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88 lines
4.0 KiB
88 lines
4.0 KiB
Merkle
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======
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For an overview of Merkle trees, see
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`wikipedia <https://en.wikipedia.org/wiki/Merkle_tree>`__.
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There are two types of Merkle trees used in Tendermint.
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- ```IAVL+ Tree`` <#iavl-tree>`__: An immutable self-balancing binary
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tree for persistent application state
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- ```Simple Tree`` <#simple-tree>`__: A simple compact binary tree for
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a static list of items
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IAVL+ Tree
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----------
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The purpose of this data structure is to provide persistent storage for
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key-value pairs (e.g. account state, name-registrar data, and
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per-contract data) such that a deterministic merkle root hash can be
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computed. The tree is balanced using a variant of the `AVL
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algorithm <http://en.wikipedia.org/wiki/AVL_tree>`__ so all operations
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are O(log(n)).
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Nodes of this tree are immutable and indexed by its hash. Thus any node
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serves as an immutable snapshot which lets us stage uncommitted
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transactions from the mempool cheaply, and we can instantly roll back to
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the last committed state to process transactions of a newly committed
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block (which may not be the same set of transactions as those from the
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mempool).
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In an AVL tree, the heights of the two child subtrees of any node differ
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by at most one. Whenever this condition is violated upon an update, the
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tree is rebalanced by creating O(log(n)) new nodes that point to
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unmodified nodes of the old tree. In the original AVL algorithm, inner
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nodes can also hold key-value pairs. The AVL+ algorithm (note the plus)
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modifies the AVL algorithm to keep all values on leaf nodes, while only
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using branch-nodes to store keys. This simplifies the algorithm while
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minimizing the size of merkle proofs
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In Ethereum, the analog is the `Patricia
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trie <http://en.wikipedia.org/wiki/Radix_tree>`__. There are tradeoffs.
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Keys do not need to be hashed prior to insertion in IAVL+ trees, so this
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provides faster iteration in the key space which may benefit some
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applications. The logic is simpler to implement, requiring only two
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types of nodes -- inner nodes and leaf nodes. The IAVL+ tree is a binary
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tree, so merkle proofs are much shorter than the base 16 Patricia trie.
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On the other hand, while IAVL+ trees provide a deterministic merkle root
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hash, it depends on the order of updates. In practice this shouldn't be
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a problem, since you can efficiently encode the tree structure when
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serializing the tree contents.
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Simple Tree
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-----------
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For merkelizing smaller static lists, use the Simple Tree. The
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transactions and validation signatures of a block are hashed using this
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simple merkle tree logic.
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If the number of items is not a power of two, the tree will not be full
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and some leaf nodes will be at different levels. Simple Tree tries to
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keep both sides of the tree the same size, but the left side may be one
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greater.
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::
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Simple Tree with 6 items Simple Tree with 7 items
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* *
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/ \ / \
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/ \ / \
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/ \ / \
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/ \ / \
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* * * *
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/ \ / \ / \ / \
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/ \ / \ / \ / \
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/ \ / \ / \ / \
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* h2 * h5 * * * h6
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/ \ / \ / \ / \ / \
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h0 h1 h3 h4 h0 h1 h2 h3 h4 h5
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Simple Tree with Dictionaries
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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The Simple Tree is used to merkelize a list of items, so to merkelize a
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(short) dictionary of key-value pairs, encode the dictionary as an
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ordered list of ``KVPair`` structs. The block hash is such a hash
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derived from all the fields of the block ``Header``. The state hash is
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similarly derived.
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