# Meta-Commitment

To attain a sublinear commitment size, the prover will commit to the commitments ΞΌ1, . . . , ΞΌπ. Letβs call this commitment Meta-Commitment. Once this meta-commitment is calculated, a value π will be sampled by the Verifier (in an interactive protocol or non-interactive through the Fiat-Shamir heuristic). The computation of the aggregated commitment πΜ will be assigned to the Prover, who will also provide proof to guarantee the correctness of this computation with respect to the meta-commitment.

Using the IPA, we can replace the KZG-like proof of opening of an unknown polynomial π with a KZG-like proof of opening of a known polynomial π, which incurs some additional logarithmic complexity checks.

By utilizing the aforementioned methods, it is possible to delegate the calculation of πΜ. To obtain a comprehensive multi-polynomial commitment scheme, a sublinear verification algorithm must be created that receives a commitment to the evaluations as input instead of the evaluations themselves. This can be achieved in a general manner by employing proof for the relation:

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