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In other words what is the probability that Bob has lied about the Merkle root after N queries? Well, here is one way Bob could cheat; he could take the list of $M$ values $$V_1, V_2, ..., V_M$$ and instead of forming a Merkle tree based on that, select a value $c$ index and a value $V'_c \ne V_c$, and instead form the list $$V_1, V_2, ..., V_{c-1}, V'_c, ...


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The point of a commitment scheme is that the commitment doesn't reveal what has been comitted to until the prover releases some secret information. For hash based shemes generally the comitment is C=H(R+V) where R is a large (128 bit) random number. An attacker can't check a guess for the value V without knowing R. For a Merkle tree vector commitment scheme, ...


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