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.

中文翻译：

---

一种基于智能合约的可公开验证的外包矩阵计算方案

矩阵计算是人工智能和密码计算等科学领域的重要数学工具。然而，资源有限的设备很难独立执行大规模矩阵计算。外包矩阵计算（OMC）是一种很有前途的解决方案，它利用云服务器为资源有限的设备处理复杂的矩阵计算。然而，现有的OMC方案缺乏公共可验证性，因此资源有限的设备无法判定计算结果的正确性。在本文中，我们首次提出了一种基于智能合约的OMC方案，公开验证外包矩阵计算结果。在我们的方案中，运行在区块链上的智能合约作为去中心化的可信第三方来保证矩阵计算结果的正确性。为了克服区块链中的验证者困境，我们提出了一种与区块链兼容的矩阵验证方法，该方法将时间复杂度降低为$O(n^{3})$到$O(n^{2})$通过利用带有校验位和填充矩阵的盲法。我们让验证变成比较两个结果是否相同的形式，而不是天真的重新计算。最后，我们在以太坊和ARM Cortex-M4上进行了实验，并进行了深入的分析和性能评估，证明了我们的方案的实用性和有效性。