对大数据进行统计分析获取更有深度和精度的信息，是当前社会的重要需求。云计算等外包技术为大数据统计分析提供了潜在的解决方案。但外包服务是由第三方提供，确保计算结果的正确性成为外包用户的首要关注问题。本课题旨在研究公开可验证的数据外包统计计算问题。. 线性同态签名仅适用于单用户数据外包线性计算验证，全同态签名支持二次函数外包计算验证，适用于单用户数据外包统计计算。但验证开销与函数涉及的数据数目成线性关系。在大数据下，可实用性公开可验证的单用户数据外包统计计算以及群用户数据外包统计计算公开验证是国际上未解决的公开问题。本课题的研究包括：1）公开可验证的统计计算安全模型；2）高效的公开可验证单用户数据外包统计计算；3）公开可验证的静态群与动态群数据外包统计计算。本课题的研究目的是提出具有实用价值的数据外包统计计算公开验证方案，以及填补国内外在群用户数据外包统计计算验证研究的空白。

Getting statistics on big data for significant information with more depth and accuracy is an important requirement of current society. Outsourcing techniques such as cloud computing provide a potential solution to the statistics computations over big data. As the outsourcing service is provided by a third party, how to ensure the correctness of the computation result is of great significance. To address this problem, our proposal aims for publicly verifiable statistic computations over outsourced data. . Homomorphic linear signatures are only suitable for the verification of linear functions on individual outsourced data, while full homomorphic signatures that support the verification of the outsourced quadratic polynomial functions can be used for quadratic statistical functions. However, the computation overhead of a verifier is proportional to the number of involved data. In the background of big data, the efficiency of publicly verifying the result of statistic computations over individual outsourced data and how to publicly verify the result of statistic computations over group’s outsourced data are two open problems. The research contents of this proposal include: 1) the formal security model of the publicly verifiable statistic computations; 2) publicly verifiable statistic computations over outsourced data of an individual user; 3) publicly verifiable statistic computations over outsourced data of static groups and dynamic groups. This proposal aims at proposing practical and public verification schemes for statistic computations over outsourced data, and filling the research vacancy of verifying the statistic computations over outsourced data of groups in domestic and abroad.