Bitcoin keys explained

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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 Bitcoin Explorer to decode the Base58Check format on the command line.

To encode into Base58Check the opposite of the previous command , we use the base58check-encode command from Bitcoin Explorer see Appendix F and provide the hex private key, followed by the WIF version prefix Public keys are also presented in different ways, usually 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.

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 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 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 WIF 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 the private key has an added one-byte suffix shown as 01 in hex in Table , which signifies that the private key is from a newer wallet and should only be used to produce compressed public keys.

Private keys are not themselves compressed and cannot be compressed. Notice that the hex-compressed private key format has one extra byte at the end 01 in hex. While the Base58 encoding version prefix is the same 0x80 for both WIF and WIF-compressed formats, the addition of one byte on the end of the number causes the first character of the Base58 encoding to change from a 5 to either a K or L.

Think of this as the Base58 equivalent of the decimal encoding difference between the number and the number While is one digit longer than 99, it also has a prefix of 1 instead of a prefix of 9. As the length changes, it affects the prefix. In Base58, the prefix 5 changes to a K or L as the length of the number increases by one byte. 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 WIF is modified, with the addition of a one-byte suffix 01 to the private key. They are not compressed; rather, WIF-compressed signifies that the keys should only be used to derive compressed public keys and their corresponding bitcoin addresses.

The code uses a predefined private key to produce the same bitcoin address every time it is run, as shown in Example If you used the uncompressed public key instead, it would produce a different bitcoin address 14K1yпїЅ.

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.

Example uses os. Caution: Depending on the OS, os. 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 anotherпїЅto upgrade or replace the wallet software, for example.

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 BIP see Appendix C.

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. The standard for encryption uses the Advanced Encryption Standard AES , a standard established by the NIST and used broadly in data encryption implementations for commercial and military applications.

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 , 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 BIP see Appendix C , 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. Encoding a P2SH 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 multisignature 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 multisignature 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 multisignature 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 6. Vanity addresses are valid bitcoin addresses that contain human-readable messages. Vanity addresses require generating and testing billions of candidate private keys, until a bitcoin address with the desired pattern is found.

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 bitcoin 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. 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 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 random number generator used here is for demonstration purposes, and it is not appropriate for generating production-quality bitcoin keys as it is not implemented with sufficient security.

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.

Used to improve security, a distinctive address makes it harder for adversaries to substitute their own address and fool your customers into paying them instead of you. Unfortunately, vanity addresses also make it possible for anyone to create an address that resembles any random address, or even another vanity address, thereby fooling your customers.

Eugenia could advertise a randomly generated address e. Or, she could generate a vanity address that starts with 1Kids, to make it more distinctive. In both cases, one of the risks of using a single fixed address rather than a separate dynamic address per donor is that a thief might be able to infiltrate your website and replace it with his own address, thereby diverting donations to himself. If you have advertised your donation address in a number of different places, your users may visually inspect the address before making a payment to ensure it is the same one they saw on your website, on your email, and on your flyer.

Using a vanity address generator, someone with the intent to steal by substituting a similar-looking address can quickly generate addresses that match the first few characters, as shown in Table So does a vanity address increase security? If Eugenia pays a pool to generate an 8-character vanity address, the attacker would be pushed into the realm of 10 characters, which is infeasible on a personal computer and expensive even with a custom vanity-mining rig or vanity pool.

What is affordable for Eugenia becomes unaffordable for the attacker, especially if the potential reward of fraud is not high enough to cover the cost of the vanity address generation. Paper wallets are bitcoin private keys printed on paper. Often the paper wallet also includes the corresponding bitcoin address for convenience, but this is not necessary because it can be derived from the private key. Paper wallets come in many shapes, sizes, and designs, but at a very basic level are just a key and an address printed on paper.

Table shows the simplest form of a paper wallet. Paper wallets can be generated easily using a tool such as the client-side JavaScript generator at bitaddress. This page contains all the code necessary to generate keys and paper wallets, even while completely disconnected from the internet. Disconnect from the internet and open the file in a browser. Any keys generated with this tool while offline can be printed on a local printer over a USB cable not wirelessly , thereby creating paper wallets whose keys exist only on the paper and have never been stored on any online system.

Figure shows a paper wallet generated from the bitaddress. The disadvantage of a simple paper wallet system is that the printed keys are vulnerable to theft. A thief who is able to gain access to the paper can either steal it or photograph the keys and take control of the bitcoin locked with those keys.

A more sophisticated paper wallet storage system uses BIP encrypted private keys. The keys printed on the paper wallet are protected by a passphrase that the owner has memorized. Without the passphrase, the encrypted keys are useless.

Yet, they still are superior to a passphrase-protected wallet because the keys have never been online and must be physically retrieved from a safe or other physically secured storage. Figure shows a paper wallet with an encrypted private key BIP created on the bitaddress.

