wallet application, because the new wallet needs to scan the blockchain to find transactions corresponding to these imported keys.

Which bitcoin addresses should the bitcoin wallet scan for? The bitcoin addresses produced by uncompressed public keys, or the bitcoin addresses produced by compressed public keys? Both are valid bitcoin addresses, and can be signed for by the private key, but they are different addresses!

To resolve this issue, when private keys are exported from a wallet, the Wallet Import Format that is used to represent them is implemented differently in newer bitcoin wallets, to indicate that these private keys have been used to produce compressed public keys and therefore compressed bitcoin addresses.

This allows the importing wallet to distinguish between private keys originating from older or newer wallets and search the blockchain for transactions with bitcoin addresses corresponding to the uncompressed, or the compressed, public keys, respectively. That is because it has the added 01 suffix, which signifies it comes from a newer wallet and should only be used to produce compressed public keys. Private keys are not compressed and cannot be compressed.

Remember, these formats are not used interchangeably. In a newer wallet that implements compressed public keys, the private keys will only ever be exported as WIF-compressed with a K or L prefix. If the wallet is an older implementation and does not use compressed public keys, the private keys will only ever be exported as WIF with a 5 prefix. The goal here is to signal to the wallet importing these private keys whether it must search the blockchain for compressed or uncompressed public keys and addresses.

If a bitcoin wallet is able to implement compressed public keys, it will use those in all transactions. The private keys in the wallet will be used to derive the public key points on the curve, which will be compressed. The compressed public keys will be used to produce bitcoin addresses and those will be used in transactions. When exporting private keys from a new wallet that implements compressed public keys, the Wallet Import Format is modified, with the addition of a one-byte suffix 01 to the private key.

They are not compressed; rather, the WIF-compressed format signifies that they should only be used to derive compressed public keys and their corresponding bitcoin addresses. The most comprehensive bitcoin library in Python is pybitcointools by Vitalik Buterin. Example shows the output from running this code. Example is another example, using the Python ECDSA library for the elliptic curve math and without using any specialized bitcoin libraries.

Example shows the output produced by running this script. Wallets are containers for private keys, usually implemented as structured files or simple databases. Another method for making keys is deterministic key generation. Here you derive each new private key, using a one-way hash function from a previous private key, linking them in a sequence.

As long as you can re-create that sequence, you only need the first key known as a seed or master key to generate them all. In this section we will examine the different methods of key generation and the wallet structures that are built around them. Bitcoin wallets contain keys, not coins. Each user has a wallet containing keys. Users sign transactions with the keys, thereby proving they own the transaction outputs their coins. The coins are stored on the blockchain in the form of transaction-ouputs often noted as vout or txout.

In the first bitcoin clients, wallets were simply collections of randomly generated private keys. This type of wallet is called a Type-0 nondeterministic wallet. For example, the Bitcoin Core client pregenerates random private keys when first started and generates more keys as needed, using each key only once.

The disadvantage of random keys is that if you generate many of them you must keep copies of all of them, meaning that the wallet must be backed up frequently. Each key must be backed up, or the funds it controls are irrevocably lost if the wallet becomes inaccessible. This conflicts directly with the principle of avoiding address re-use, by using each bitcoin address for only one transaction. Address re-use reduces privacy by associating multiple transactions and addresses with each other.

A Type-0 nondeterministic wallet is a poor choice of wallet, especially if you want to avoid address re-use because that means managing many keys, which creates the need for frequent backups. Although the Bitcoin Core client includes a Type-0 wallet, using this wallet is discouraged by developers of Bitcoin Core. Figure shows a nondeterministic wallet, containing a loose collection of random keys. In a deterministic wallet, the seed is sufficient to recover all the derived keys, and therefore a single backup at creation time is sufficient.

Mnemonic codes are English word sequences that represent encode a random number used as a seed to derive a deterministic wallet. The sequence of words is sufficient to re-create the seed and from there re-create the wallet and all the derived keys. A wallet application that implements deterministic wallets with mnemonic code will show the user a sequence of 12 to 24 words when first creating a wallet.

That sequence of words is the wallet backup and can be used to recover and re-create all the keys in the same or any compatible wallet application. Mnemonic code words make it easier for users to back up wallets because they are easy to read and correctly transcribe, as compared to a random sequence of numbers. Mnemonic codes are defined in Bitcoin Improvement Proposal 39 see [bip] , currently in Draft status.

