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more outline from re-org
This commit is contained in:
Andreas M. Antonopoulos
parent
1722dd4088
commit
0bccc87dba
@ -10,6 +10,14 @@
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=== Network Discovery
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=== Network Protocol Messages
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=== Node Types
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=== Full Node
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=== Simple Payment Verification Node
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=== Bloom Filters
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=== Independently Verifying Transactions
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In the previous chapter we saw how wallet software creates transactions by collecting UTXO, providing the appropriate unlocking scripts and then constructing new outputs assigned to a new owner. The resulting transaction is then sent to the neighboring nodes in the bitcoin network so that it may be propagated across the entire bitcoin network.
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@ -53,3 +61,64 @@ When a transaction is added to the transaction pool, the orphan pool is checked
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Some implementations of the bitcoin client also maintain a UTXO pool which is the set of all unspent outputs on the blockchain. This may be housed in local memory or as an indexed database table on persistent storage. Unlike the transaction and orphan pools, the UTXO pool is not initialized empty but instead contains millions of entries of unspent transaction outputs including some dating back to 2009. Whereas the transaction and orphan pools represent a nodes local perspective and may vary significantly from node to node depending upon when the node was started or restarted, the UTXO pool represents the emergent consensus of the network and therefore will vary little between nodes. Furthermore the transaction and orphan pools only contain unconfirmed transactions, while the UTXO pool only contains confirmed outputs.
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[[merkle_trees]]
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=== Merkle Trees
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As part of populating the block header, a mining node will create a summary of all the transactions added to the block. This summary is created by computing the _root_ of the Merkle Tree, which is a binary hash tree data structure. The merkle root is a 32-byte hash that provides a shortcut to identify individual transactions contained within that block.
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A _Merkle Tree_, also known as a _Binary Hash Tree_ is a data structure created by Ralph Merkle used for efficiently summarizing and verifying the integrity of large sets of data. Merkle Trees are binary trees containing cryptographic hashes. When N data elements are hashed and summarized in a Merkle Tree, you can check to see if any one data element is included in the tree with at most +2*log~2~(N)+ calculations, making this a very efficient data structure. The term "tree" is used in computer science to describe a branching data structure, but these trees are usually displayed upside down with the "root" at the top and the "leaves" at the bottom of a diagram, as you will see in the examples that follow.
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Merkle trees are used in bitcoin to summarize all the transactions in a block, producing an overall digital fingerprint of the entire set of transactions, which can be used to prove that a transaction is included in the set. A merkle tree is constructed by recursively hashing pairs of nodes until there is only one hash, called the _root_, or _merkle root_. The cryptographic hash algorithm used in bitcoin's merkle trees is SHA256 applied twice, also known as double-SHA256.
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The merkle tree is constructed bottom-up. In the example below, we start with four transactions A, B, C and D, which form the _leaves_ of the Merkle Tree, shown in the diagram at the bottom. The transactions are not stored in the merkle tree, rather their data is hashed and the resulting hash is stored in each leaf node as H~A~, H~B~, H~C~ and H~D~:
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+H~A~ = SHA256(SHA256(Transaction A))+
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Consecutive pairs of leaf nodes are then summarized in a parent node, by concatenating the two hashes and hashing them together. For example, to construct the parent node H~AB~, the two 32-byte hashes of the children are concatenated to create a 64-byte string. That string is then double-hashed to produce the parent node's hash:
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+H~AB~ = SHA256(SHA256(H~A~ + H~B~))+
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The process continues until there is only one node at the top, the node known as the Merkle Root. That 32-byte hash is stored in the block header and summarizes all the data in all four transactions.
