We formulate a new secure distributed computation problem, where a simulation center can require any linear combination of $ K $ users' data through a caching layer consisting of $ N $ servers. The users, servers, and data collector do not trust each other. For users, any data is required to be protected from up to $ E $ servers; for servers, any more information than the desired linear combination cannot be leaked to the data collector; and for the data collector, any single server knows nothing about the coefficients of the linear combination. Our goal is to find the optimal download cost, which is defined as the size of message uploaded to the simulation center by the servers, to the size of desired linear combination. We proposed a scheme with the optimal download cost when $E < N-1$. We also prove that when $E\geq N-1$, the scheme is not feasible.

翻译：我们制定了一个新的安全分布计算问题, 模拟中心可以通过由 N美元服务器组成的缓存层要求将 K 美元用户的数据进行线性组合。 用户、 服务器和数据收集器彼此互不信任。 对于用户, 任何数据都必须被保护在最高为 E 美元服务器上; 对于服务器, 任何比所希望的线性组合更多的信息都不能泄露给数据收集器; 对于数据收集器, 任何单个服务器都对线性组合的系数一无所知。 我们的目标是找到最佳下载成本, 即服务器上传到模拟中心的信息的大小, 与理想线性组合的大小相同。 我们提出了一个计划, 当 $ < N-1 美元时, 最优下载成本是 $ < N-1 。 我们还证明当$ E\ geq N-1 时, 计划是不可行的 。