Although you can deposit funds into a paper wallet several times, you should withdraw all funds only once, spending everything. This is because in the process of unlocking and spending funds some wallets might generate a change address if you spend less than the whole amount. Additionally, if the computer you use to sign the transaction is compromised, you risk exposing the private key. By spending the entire balance of a paper wallet only once, you reduce the risk of key compromise. If you need only a small amount, send any remaining funds to a new paper wallet in the same transaction.

Paper wallets come in many designs and sizes, with many different features. Others are designed for storage in a bank vault or safe with the private key hidden in some way, either with opaque scratch-off stickers, or folded and sealed with tamper-proof adhesive foil. Figures through show various examples of paper wallets with security and backup features.

Other designs feature additional copies of the key and address, in the form of detachable stubs similar to ticket stubs, allowing you to store multiple copies to protect against fire, flood, or other natural disasters.

Skip to main content. Mastering Bitcoin, 2nd Edition by Andreas M. Start your free trial. Chapter 4. Keys, Addresses You may have heard that bitcoin is based on cryptography , which is a branch of mathematics used extensively in computer security. Introduction Ownership of bitcoin is established through digital keys , bitcoin addresses , and digital signatures. Public Key Cryptography and Cryptocurrency Public key cryptography was invented in the s and is a mathematical foundation for computer and information security.

Tip In most wallet implementations, the private and public keys are stored together as a key pair for convenience. Private and Public Keys A bitcoin wallet contains a collection of key pairs, each consisting of a private key and a public key. Figure Private key, public key, and bitcoin address. Private Keys A private key is simply a number, picked at random.

Tip The bitcoin private key is just a number. Generating a private key from a random number The first and most important step in generating keys is to find a secure source of entropy, or randomness. Tip The dumpprivkey command does not generate a private key from a public key, as this is impossible. Elliptic Curve Cryptography Explained 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.

An elliptic curve. Example Using Python to confirm that this point is on the elliptic curve Python 3. Generating a Public Key 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. Tip 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.

Tip Most bitcoin implementations use the OpenSSL cryptographic library to do the elliptic curve math. Elliptic curve cryptography: visualizing the multiplication of a point G by an integer k on an elliptic curve.

Bitcoin Addresses A bitcoin address is a string of digits and characters that can be shared with anyone who wants to send you money. Tip A bitcoin address is not the same as a public key. Public key to bitcoin address: conversion of a public key into a bitcoin address. Base58 and Base58Check Encoding 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 Base58Check encoding: a Base58, versioned, and checksummed format for unambiguously encoding bitcoin data.

Key Formats Both private and public keys can be represented in a number of different formats. Private key formats The private key can be represented in a number of different formats, all of which correspond to the same bit number. There are also hardware wallets, where your keys are stored offline, which some deem more secure.

A private key is a secure code that enables the holder to make cryptocurrency transactions and prove ownership of their holdings. Bitcoin keys specifically feature a bit string displayed as a combination of letters and numbers. Regulations around the use and safekeeping of private keys are still in development; in Germany, for example, the safekeeping of private keys for customers is a regulated financial service. Unlike a private key, a public key is designed to be disclosed to other people so they can send you cryptocurrency.

Sometimes a Bitcoin address is used for transactions instead, since they are essentially compressed versions of the public key.

Imagine public and private keys like you would your house address and house keys, respectively. People will need your house address so they can stop by, yet will only be able to enter with your house keys. A Bitcoin address is a unique string of numbers and letters of characters in length that shows where a Bitcoin payment has been sent to and from. For security reasons, experts recommend generating a fresh Bitcoin address for each transaction. Absolutely not. You should never share your Bitcoin private key, but you can share a Bitcoin address with anyone who wants to send you Bitcoin.

Think of the Bitcoin address as a hashed form of your Bitcoin public key for easier use in transactions. As we mentioned earlier, keeping your private key safe is the most important part of making sure no one else has access to your Bitcoin.

Never share your private key with anyone. Remember that for transactions, other people only need your public key or Bitcoin address. It may be a good idea to back up your private keys in case you lose them. The types of backup available to you will depend on the crypto wallet you use. There are three main ways you can back up your private key:. If you use an online wallet to store your cryptocurrencies, it will generate the private key for you.

A private Bitcoin key is a character string of letters and numbers. What is cryptocurrency? A guide for beginners. What is the digital euro and how does it work? The pros and cons of cryptocurrency: A guide for new investors. What is DeFi?

Find out which are the pros and cons of cryptocurrency. What is a crypto wallet? A crypto wallet is a secure, digital wallet for your cryptocurrency. What is a blockchain? Blockchain technology is at the heart of cryptocurrencies like Bitcoin. Bitcoin How do private and public keys work?

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