Info-Commit: Information-Theoretic Polynomial Commitment

We introduce Info-Commit , an information-theoretic protocol for polynomial commitment and verification. With the help of a trusted initializer, succinct to private $f$ is provided user. The user then queries server obtain evaluations at several inputs chosen by provides along with proofs correctness which can verify against initial commitment. has four main features. Firstly, able detect, high probability, if responded same initially committed to. Secondly, rigorous privacy guarantees server: upon observing response notation="LaTeX">$m$ evaluation queries, only learns notation="LaTeX">$O(m^{2})$ symbols about coefficients . Thirdly, verifiability are unconditional regardless computational power two parties. Lastly, doubly-efficient in sense that phase, runs notation="LaTeX">$O(\sqrt {d})$ time notation="LaTeX">$O(d)$ time, where notation="LaTeX">$d-1$ degree