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"The intuition between this definition is that if the transcript of the interaction cannot be distinguished from something that could have been produced without even knowing the secret value, then it cannot convey anything useful about this value to the verifier". The prover estabilishes a TLS tunnel with the verifier, and sends the secret through it. Nobody can learn anything from the transcript, and yet this will clearly let the verifier learn the secret. Am I missing something?
Let's say for a moment that the constant part was not anything "random-looking", but "Here is your license key: ". Would that be any weakness? What's the difference between the former and the latter? Also, is the similarity to a ssh key the fact it uses base64?
@SwapnilPandey say you want me to prove that I included C in the tree. With your approach, I need to give you A, B, and D. With a Merkle tree, only H(H(A)+H(B)), and H(D) are needed. The difference is small in this example, because there is a small number of leaf nodes, but for a tree with $n$ levels (here $n = 3$), you only need to provide $n-1$ pieces of data (all being short hashes), instead of all of the $2^{n-1}-1$ leaves in the tree, all being potentially very long.
