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There's also live online events, interactive content, certification prep materials, and more. Ownership of bitcoin is established through digital keys , bitcoin addresses , and digital signatures. The digital keys are not actually stored in the network, but are instead created and stored by users in a file, or simple database, called a wallet. Keys enable many of the interesting properties of bitcoin, including de-centralized trust and control, ownership attestation, and the cryptographic-proof security model.
Every bitcoin transaction requires a valid signature to be included in the blockchain, which can only be generated with valid digital keys; therefore, anyone with a copy of those keys has control of the bitcoin in that account. Keys come in pairs consisting of a private secret key and a public key. Think of the public key as similar to a bank account number and the private key as similar to the secret PIN, or signature on a check that provides control over the account.
These digital keys are very rarely seen by the users of bitcoin. For the most part, they are stored inside the wallet file and managed by the bitcoin wallet software. In most cases, a bitcoin address is generated from and corresponds to a public key. However, not all bitcoin addresses represent public keys; they can also represent other beneficiaries such as scripts, as we will see later in this chapter. The bitcoin address is the only representation of the keys that users will routinely see, because this is the part they need to share with the world.
In this chapter we will introduce wallets, which contain cryptographic keys. We will look at how keys are generated, stored, and managed.
We will review the various encoding formats used to represent private and public keys, addresses, and script addresses.
Finally, we will look at special uses of keys: to sign messages, to prove ownership, and to create vanity addresses and paper wallets. Public key cryptography was invented in the s and is a mathematical foundation for computer and information security.
Since the invention of public key cryptography, several suitable mathematical functions, such as prime number exponentiation and elliptic curve multiplication, have been discovered.
These mathematical functions are practically irreversible, meaning that they are easy to calculate in one direction and infeasible to calculate in the opposite direction. Based on these mathematical functions, cryptography enables the creation of digital secrets and unforgeable digital signatures. Bitcoin uses elliptic curve multiplication as the basis for its public key cryptography.
In bitcoin, we use public key cryptography to create a key pair that controls access to bitcoins. The key pair consists of a private key and—derived from it—a unique public key.
The public key is used to receive bitcoins, and the private key is used to sign transactions to spend those bitcoins. There is a mathematical relationship between the public and the private key that allows the private key to be used to generate signatures on messages. This signature can be validated against the public key without revealing the private key. When spending bitcoins, the current bitcoin owner presents her public key and a signature different each time, but created from the same private key in a transaction to spend those bitcoins.
Through the presentation of the public key and signature, everyone in the bitcoin network can verify and accept the transaction as valid, confirming that the person transferring the bitcoins owned them at the time of the transfer. In most wallet implementations, the private and public keys are stored together as a key pair for convenience.
However, the public key can be calculated from the private key, so storing only the private key is also possible. A bitcoin wallet contains a collection of key pairs, each consisting of a private key and a public key. The private key k is a number, usually picked at random. From the private key, we use elliptic curve multiplication, a one-way cryptographic function, to generate a public key K.
From the public key K , we use a one-way cryptographic hash function to generate a bitcoin address A. In this section, we will start with generating the private key, look at the elliptic curve math that is used to turn that into a public key, and finally, generate a bitcoin address from the public key.
The relationship between private key, public key, and bitcoin address is shown in Figure A private key is simply a number, picked at random.
Ownership and control over the private key is the root of user control over all funds associated with the corresponding bitcoin address. The private key is used to create signatures that are required to spend bitcoins by proving ownership of funds used in a transaction. The private key must remain secret at all times, because revealing it to third parties is equivalent to giving them control over the bitcoins secured by that key. The bitcoin private key is just a number. You can pick your private keys randomly using just a coin, pencil, and paper: toss a coin times and you have the binary digits of a random private key you can use in a bitcoin wallet.
The public key can then be generated from the private key. The first and most important step in generating keys is to find a secure source of entropy, or randomness. Usually, the OS random number generator is initialized by a human source of randomness, which is why you may be asked to wiggle your mouse around for a few seconds. For the truly paranoid, nothing beats dice, pencil, and paper.
To create such a key, we randomly pick a bit number and check that it is less than n - 1. In programming terms, this is usually achieved by feeding a larger string of random bits, collected from a cryptographically secure source of randomness, into the SHA hash algorithm that will conveniently produce a bit number.
If the result is less than n - 1 , we have a suitable private key. Otherwise, we simply try again with another random number. Study the documentation of the random number generator library you choose to make sure it is cryptographically secure. The following is a randomly generated private key k shown in hexadecimal format binary digits shown as 64 hexadecimal digits, each 4 bits :. It is approximately 10 77 in decimal. The visible universe is estimated to contain 10 80 atoms.
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.
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Clear linking rules are abided to meet reference reputability standards. Only authoritative sources like academic associations or journals are used for research references while creating the content. If there's a disagreement of interest behind a referenced study, the reader must always be informed. Finding a viable cryptocurrency wallet for yourself these days can be a bit of a hassle.
WalletConnect is the web3 standard to connect blockchain wallets to dapps. WalletConnect is not an app, but an open protocol to communicate securely between Wallets and Dapps Web3 Apps. These payloads are symmetrically encrypted through a shared key between the two peers. The connection is initiated by one peer displaying a QR Code or deep link with a standard WalletConnect URI and is established when the counter-party approves this connection request.
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All encryption is handled client-side. Neither your passphrase nor any of your private information ever leaves your browser, workstation, or mobile device. FreeWallet passphrases are highly secure, and protect your wallet from any brute force attacks.