Note that BIP is a draft proposal and not a standard. Specifically, there is a different standard, with a different set of words, used by the Electrum wallet and predating BIP Table shows the relationship between the size of entropy data and the length of mnemonic codes in words.

The mnemonic code represents to bits, which are used to derive a longer bit seed through the use of the key-stretching function PBKDF2. The resulting seed is used to create a deterministic wallet and all of its derived keys. Tables and show some examples of mnemonic codes and the seeds they produce.

Hierarchical deterministic wallets contain keys derived in a tree structure, such that a parent key can derive a sequence of children keys, each of which can derive a sequence of grandchildren keys, and so on, to an infinite depth.

This tree structure is illustrated in Figure HD wallets offer two major advantages over random nondeterministic keys. First, the tree structure can be used to express additional organizational meaning, such as when a specific branch of subkeys is used to receive incoming payments and a different branch is used to receive change from outgoing payments.

Branches of keys can also be used in a corporate setting, allocating different branches to departments, subsidiaries, specific functions, or accounting categories. The second advantage of HD wallets is that users can create a sequence of public keys without having access to the corresponding private keys. This allows HD wallets to be used on an insecure server or in a receive-only capacity, issuing a different public key for each transaction.

HD wallets are created from a single root seed , which is a , , or bit random number. Everything else in the HD wallet is deterministically derived from this root seed, which makes it possible to re-create the entire HD wallet from that seed in any compatible HD wallet. This makes it easy to back up, restore, export, and import HD wallets containing thousands or even millions of keys by simply transferring only the root seed. The root seed is most often represented by a mnemonic word sequence , as described in the previous section Mnemonic Code Words , to make it easier for people to transcribe and store it.

The process of creating the master keys and master chain code for an HD wallet is shown in Figure The root seed is input into the HMAC-SHA algorithm and the resulting hash is used to create a master private key m and a master chain code. The chain code is used to introduce entropy in the function that creates child keys from parent keys, as we will see in the next section. Hierarchical deterministic wallets use a child key derivation CKD function to derive children keys from parent keys.

The chain code is used to introduce seemingly random data to the process, so that the index is not sufficient to derive other child keys. Thus, having a child key does not make it possible to find its siblings, unless you also have the chain code. The initial chain code seed at the root of the tree is made from random data, while subsequent chain codes are derived from each parent chain code.

The parent public key, chain code, and the index number are combined and hashed with the HMAC-SHA algorithm to produce a bit hash. The resulting hash is split into two halves. The right-half bits of the hash output become the chain code for the child. The left-half bits of the hash and the index number are added to the parent private key to produce the child private key.

Changing the index allows us to extend the parent and create the other children in the sequence, e. Each parent key can have 2 billion children keys. Repeating the process one level down the tree, each child can in turn become a parent and create its own children, in an infinite number of generations. Child private keys are indistinguishable from nondeterministic random keys.

Because the derivation function is a one-way function, the child key cannot be used to find the parent key. The child key also cannot be used to find any siblings. Only the parent key and chain code can derive all the children. Without the child chain code, the child key cannot be used to derive any grandchildren either.

You need both the child private key and the child chain code to start a new branch and derive grandchildren. So what can the child private key be used for on its own? It can be used to make a public key and a bitcoin address. Then, it can be used to sign transactions to spend anything paid to that address. A child private key, the corresponding public key, and the bitcoin address are all indistinguishable from keys and addresses created randomly.

The fact that they are part of a sequence is not visible, outside of the HD wallet function that created them. As we saw earlier, the key derivation function can be used to create children at any level of the tree, based on the three inputs: a key, a chain code, and the index of the desired child.

The two essential ingredients are the key and chain code, and combined these are called an extended key. Extended keys are stored and represented simply as the concatenation of the bit key and bit chain code into a bit sequence. There are two types of extended keys. An extended private key is the combination of a private key and chain code and can be used to derive child private keys and from them, child public keys.

An extended public key is a public key and chain code, which can be used to create child public keys, as described in Generating a Public Key. Think of an extended key as the root of a branch in the tree structure of the HD wallet. With the root of the branch, you can derive the rest of the branch. The extended private key can create a complete branch, whereas the extended public key can only create a branch of public keys. An extended key consists of a private or public key and chain code.

An extended key can create children, generating its own branch in the tree structure. Sharing an extended key gives access to the entire branch. Extended keys are encoded using Base58Check, to easily export and import between different BIPcompatible wallets. Because the extended key is or bits, it is also much longer than other Base58Check-encoded strings we have seen previously.

