The following article explains the process of "Merkle Audit Proofs of Certification". (Link to the article)
- Is the process the same as "Merkle Proofs in Bitcoin" ?
- If their process is not the same, what are differences?
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We have a unique merkle root for each block in Bitcoin. Next block's merkle root does not use the merkle root of the previous blocks as a proof. As a result we do not have old merkle tree hash and new merkle tree hash. Also, the way of pairwise hashing is different. If you look at Figure 2 in your link, the certificates d4 and d5 are at a higher level than d1-3. In Bitcoin, all the certificates would have been at the same level, resulting in hashing between i & j and k & k (yes, in case of odd number, we hash the same result with it self).
However, if you look in figure 5 of the link you attached, the way of providing proof that a certificate exists is the same way a proof is provide to a SPV node in Bitcoin.