This work considers the problem of privately outsourcing the computation of a matrix product over a finite field $\mathbb{F}_q$ to $N$ helper servers. These servers are considered to be honest but curious, i.e., they behave according to the protocol but will try to deduce information about the user's data. Furthermore, any set of up to $X$ servers is allowed to share their data. Previous works considered this collusion a hindrance and the download cost of the schemes increases with growing $X$. We propose to utilize such linkage between servers to the user's advantage by allowing servers to cooperate in the computational task. This leads to a significant gain in the download cost for the proposed schemes. The gain naturally comes at the cost of increased communication load between the servers. Hence, the proposed cooperative schemes can be understood as outsourcing both computational cost and communication cost. Both information--theoretically secure and computationally secure schemes are considered, showing that allowing information leakage that is computationally hard to utilize will lead to further gains. The proposed server cooperation is then exemplified for specific secure distributed matrix multiplication (SDMM) schemes and linear private information retrieval (PIR). Similar ideas naturally apply to many other use cases as well, but not necessarily always with lowered costs.
翻译:这项工作考虑了将一个有限字段的矩阵产品的计算外包给一个固定字段$mathbb{F ⁇ {F ⁇ qq$至$N美元帮助服务器的私人外包问题。这些服务器被认为是诚实但好奇的,即它们按照协议行事,但将试图推断用户数据的信息。此外,允许任何一套高达$X的服务器共享数据。以前的工作认为这种串通是一种障碍,计划下载费用随着增加X美元而增加。我们提议利用服务器之间的这种联系使用户受益,允许服务器在计算任务中合作。这导致拟议计划的下载费用大增。收益自然是增加服务器之间的通信负荷。因此,拟议的合作计划可以理解为将计算成本和通信费用都外包。考虑到信息-理论上安全和计算上安全的两种计划,表明允许信息渗漏在计算上很难使用将带来进一步收益。拟议的服务器合作随后将具体的安全分布矩阵增殖计划(SDMM)和线性私人信息检索费用(P)作为例子,自然地将类似的想法应用于许多类似的例子,例如不断降低成本。