Abstract: The widely usage of cloud computing inevitably brings in new security concerns and challenges,  such as input/output privacy and efficiency. Since large matrix Determinant Computation（DC） is a quite common scientific and engineering computational task. A protocol is designed that enables clients to securely and efficiently outsource DC to a semi-honest cloud. The main idea to protect the privacy is employing some transformations on the original matrix to get an encrypted matrix which is sent to the cloud; and then transforming the result returned from the cloud to get the correct determinant of the original matrix. The proposed protocol is correct and secure. Extensive theoretical analysis and experimental evaluation also show its high-efficiency and immediate practicability.

Key words: cloud computing, Determinant Computation（DC）, secure outsourcing

摘要： 云计算的应用，在给大家带来便利的同时，也带来一些新的安全问题：如客户端输入/输出的私密性以及云端运算的高效性等。针对此类问题，构建了一个适用于大矩阵行列式计算的云外包协议：在客户端将原始矩阵加密后再传送到云服务器端求解，在保证云服务器端运算高效性的同时，将其返回的结果解密后得到原始矩阵的行列式值。经理论分析和实验评估证明，协议满足正确性、输入/输出私密性和高效性。

关键词: 云计算, 行列式计算, 安全计算外包