中文摘要：

随着云计算的发展，可验证的外包计算受到了越来越多的关注。对普通用户来说，大型线性方程组的求解是一个困难问题，可通过外包计算进行解决。现有的大型线性方程组外包求解方案计算效率较低或计算结果无法完全验证。提出了一个可验证的大型线性方程组求解的外包计算协议。在完全保护用户隐私的前提下，所提方案大大提高了用户的计算效率。与同类方案相比，所提方案降低了用户的计算代价，且用户可以完全验证服务器的外包计算结果。实验表明，所提方案用户的计算时间远小于直接计算所用的时间，且小于服务器的计算时间。

英文摘要：

With the development of cloud computing,verifiable outsourcing computation are getting more and more attentions. For ordinary users, the large-scale system of linear equations is a difficult problem. It can be solved through outsourcing computation. The outsourcing scheme for large-scale systems of linear equations always has a low computational efficiency or can＇ t be fully verifiable nowadays. This paper proposed a verifiable outsourcing protocol for large-scale systems of linear equations. The proposed protocol greatly improved the user＇ s computational efficiency when fully protect user privacy. Compared with the state-of-the-art schemes, the proposed scheme reduced user computational cost, and user could fully verify the computation re- sult output from server. Experiments show that user computing time is far less than direct calculation time, and less than the computation time of the server.