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Reapplying the merge from Issue #29 which has been (accidentally?) overwritten recently

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Minh T. Nguyen 2014-05-26 23:52:28 -07:00
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@ -18,7 +18,7 @@ In this chapter we will introduce wallets, which contain cryptographic keys. We
((("public key"))) ((("public key")))
Public key cryptography was invented in the 1970s and is mathematics applied to computer 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. Public key cryptography was invented in the 1970s and is mathematics applied to computer 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 special relationship between the public key and private key that allows the private key to be used to generate a signature. This signature can be validated against the public key without revealing the private key. When spending bitcoins, the current bitcoin owner presents their public key and a signature (different each time, but created from the same private key, see <<signature>>) 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 that transaction as valid, meaning the person transferring the bitcoin owned them at the time of the transfer. 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 special relationship between the public and the private key that allows the private key to be used to generate a signature. This signature can be validated against the public key without revealing the private key. When spending bitcoins, the current bitcoin owner presents their public key and a signature (different each time, but created from the same private key, see <<signature>>) 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 that transaction as valid, meaning the person transferring the bitcoins owned them at the time of the transfer.
[TIP] [TIP]
==== ====
@ -27,7 +27,7 @@ In most implementations, the private and public keys are stored together as a _k
=== Keys === Keys
Your 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 below: 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 below:
[[k_to_K_to_A]] [[k_to_K_to_A]]
.Private Key, Public Key and Bitcoin Address .Private Key, Public Key and Bitcoin Address
@ -343,7 +343,7 @@ K = 02325D52E3B7...E5D378
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. 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.
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, both 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 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!
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 compressed, or the uncompressed public keys. 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 compressed, or the uncompressed public keys. Let's look at how this works in more detail, in the next section.