Made changes to ch07.asciidoc

ch07.asciidoc

@@ -185,7 +185,9 @@ 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 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). 
+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-size 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
@@ -239,10 +241,10 @@ The efficiency of merkle trees becomes obvious as the scale increases. <<block_s
 | 65,535 transactions | 16 megabytes | 16 hashes | 512 bytes
 |=======
 
-As you can see from the table, while the block size increases rapidly, from 4 KB 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 that do not maintain a full blockchain, called Simplified Payment Verification or SPV nodes, use merkle paths to verify transactions without downloading full blocks.(((range="endofrange", startref="ix_ch07-asciidoc2")))(((range="endofrange", startref="ix_ch07-asciidoc1")))
+As you can see from the table, while the block size increases rapidly, from 4 KB 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 might be several gigabytes in size. Nodes that do not maintain a full block chain, called simplified payment verification (SPV nodes), use merkle paths to verify transactions without downloading full blocks.(((range="endofrange", startref="ix_ch07-asciidoc2")))(((range="endofrange", startref="ix_ch07-asciidoc1")))
 
 === Merkle Trees and Simplified Payment Verification (SPV)
 
-((("merkle trees","SPV and")))((("Simplified Payment Verification (SPV) nodes","merkle trees and")))Merkle trees are used extensively by Simplified Payment Verification nodes. SPV nodes don't have all transactions and do not download full blocks, just block headers. In order to verify that a transaction is included in a block, without having to download all the transactions in the block, they use an _authentication path_, or merkle path. 
+((("merkle trees","SPV and")))((("Simplified Payment Verification (SPV) nodes","merkle trees and")))Merkle trees are used extensively by SPV nodes. SPV nodes don't have all transactions and do not download full blocks, just block headers. In order to verify that a transaction is included in a block, without having to download all the transactions in the block, they use an authentication path, or merkle path. 
 
-Consider, for example, an SPV node that is interested in incoming payments to an address contained in its wallet. The SPV node will establish a bloom filter on its connections to peers to limit the transactions received to only those containing addresses of interest. When a peer sees a transaction that matches the bloom filter, it will send that block using a((("merkleblock message"))) +merkleblock+ message. The +merkleblock+ message contains the block header as well as a merkle path that links the transaction of interest to the merkle root in the block. The SPV node can use this merkle path to connect the transaction to the block and verify that the transaction is included in the block. The SPV node also uses the block header to link the block to the rest of the blockchain. The combination of these two links, between the transaction and block, and between the block and blockchain, proves that the transaction is recorded in the blockchain. All in all, the SPV node will have received less than a kilobyte of data for the block header and merkle path, an amount of data that is more than a thousand times less than a full block (about 1 megabyte currently).(((range="endofrange", startref="ix_ch07-asciidoc0")))
+Consider, for example, an SPV node that is interested in incoming payments to an address contained in its wallet. The SPV node will establish a bloom filter on its connections to peers to limit the transactions received to only those containing addresses of interest. When a peer sees a transaction that matches the bloom filter, it will send that block using a((("merkleblock message"))) +merkleblock+ message. The +merkleblock+ message contains the block header as well as a merkle path that links the transaction of interest to the merkle root in the block. The SPV node can use this merkle path to connect the transaction to the block and verify that the transaction is included in the block. The SPV node also uses the block header to link the block to the rest of the block chain. The combination of these two links, between the transaction and block, and between the block and block chain, proves that the transaction is recorded in the block chain. All in all, the SPV node will have received less than a kilobyte of data for the block header and merkle path, an amount of data that is more than a thousand times less than a full block (about 1 megabyte currently).(((range="endofrange", startref="ix_ch07-asciidoc0")))