# INTERPOL: Information Theoretically Verifiable Polynomial Evaluation

## TL;DR

INTERPOL introduces an information-theoretically verifiable polynomial evaluation method that enables high-probability correctness verification without cryptographic assumptions, suitable for user-server and multi-party scenarios.

## Contribution

It presents a novel, cryptography-free verification algorithm for polynomial evaluation that is efficient, adaptable, and applicable to multi-party networks with untrusted nodes.

## Key findings

- Achieves sublinear verification complexity.
- Provides public and adaptive verifiability.
- Operates without cryptographic assumptions.

## Abstract

We study the problem of verifiable polynomial evaluation in the user-server and multi-party setups. We propose {INTERPOL}, an information-theoretically verifiable algorithm that allows a user to delegate the evaluation of a polynomial to a server, and verify the correctness of the results with high probability and in sublinear complexity. Compared to the existing approaches which typically rely on cryptographic assumptions, {INTERPOL} stands out in that it does not assume any computational limitation on the server. {INTERPOL} relies on decomposition of polynomial evaluation into two matrix multiplications, and injection of computation redundancy in the form of locally computed parities with secret coefficients for verification. We show that {INTERPOL} has several desirable properties such as adaptivity and public verifiability. Furthermore, by generalizing {INTERPOL} to a multi-party setting consisting of a network of $n$ untrusted nodes, where each node is interested in evaluating the same polynomial, we demonstrate that we can achieve an overall computational complexity comparable to a trusted setup, while guaranteeing information-theoretic verification at each node.