As mentioned previously, a very useful characteristic of hierarchical deterministic wallets is the ability to derive public child keys from public parent keys, without having the private keys. This gives us two ways to derive a child public key: either from the child private key, or directly from the parent public key. An extended public key can be used, therefore, to derive all of the public keys and only the public keys in that branch of the HD wallet structure. This shortcut can be used to create very secure public-key-only deployments where a server or application has a copy of an extended public key and no private keys whatsoever.

That kind of deployment can produce an infinite number of public keys and bitcoin addresses, but cannot spend any of the money sent to those addresses. Meanwhile, on another, more secure server, the extended private key can derive all the corresponding private keys to sign transactions and spend the money.

One common application of this solution is to install an extended public key on a web server that serves an ecommerce application. The web server can use the public key derivation function to create a new bitcoin address for every transaction e. The web server will not have any private keys that would be vulnerable to theft. Without HD wallets, the only way to do this is to generate thousands of bitcoin addresses on a separate secure server and then preload them on the ecommerce server.

Another common application of this solution is for cold-storage or hardware wallets. In that scenario, the extended private key can be stored on a paper wallet or hardware device such as a Trezor hardware wallet , while the extended public key can be kept online.

To spend the funds, the user can use the extended private key on an offline signing bitcoin client or sign transactions on the hardware wallet device e. Figure illustrates the mechanism for extending a parent public key to derive child public keys.

The ability to derive a branch of public keys from an extended public key is very useful, but it comes with a potential risk. Access to an extended public key does not give access to child private keys. However, because the extended public key contains the chain code, if a child private key is known, or somehow leaked, it can be used with the chain code to derive all the other child private keys.

A single leaked child private key, together with a parent chain code, reveals all the private keys of all the children. Worse, the child private key together with a parent chain code can be used to deduce the parent private key. The hardened derivation function uses the parent private key to derive the child chain code, instead of the parent public key. The hardened derivation function looks almost identical to the normal child private key derivation, except that the parent private key is used as input to the hash function, instead of the parent public key, as shown in the diagram in Figure When the hardened private derivation function is used, the resulting child private key and chain code are completely different from what would result from the normal derivation function.

In simple terms, if you want to use the convenience of an extended public key to derive branches of public keys, without exposing yourself to the risk of a leaked chain code, you should derive it from a hardened parent, rather than a normal parent. As a best practice, the level-1 children of the master keys are always derived through the hardened derivation, to prevent compromise of the master keys. The index number used in the derivation function is a bit integer.

To easily distinguish between keys derived through the normal derivation function versus keys derived through hardened derivation, this index number is split into two ranges. Therefore, if the index number is less than 2 31 , that means the child is normal, whereas if the index number is equal or above 2 31 , the child is hardened. To make the index number easier to read and display, the index number for hardened children is displayed starting from zero, but with a prime symbol.

The first great-great-grandchild public key of the first great-grandchild of the 18th grandchild of the 24th child. The HD wallet tree structure offers tremendous flexibility. Each parent extended key can have 4 billion children: 2 billion normal children and 2 billion hardened children. Each of those children can have another 4 billion children, and so on. The tree can be as deep as you want, with an infinite number of generations.

With all that flexibility, however, it becomes quite difficult to navigate this infinite tree. It is especially difficult to transfer HD wallets between implementations, because the possibilities for internal organization into branches and subbranches are endless. Based on BIP, an HD wallet should use only one level-1 branch of the tree, with the index number identifying the structure and namespace of the rest of the tree by defining its purpose. Each account is the root of its own subtree.

Note that whereas the previous levels used hardened derivation, this level uses normal derivation. This is to allow this level of the tree to export extended public keys for use in a nonsecured environment. Table shows a few more examples. Using the command-line tool sx , introduced in Chapter 3 , you can experiment with generating and extending BIP deterministic keys, as well as displaying them in different formats:.

In the following sections we will look at advanced forms of keys and addresses, such as encrypted private keys, script and multisignature addresses, vanity addresses, and paper wallets. Private keys must remain secret. The need for confidentiality of the private keys is a truism that is quite difficult to achieve in practice, because it conflicts with the equally important security objective of availability. Keeping the private key private is much harder when you need to store backups of the private key to avoid losing it.

A private key stored in a wallet that is encrypted by a password might be secure, but that wallet needs to be backed up. At times, users need to move keys from one wallet to another—to upgrade or replace the wallet software, for example. Private key backups might also be stored on paper see Paper Wallets or on external storage media, such as a USB flash drive.

