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Address 1MzHMuxXTuR2R1t78mGSdzaAtNbBWX has transacted times on the Bitcoin blockchain. It has received a total of BTC.
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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.

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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.

BTC Address 3P3QsMVK89JBNqZQv5zMAKG8FK3kJM4rjt | BlockCypher

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.

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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.

bitcoinaddress 0.1.5

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.

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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.


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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.