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[[simple_merkle]]
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.Calculating the nodes in a Merkle Tree
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image::images/MerkleTree.png["merkle_tree"]
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Since the merkle tree is a binary tree, it needs an even number of leaf nodes. If there is an odd number of transactions to summarize, the last transaction hash is duplicated to create an even number of leaf nodes, also known as a _balanced tree_. This is shown in the example below, where transaction C is duplicated:
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[[merkle_tree_odd]]
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.An even number of data elements, by duplicating one data element
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image::images/MerkleTreeOdd.png["merkle_tree_odd"]
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The same method for constructing a tree from four transactions can be generalized to construct trees of any size. In bitcoin it is common to have several hundred to more than a thousand transactions in a single block, which are summarized in exactly the same way producing just 32-bytes of data from a single merkle root. In the diagram below, you will see a tree built from 16 transactions:
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[[merkle_tree_large]]
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.A Merkle Tree summarizing many data elements
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image::images/MerkleTreeLarge.png["merkle_tree_large"]
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To prove that a specific transaction is included in a block, a node need only produce +log~2~(N)+ 32-byte hashes, constituting an _authentication path_ or _merkle path_ connecting the specific transaction to the root of the tree. This is especially important as the number of transactions increases, because the base-2 logarithm of the number of transactions increases much more slowly. This allows bitcoin nodes to efficiently produce paths of ten or twelve hashes (320-384 bytes) which can provide proof of a single transaction out of more than a thousand transactions in a megabyte sized block. In the example below, a node can prove that a transaction K is included in the block by producing a merkle path that is only four 32-byte hashes long (128 bytes total). The path consists of the four hashes H~L~, H~IJ~, H~MNOP~ and H~ABCDEFGH~. With those four hashes provided as an authentication path, any node can prove that H~K~ is included in the merkle root by computing four additional pair-wise hashes H~KL~, H~IJKL~ and H~IJKLMNOP~ that lead to the merkle root.
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[[merkle_tree_path]]
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.A Merkle Path used to prove inclusion of a data element
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image::images/MerkleTreePathToK.png["merkle_tree_path"]
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The efficiency of merkle trees becomes obvious as the scale increases. For example, proving that a transaction is part of a block requires:
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[[block_structure]]
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.Merkle Tree Efficiency
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[options="header"]
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|=======
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|Number of Transactions| Approx. Size of Block | Path Size (Hashes) | Path Size (Bytes)
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| 16 transactions | 4 kilobytes | 4 hashes | 128 bytes
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| 512 transactions | 128 kilobytes | 9 hashes | 288 bytes
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| 2048 transactions | 512 kilobytes | 11 hashes | 352 bytes
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| 65,535 transactions | 16 megabytes | 16 hashes | 512 bytes
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|=======
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As you can see from the table above, while the block size increases rapidly, from 4KB with 16 transactions to a block size of 16 MB to fit 65,535 transactions, the merkle path required to prove the inclusion of a transaction increases much more slowly, from 128 bytes to only 512 bytes. With merkle trees, a node can download just the block headers (80 bytes per block) and still be able to identify a transaction's inclusion in a block by retrieving a small merkle path from a full node, without storing or transmitting the vast majority of the blockchain which may be several gigabytes in size. Nodes which do not maintain a full blockchain, called Simple Payment Verification or SPV nodes use merkle paths to verify transactions without downloading full blocks.
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=== Block Propagation and Verification
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=== Alert Messages
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122
ch07.asciidoc
122
ch07.asciidoc
@ -1,6 +1,8 @@
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[[ch7]]
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== Chapter 7 - The Blockchain
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*DRAFT - DO NOT SUBMIT ISSUES OR PULL REQUESTS YET PLEASE - CONSTANT CHANGES HAPPENING*
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[[blockchain]]
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=== The Blockchain
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@ -12,39 +14,6 @@ Each block within the blockchain is identified by a hash, generated using the SH
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The hash of the parent is also part of the data (the block header) that creates the hash of the child, making the ancestry of each block an immutable part of its identity. The chain of hashes guarantees that a block cannot be modified retrospectively without forcing the re-computation of all following blocks (children), because a retrospective change in any block would change its hash, thereby changing the reference in any children whose hash also changes, and so on. As new blocks are added to the chain, they strengthen the immutability of the ledger by effectively incorporating all previous blocks by reference in their cryptographic hash.
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=== The Genesis Block
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The first block in the blockchain is called the _genesis block_ and was created in 2009. It is the "common ancestor" of all the blocks in the blockchain, meaning that if you start at any block and follow the chain backwards in time you will eventually arrive at the _genesis block_.
