# Interactive Verifiable Polynomial Evaluation

## TL;DR

This paper introduces a highly efficient, interactive, and information-theoretically sound verifiable polynomial evaluation protocol suitable for cloud computing, with low user and server complexity and logarithmic rounds.

## Contribution

It presents a novel doubly-efficient, information-theoretic verifiable polynomial evaluation algorithm that outperforms existing methods in efficiency and security.

## Key findings

- Achieves user complexity of O(d^{psilon})
- Requires O(psilon) rounds of interaction
- Provides information-theoretic soundness against unbounded adversaries

## Abstract

Cloud computing platforms have created the possibility for computationally limited users to delegate demanding tasks to strong but untrusted servers. Verifiable computing algorithms help build trust in such interactions by enabling the server to provide a proof of correctness of his results which the user can check very efficiently. In this paper, we present a doubly-efficient interactive algorithm for verifiable polynomial evaluation. Unlike the mainstream literature on verifiable computing, the soundness of our algorithm is information-theoretic and cannot be broken by a computationally unbounded server. By relying on basic properties of error correcting codes, our algorithm enforces a dishonest server to provide false results to problems which become progressively easier to verify. After roughly $\log d$ rounds, the user can verify the response of the server against a look-up table that has been pre-computed during an initialization phase. For a polynomial of degree $d$, we achieve a user complexity of $O(d^{\epsilon})$, a server complexity of $O(d^{1+\epsilon})$, a round complexity of $O(\log d)$ and an initialization complexity of $O(d^{1+\epsilon})$.