Sergio Lerner on Compact Inclusion Proofs
A new paper by Fairgate’s CTO, Sergio Lerner, introduces a way to achieve compact, logarithmic-size inclusion proofs using a single linear hash stream, without requiring a traditional Merkle tree.
eprint.iacr.org
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Verifiable Data on Bitcoin: FlatMerkle Commitments, Refutable Proofs, and FlatChecks

We give a method to publish data on Bitcoin and to verify properties of that data on Bitcoin itself, against a publisher who may lie. The data is a FlatMerkle file – a structured byte string whose ordinary SHA-256 supports logarithmic inclusion proofs and logarithmic proofs of malformation – placed in a transaction's annex or, at four times the cost but relayable by Bitcoin Core, in an output.