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The genesis block has the identifier hash +000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f+. You can search for that block hash in any block explorer website, such as blockchain.info, and you will find a page describing the contents of this block, with a URL containing that hash:
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https://blockchain.info/block/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
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https://blockexplorer.com/block/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
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Using the Bitcoin Core reference client on the command-line:
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----
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$ bitcoind getblock 000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
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{
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"hash" : "000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f",
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"confirmations" : 308321,
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"size" : 285,
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"height" : 0,
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"version" : 1,
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"merkleroot" : "4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b",
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"tx" : [
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"4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b"
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],
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"time" : 1231006505,
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"nonce" : 2083236893,
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"bits" : "1d00ffff",
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"difficulty" : 1.00000000,
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"nextblockhash" : "00000000839a8e6886ab5951d76f411475428afc90947ee320161bbf18eb6048"
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}
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----
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=== Structure of a Block
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A block is a container data structure that aggregates transactions for inclusion in the public ledger, the blockchain. The block is made of a header, containing metadata, followed by a long list of transactions that make up the bulk of it's size.
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@ -101,6 +70,38 @@ Unlike the block hash, the block height is not a unique identifier. While a sing
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A block's _block hash_ always identifies a single block uniquely. A block also always has a specific _block height_. However, it is not always the case that a specific block height can identify a single block, rather more than one blocks can compete for a single position in the blockchain.
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====
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=== The Genesis Block
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The first block in the blockchain is called the _genesis block_ and was created in 2009. It is the "common ancestor" of all the blocks in the blockchain, meaning that if you start at any block and follow the chain backwards in time you will eventually arrive at the _genesis block_.
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The genesis block has the identifier hash +000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f+. You can search for that block hash in any block explorer website, such as blockchain.info, and you will find a page describing the contents of this block, with a URL containing that hash:
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https://blockchain.info/block/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
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https://blockexplorer.com/block/000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
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Using the Bitcoin Core reference client on the command-line:
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----
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$ bitcoind getblock 000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f
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{
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"hash" : "000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f",
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"confirmations" : 308321,
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"size" : 285,
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"height" : 0,
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"version" : 1,
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"merkleroot" : "4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b",
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"tx" : [
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"4a5e1e4baab89f3a32518a88c31bc87f618f76673e2cc77ab2127b7afdeda33b"
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],
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"time" : 1231006505,
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"nonce" : 2083236893,
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"bits" : "1d00ffff",
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"difficulty" : 1.00000000,
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"nextblockhash" : "00000000839a8e6886ab5951d76f411475428afc90947ee320161bbf18eb6048"
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}
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----
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=== Linking Blocks in the Blockchain
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@ -139,61 +140,6 @@ The moment Jing's node received this block (height 277315), this event signified
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.Blocks linked in a chain, by reference to the previous block header hash
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image::images/ChainOfBlocks.png["chain_of_blocks"]
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[[merkle_trees]]
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=== Merkle Trees
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As part of populating the block header, a mining node will create a summary of all the transactions added to the block. This summary is created by computing the _root_ of the Merkle Tree, which is a binary hash tree data structure. The merkle root is a 32-byte hash that provides a shortcut to identify individual transactions contained within that block.
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A _Merkle Tree_, also known as a _Binary Hash Tree_ is a data structure created by Ralph Merkle used for efficiently summarizing and verifying the integrity of large sets of data. Merkle Trees are binary trees containing cryptographic hashes. When N data elements are hashed and summarized in a Merkle Tree, you can check to see if any one data element is included in the tree with at most +2*log~2~(N)+ calculations, making this a very efficient data structure. The term "tree" is used in computer science to describe a branching data structure, but these trees are usually displayed upside down with the "root" at the top and the "leaves" at the bottom of a diagram, as you will see in the examples that follow.
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Merkle trees are used in bitcoin to summarize all the transactions in a block, producing an overall digital fingerprint of the entire set of transactions, which can be used to prove that a transaction is included in the set. A merkle tree is constructed by recursively hashing pairs of nodes until there is only one hash, called the _root_, or _merkle root_. The cryptographic hash algorithm used in bitcoin's merkle trees is SHA256 applied twice, also known as double-SHA256.