But what if the backup itself is stolen or lost? These conflicting security goals led to the introduction of a portable and convenient standard for encrypting private keys in a way that can be understood by many different wallets and bitcoin clients, standardized by Bitcoin Improvement Proposal 38 or BIP see [bip].

BIP proposes a common standard for encrypting private keys with a passphrase and encoding them with Base58Check so that they can be stored securely on backup media, transported securely between wallets, or kept in any other conditions where the key might be exposed. Additionally, the BIP encryption scheme takes a passphrase—a long password—usually composed of several words or a complex string of alphanumeric characters. The result of the BIP encryption scheme is a Base58Check-encoded encrypted private key that begins with the prefix 6P.

If you see a key that starts with 6P , that means it is encrypted and requires a passphrase in order to convert decrypt it back into a WIF-formatted private key prefix 5 that can be used in any wallet. Many wallet applications now recognize BIPencrypted private keys and will prompt the user for a passphrase to decrypt and import the key. Third-party applications, such as the incredibly useful browser-based Bit Address Wallet Details tab , can be used to decrypt BIP keys. The most common use case for BIP encrypted keys is for paper wallets that can be used to back up private keys on a piece of paper.

Test the encrypted keys in Table using bitaddress. They designate the beneficiary of a bitcoin transaction as the hash of a script, instead of the owner of a public key. The feature was introduced in January with Bitcoin Improvement Proposal 16, or BIP see [bip] , and is being widely adopted because it provides the opportunity to add functionality to the address itself.

The requirements are designated at the time the address is created, within the script, and all inputs to this address will be encumbered with the same requirements. A pay-to-script hash address is created from a transaction script, which defines who can spend a transaction output for more detail, see Pay-to-Script-Hash P2SH. Encoding a pay-to-script hash address involves using the same double-hash function as used during creation of a bitcoin address, only applied on the script instead of the public key:.

P2SH is not necessarily the same as a multi-signature standard transaction. A P2SH address most often represents a multi-signature script, but it might also represent a script encoding other types of transactions. Currently, the most common implementation of the P2SH function is the multi-signature address script. As the name implies, the underlying script requires more than one signature to prove ownership and therefore spend funds.

For example, Bob the coffee shop owner from Chapter 1 could use a multi-signature address requiring 1-of-2 signatures from a key belonging to him and a key belonging to his spouse, ensuring either of them could sign to spend a transaction output locked to this address.

Or Gopesh, the web designer paid by Bob to create a website, might have a 2-of-3 multi-signature address for his business that ensures that no funds can be spent unless at least two of the business partners sign a transaction. We will explore how to create transactions that spend funds from P2SH and multi-signature addresses in Chapter 5.

Vanity addresses are valid bitcoin addresses that contain human-readable messages. Vanity addresses require generating and testing billions of candidate private keys, until one derives a bitcoin address with the desired pattern. Although there are some optimizations in the vanity generation algorithm, the process essentially involves picking a private key at random, deriving the public key, deriving the bitcoin address, and checking to see if it matches the desired vanity pattern, repeating billions of times until a match is found.

Once a vanity address matching the desired pattern is found, the private key from which it was derived can be used by the owner to spend bitcoins in exactly the same way as any other address. Vanity addresses are no less or more secure than any other address. You can no more easily find the private key of an address starting with a vanity pattern than you can any other address.

There are approximately 58 29 approximately 1. Table shows the range of addresses that have the prefix 1Kids. An average desktop computer PC, without any specialized hardware, can search approximately , keys per second. Each additional character increases the difficulty by a factor of Patterns with more than seven characters are usually found by specialized hardware, such as custom-built desktops with multiple graphical processing units GPUs.

Another way to find a vanity address is to outsource the work to a pool of vanity miners, such as the pool at Vanity Pool. A pool is a service that allows those with GPU hardware to earn bitcoin searching for vanity addresses for others.

For a small payment 0. Generating a vanity address is a brute-force exercise: try a random key, check the resulting address to see if it matches the desired pattern, repeat until successful. The example uses the libbitcoin library, which we introduced in Alternative Clients, Libraries, and Toolkits. The example code must be compiled using a C compiler and linked against the libbitcoin library which must be first installed on that system. Change the search pattern in the source code and see how much longer it takes for four- or five-character patterns!

Vanity addresses can be used to enhance and to defeat security measures; they are truly a double-edged sword.