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@ -415,37 +415,36 @@ Compressed public keys were introduced to bitcoin to reduce the size of transact
As we saw in the section <<pubkey>>, a public key is a point (x,y) on an elliptic curve. Because the curve expresses a mathematical function, a point on the curve represents a solution to the equation and, therefore, if we know the _x_ coordinate we can calculate the _y_ coordinate by solving the equation y^2^ mod p = (x^3^ + 7) mod p. 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 256 bits. An almost 50% reduction in size in every transaction adds up to a lot of data saved over time!
Whereas uncompressed public keys have a prefix of +04+, compressed public keys start with either a +02+ or a +03+ prefix. Let's look at why there are two possible prefixes: because the left side of the equation is y^2^, that means the solution for y is a square root, which can have a positive or negative value. 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 <<ecc-curve>>, 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. When calculating the elliptic curve in binary arithmetic on the finite field of prime order p, the _y_ coordinate is either even or odd, which corresponds to the positive/negative sign as explained above. 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.
Whereas uncompressed public keys have a prefix of +04+, compressed public keys start with either a +02+ or a +03+ prefix. Let's look at why there are two possible prefixes: because the left side of the equation is y^2^, that means the solution for y is a square root, which can have a positive or negative value. 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 <<ecc-curve>>, 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. When calculating the elliptic curve in binary arithmetic on the finite field of prime order p, the _y_ coordinate is either even or odd, which corresponds to the positive/negative sign as explained earlier. 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 <<pubkey_compression>>.
[[pubkey_compression]]
.Public Key Compression
.Public key compression
image::images/msbt_0407.png["pubkey_compression"]
Here's the same public key generated previously, shown as a +compressed public key+ stored in 264-bits (66 hex digits) with the prefix +03+ indicating the +y+ coordinate is odd:
Here's the same public key generated previously, shown as a compressed public key stored in 264 bits (66 hex digits) with the prefix +03+ indicating the _y_ coordinate is odd:
.Compressed Public Key K shown in hex (66 hex digits) as +K = {02 or 03} x+
----
K = 03F028892BAD...DC341A
----
The compressed public key, above, 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. More importantly, if we convert this compressed public key to a bitcoin address using the double-hash function (RIPEMD160(SHA256(K))) it will produce a _different_ bitcoin address. 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) which produce two different bitcoin addresses. However, the private key is identical for both bitcoin addresses.
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. More importantly, if we convert this compressed public key to a bitcoin address using the double-hash function (+RIPEMD160(SHA256(K))+) it will produce a _different_ bitcoin address. 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 which 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!
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. Let's look at how this works in more detail, in the next section.
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. Let's look at how this works in more detail, in the next section.
[[comp_priv]]
===== Compressed Private Keys
===== Compressed private keys
Ironically, the name "compressed private key" is misleading, because when a private key is exported as WIF-compressed it is actually one byte _longer_ than an "uncompressed" private key. 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. The term "compressed private key" really means "private key from which compressed public keys should be derived", whereas "uncompressed private key" really means "private key from which uncompressed public keys should be derived". You should only refer to the export format as "WIF-compressed" or "WIF" and not refer to the private key as "compressed" to avoid further confusion.
Ironically, the name "compressed private key" is misleading, because when a private key is exported as WIF-compressed it is actually one byte _longer_ than an "uncompressed" private key. 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. The term "compressed private key" really means "private key from which compressed public keys should be derived," whereas "uncompressed private key" really means "private key from which uncompressed public keys should be derived." You should only refer to the export format as "WIF-compressed" or "WIF" and not refer to the private key as "compressed" to avoid further confusion.
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 (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.
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, then 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. The resulting base58check encoded private key is called a "Compressed WIF" and starts with the letter K or L, instead of starting with "5" as is the case with WIF encoded (non-compressed) keys from older wallets.
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. The resulting Base58Check-encoded private key is called a "Compressed WIF" and starts with the letter K or L, instead of starting with "5" as is the case with WIF-encoded (non-compressed) keys from older wallets.
Here's the same key, encoded in WIF and WIF-compressed formats
Table 4-4 shows the same key, encoded in WIF and WIF-compressed formats.
.Example: Same Key, Different Formats
.Example: Same key, different formats
[options="header"]
|=======
|Format | Private Key
@ -458,15 +457,15 @@ Here's the same key, encoded in WIF and WIF-compressed formats
[TIP]
====
"Compressed private keys" is a misnomer! 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. Ironically, a "WIF-compressed" encoded private key is one byte longer because it has the added 01 suffix to distinguish it from an "uncompressed" one.
"Compressed private keys" is a misnomer! 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. Ironically, a "WIF-compressed" encoded private key is one byte longer because it has the added 01 suffix to distinguish it from an "uncompressed" one.
====
=== Implementing Keys and Addresses in Python
The most comprehensive bitcoin library in Python is "pybitcointools"by Vitalik Buterin (https://github.com/vbuterin/pybitcointools). In the following code example, we use the pybitcointools library (imported as "bitcoin") to generate and display keys and addresses in various formats:
The most comprehensive bitcoin library in Python is https://github.com/vbuterin/pybitcointools[pybitcointools] by Vitalik Buterin. In <<key-to-address_script>>, we use the pybitcointools library (imported as "bitcoin") to generate and display keys and addresses in various formats.
[[key-to-address_script]]
.Key and Address generation and formatting with the pybitcointools library
.Key and address generation and formatting with the pybitcointools library
====
[source,python]
----