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As you may already know, proofs of retrievability (PoR) can be constructed using MACs, Signatures (as stated here) or Merkle tree (like this).

The PoRs that are based on MACs or signatures usually use the notion of extractability. Informally, it states that if a prover can convince the verifier (with a high probability), then the prover must know the file. So there exists an extractor that can interact with the prover and after a polynomial number of iterations, it can extract the full file.

However, I have not seen any Merkle tree-based PoR that uses any notion of extractability.

Question: Can Merkle tree-based PoRs also support extractability too?

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