# Prover efficient public verification of dense or sparse/structured matrix-vector multiplication

## TL;DR

This paper introduces efficient public verification protocols for matrix-vector multiplication that are secure against malicious servers, significantly reducing computational overhead and outperforming existing methods by over two orders of magnitude.

## Contribution

The paper presents novel protocols for verifying matrix-vector multiplications that are both secure and highly efficient, especially for sparse or structured matrices, with minimal cryptographic overhead.

## Key findings

- Over two orders of magnitude faster than existing protocols
- Linear verification time in the dimension
- Limited cryptographic operations for practicality

## Abstract

With the emergence of cloud computing services, computationally weak devices (Clients) can delegate expensive tasks to more powerful entities (Servers). This raises the question of verifying a result at a lower cost than that of recomputing it. This verification can be private, between the Client and the Server, or public, when the result can be verified by any third party. We here present protocols for the verification of matrix-vector multiplications, that are secure against malicious Servers. The obtained algorithms are essentially optimal in the amortized model: the overhead for the Server is limited to a very small constant factor, even in the sparse or structured matrix case; and the computational time for the public Verifier is linear in the dimension. Our protocols combine probabilistic checks and cryptographic operations, but minimize the latter to preserve practical efficiency. Therefore our protocols are overall more than two orders of magnitude faster than existing ones.