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The merkle tree is constructed bottom-up. In the example below, we start with four transactions A, B, C and D, which form the _leaves_ of the Merkle Tree, shown in the diagram at the bottom. The transactions are not stored in the merkle tree, rather their data is hashed and the resulting hash is stored in each leaf node as H~A~, H~B~, H~C~ and H~D~:
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+H~A~ = SHA256(SHA256(Transaction A))+
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Consecutive pairs of leaf nodes are then summarized in a parent node, by concatenating the two hashes and hashing them together. For example, to construct the parent node H~AB~, the two 32-byte hashes of the children are concatenated to create a 64-byte string. That string is then double-hashed to produce the parent node's hash:
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+H~AB~ = SHA256(SHA256(H~A~ + H~B~))+
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The process continues until there is only one node at the top, the node known as the Merkle Root. That 32-byte hash is stored in the block header and summarizes all the data in all four transactions.
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[[simple_merkle]]
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.Calculating the nodes in a Merkle Tree
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image::images/MerkleTree.png["merkle_tree"]
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Since the merkle tree is a binary tree, it needs an even number of leaf nodes. If there is an odd number of transactions to summarize, the last transaction hash is duplicated to create an even number of leaf nodes, also known as a _balanced tree_. This is shown in the example below, where transaction C is duplicated:
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[[merkle_tree_odd]]
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.An even number of data elements, by duplicating one data element
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image::images/MerkleTreeOdd.png["merkle_tree_odd"]
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The same method for constructing a tree from four transactions can be generalized to construct trees of any size. In bitcoin it is common to have several hundred to more than a thousand transactions in a single block, which are summarized in exactly the same way producing just 32-bytes of data from a single merkle root. In the diagram below, you will see a tree built from 16 transactions:
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[[merkle_tree_large]]
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.A Merkle Tree summarizing many data elements
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image::images/MerkleTreeLarge.png["merkle_tree_large"]
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To prove that a specific transaction is included in a block, a node need only produce +log~2~(N)+ 32-byte hashes, constituting an _authentication path_ or _merkle path_ connecting the specific transaction to the root of the tree. This is especially important as the number of transactions increases, because the base-2 logarithm of the number of transactions increases much more slowly. This allows bitcoin nodes to efficiently produce paths of ten or twelve hashes (320-384 bytes) which can provide proof of a single transaction out of more than a thousand transactions in a megabyte sized block. In the example below, a node can prove that a transaction K is included in the block by producing a merkle path that is only four 32-byte hashes long (128 bytes total). The path consists of the four hashes H~L~, H~IJ~, H~MNOP~ and H~ABCDEFGH~. With those four hashes provided as an authentication path, any node can prove that H~K~ is included in the merkle root by computing four additional pair-wise hashes H~KL~, H~IJKL~ and H~IJKLMNOP~ that lead to the merkle root.
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[[merkle_tree_path]]
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.A Merkle Path used to prove inclusion of a data element
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image::images/MerkleTreePathToK.png["merkle_tree_path"]
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The efficiency of merkle trees becomes obvious as the scale increases. For example, proving that a transaction is part of a block requires:
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[[block_structure]]
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.Merkle Tree Efficiency
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[options="header"]
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|=======
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|Number of Transactions| Approx. Size of Block | Path Size (Hashes) | Path Size (Bytes)
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| 16 transactions | 4 kilobytes | 4 hashes | 128 bytes
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| 512 transactions | 128 kilobytes | 9 hashes | 288 bytes
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| 2048 transactions | 512 kilobytes | 11 hashes | 352 bytes
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| 65,535 transactions | 16 megabytes | 16 hashes | 512 bytes
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|=======
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As you can see from the table above, while the block size increases rapidly, from 4KB with 16 transactions to a block size of 16 MB to fit 65,535 transactions, the merkle path required to prove the inclusion of a transaction increases much more slowly, from 128 bytes to only 512 bytes. With merkle trees, a node can download just the block headers (80 bytes per block) and still be able to identify a transaction's inclusion in a block by retrieving a small merkle path from a full node, without storing or transmitting the vast majority of the blockchain which may be several gigabytes in size. Nodes which do not maintain a full blockchain, called Simple Payment Verification or SPV nodes use merkle paths to verify transactions without downloading full blocks.
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==== Highest Difficulty Chain Selection
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Loading…
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