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@ -185,7 +185,7 @@ The same method for constructing a tree from four transactions can be generalize
.A merkle tree summarizing many data elements
image::images/msbt_0704.png["merkle_tree_large"]
To prove that a specific transaction is included in a block, a node only needs to produce +log~2~(N)+ 32-byte hashes, constituting an((("authentication path")))((("merkle path"))) _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 <<merkle_tree_path>>, 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 (noted in blue in <<merkle_tree_path>>) 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~ (noted in green in the diagram) is included in the merkle root by computing four additional pair-wise hashes H~KL~, H~IJKL~, H~IJKLMNOP~, and the merkle tree root (outlined in a dotted line in the diagram).
To prove that a specific transaction is included in a block, a node only needs to produce +log~2~(N)+ 32-byte hashes, constituting an((("authentication path")))((("merkle path"))) _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 10 or 12 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 <<merkle_tree_path>>, 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 (noted in blue in <<merkle_tree_path>>) 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~ (noted in green in the diagram) is included in the merkle root by computing four additional pair-wise hashes H~KL~, H~IJKL~, H~IJKLMNOP~, and the merkle tree root (outlined in a dotted line in the diagram).
[[merkle_tree_path]]
.A merkle path used to prove inclusion of a data element