A Publicly Verifiable Outsourcing Matrix Computation Scheme Based on Smart Contracts

Abstract

Matrix computation is a crucial mathematical tool in scientific fields such as Artificial Intelligence and Cryptographic computation. However, it is difficult for resource-limited devices to execute large-scale matrix computations independently. Outsourcing matrix computation (OMC) is a promising solution that engages a cloud server to process complicated matrix computations for resource-limited devices. However, existing OMC schemes lack public verifiability, and thus resource-limited devices cannot verdict the correctness of the computing results. In this paper, for the first time, we propose a smart contract-based OMC scheme that publicly verifies the outsourcing matrix computation results. In our scheme, a smart contract running over the blockchain serves as a decentralized trusted third party to ensure the correctness of the matrix computation results. To overcome the Verifier's Dilemma in the blockchain, we present a blockchain-compatible matrix verification method that decreases the time complexity from$O(n^{3})$to$O(n^{2})$by utilizing a blinding method with the check digit and padding matrices. We make the verification become the form of comparing whether two results are identical rather than naive re-computing. Finally, we perform experiments on Ethereum and ARM Cortex-M4 and give in-depth analysis and performance evaluation, demonstrating our scheme's practicability and effectiveness.