Interesting bitcoin addresses
Private key, public key, and bitcoin address Private Keys 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. Tip 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. 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. 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. It is approximately in decimal.
The visible universe is estimated to contain 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.
It is not otherwise possible for bitcoind to know the private key from the public key, unless they are both stored in the wallet. Tip 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.
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.
Figure is an example of an elliptic curve, similar to that used by bitcoin. An elliptic curve 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. 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. Geometrically, this third point P3 is calculated by drawing a line between P1 and P2. 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. 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.
The generator point is specified as part of the secpk1 standard and is always the same for all keys in bitcoin: where k is the private key, G is the generator point, and K is the resulting public key, a point on the curve. 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.
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. 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. 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.
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.
Tip 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. 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 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. How to Get a Bitcoin Address To get a Bitcoin address, you first need to download a Bitcoin wallet, which is software that allows you to securely send, receive, and store Bitcoin funds in the Bitcoin network. Bitcoin wallets also store your private key, which is essentially your Bitcoin password. The software will generate a brand new Bitcoin address for you every time you create an invoice or receive a payment request for Bitcoins too.
There are four types of Bitcoin wallets that you can use: mobile, web, desktop, and hardware. To combat this security issue, consider only letting fingerprint authentication open your mobile wallet app.
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