Private keys can be stored on paper wallets , which are documents that have been printed with the private key and QR code on them so that they can easily be scanned when a transaction needs to be signed. Private keys can be stored using a hardware wallet that uses smartcards or USB devices to generate and secure private keys offline. The private keys can also be stored using a hardware wallet that uses smartcards or USB devices to generate and secure private keys offline.
An offline software wallet could also be used to store private keys. This wallet has an offline partition for private keys and an online division that has the public keys stored. With an offline software wallet, a new transaction is moved offline to be signed digitally and then moved back online to be broadcasted to the cryptocurrency network.
These types of storage mentioned above are called cold storage , as private keys are stored offline. The other type of wallet, hot wallet, stores private keys on devices or systems that are connected to the internet. Examples of these wallets include desktop wallets e. A private key is an extremely large number that is used in cryptography, similar to a password. Private keys are used to create digital signatures that can easily be verified, without revealing the private key.
Private keys are also used in cryptocurrency transactions in order to show ownership of a blockchain address. Private keys can be stored on computers or mobile phones, USB drives, a specialized hardware wallet, or even a piece of paper. The ideal form of storage will depend on how often you plan to use your cryptocurrency. A password-protected mobile phone or computer is the most convenient way to store cryptocurrency for everyday use. For long-term or "cold" storage, private keys should always be kept offline, ideally on devices that have never touched the internet.
Even printers can be compromised. Hardware wallets can facilitate cold storage by signing transactions in a way that does not compromise the private keys. A custodial wallet is a third-party service that allows users to store cryptocurrency, similar to a bank. This allows users to skip over the complication of private key storage, relying instead on the technological expertise of the company offering the service.
However, there are tradeoffs. Custodial wallets are often targets for hackers or phishing scams, and they can also be seized or frozen by legal authorities. The best solution is to determine what type of wallet fits your individual risk tolerance and technological skill. Andreas Antonopoulos. Accessed Dec. Your Money. Personal Finance. Your Practice. Popular Courses. Table of Contents Expand. Table of Contents. What Is a Private Key? Understanding Private Keys. Digital Wallets.
Private Keys FAQs. Key Takeaways A private key is a secret number that is used in cryptography and cryptocurrency. A private key is a large, randomly-generated number with hundreds of digits. For simplicity, they are usually represented as strings of alphanumeric characters.
A cryptocurrency wallet consists of a set of public addresses and private keys. Anyone can deposit cryptocurrency in a public address, but funds cannot be removed from an address without the corresponding private key. Private keys represent final control and ownership of cryptocurrency. It is vitally important to prevent one's private keys from being lost or compromised. How Do Private Keys Work?
Should You Trust a Custodial Wallet? Article Sources. Investopedia requires writers to use primary sources to support their work. These include white papers, government data, original reporting, and interviews with industry experts. We also reference original research from other reputable publishers where appropriate. You can learn more about the standards we follow in producing accurate, unbiased content in our editorial policy.
To generate a new key with the Bitcoin Core client see Chapter 3 , use the getnewaddress command. For security reasons it displays the public key only, not the private key. To ask bitcoind to expose the private key, use the dumpprivkey command. The dumpprivkey command shows the private key in a Base58 checksum-encoded format called the Wallet Import Format WIF , which we will examine in more detail in Private key formats.
The dumpprivkey command opens the wallet and extracts the private key that was generated by the getnewaddress command. It is not otherwise possible for bitcoind to know the private key from the public key, unless they are both stored in the wallet. The dumpprivkey command is not generating a private key from a public key, as this is impossible. The command simply reveals the private key that is already known to the wallet and which was generated by the getnewaddress command.
You can also use the command-line sx tools see Libbitcoin and sx Tools to generate and display private keys with the sx command newkey :. The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: where k is the private key, G is a constant point called the generator point and K is the resulting public key.
Elliptic curve cryptography is a type of asymmetric or public-key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve. Figure is an example of an elliptic curve, similar to that used by bitcoin. Bitcoin uses a specific elliptic curve and set of mathematical constants, as defined in a standard called secpk1 , established by the National Institute of Standards and Technology NIST.
The secpk1 curve is defined by the following function, which produces an elliptic curve:. Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize.
However, the math is identical as that of an elliptic curve over the real numbers. As an example, Figure shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid.
The secpk1 bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid. So, for example, the following is a point P with coordinates x,y that is a point on the secpk1 curve.
You can check this yourself using Python:. Geometrically, this third point P 3 is calculated by drawing a line between P 1 and P 2. This line will intersect the elliptic curve in exactly one additional place. This tangent will intersect the curve in exactly one new point. You can use techniques from calculus to determine the slope of the tangent line. These techniques curiously work, even though we are restricting our interest to points on the curve with two integer coordinates!
In some cases i. This shows how the point at infinity plays the role of 0. Now that we have defined addition, we can define multiplication in the standard way that extends addition. Starting with a private key in the form of a randomly generated number k , we multiply it by a predetermined point on the curve called the generator point G to produce another point somewhere else on the curve, which is the corresponding public key K.
The generator point is specified as part of the secpk1 standard and is always the same for all keys in bitcoin:. Because the generator point is always the same for all bitcoin users, a private key k multiplied with G will always result in the same public key K. The relationship between k and K is fixed, but can only be calculated in one direction, from k to K.
A private key can be converted into a public key, but a public key cannot be converted back into a private key because the math only works one way. Implementing the elliptic curve multiplication, we take the private key k generated previously and multiply it with the generator point G to find the public key K:. To visualize multiplication of a point with an integer, we will use the simpler elliptic curve over the real numbers—remember, the math is the same.
Our goal is to find the multiple kG of the generator point G. That is the same as adding G to itself, k times in a row. In elliptic curves, adding a point to itself is the equivalent of drawing a tangent line on the point and finding where it intersects the curve again, then reflecting that point on the x-axis. Figure shows the process for deriving G, 2G, 4G, as a geometric operation on the curve.
Most bitcoin implementations use the OpenSSL cryptographic library to do the elliptic curve math. A bitcoin address is a string of digits and characters that can be shared with anyone who wants to send you money. Because paper checks do not need to specify an account, but rather use an abstract name as the recipient of funds, that makes paper checks very flexible as payment instruments.
Bitcoin transactions use a similar abstraction, the bitcoin address, to make them very flexible. The bitcoin address is derived from the public key through the use of one-way cryptographic hashing. Cryptographic hash functions are used extensively in bitcoin: in bitcoin addresses, in script addresses, and in the mining proof-of-work algorithm. A bitcoin address is not the same as a public key.
Bitcoin addresses are derived from a public key using a one-way function. Base58Check is also used in many other ways in bitcoin, whenever there is a need for a user to read and correctly transcribe a number, such as a bitcoin address, a private key, an encrypted key, or a script hash.
In the next section we will examine the mechanics of Base58Check encoding and decoding, and the resulting representations. Figure illustrates the conversion of a public key into a bitcoin address. In order to represent long numbers in a compact way, using fewer symbols, many computer systems use mixed-alphanumeric representations with a base or radix higher than For example, whereas the traditional decimal system uses the 10 numerals 0 through 9, the hexadecimal system uses 16, with the letters A through F as the six additional symbols.
A number represented in hexadecimal format is shorter than the equivalent decimal representation. 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 normal child key is therefore displayed as 0, whereas the first hardened child index 0x is displayed as 0'. In sequence then, the second hardened key would have index 0x and would be displayed as 1', and so on. 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.
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