Polynomial Commitment¶
Note
A polynomial commitment is a succinct representation of a polynomial, enabling the verification of specific polynomial evaluations without requiring knowledge of the entire polynomial.
In simpler terms, if someone provides a commitment \(c\) representing \(P(x)\), they can also generate a proof convincing you of the value of \(P(z)\) for a particular \(z\). (Refer to Reed-solomon fingerprinting for a related concept).
There are two crucial components to this process: the commitment to the polynomial and the opening to a value at a specific point.
Various techniques exist for making commitments: