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  • To verify that a transaction: How do we know the exact location of Hk on the Merkle Tree? @Geremia Commented Dec 5, 2017 at 14:19
  • @Avatar To construct Merkle paths from scratch requires knowing all the transactions. Also, forge a fake Merkle path that corresponds to a given Merkle root would be even more difficult than to crack SHA256. Commented Dec 5, 2017 at 15:53
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    @Avator Verification of a Merkle path proceed from the leaf node to the Merkle root. Commented Dec 5, 2017 at 17:41
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    @Avatar Sorry, I meant to say that one simply needs to search for the transaction in the "list of transactions." Commented Dec 5, 2017 at 18:56
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    The 2nd diagram is the only thing you need to understand everything. The "green" hash H_K is the /claim/ given to the PAYEE (who also has the Merkle root). The VERIFIER (full node) sends the "blue" hashes as /proof/, because they can be used to calculate all of the "blue dashed" hashes all the way up to the Merkle root. If the calculated Merkle root matches the known Merkle root, H_K is in the block. Obviously, the "blue" hashes are a small subset of ALL the hashes, i.e. 2*log_2(N) is less than the whole set N for N > 4. Graph it for yourself at desmos.com, with y=2log(N)/log(2) vs y=N. Commented Nov 6, 2019 at 1:17