In this paper, we investigate function computation problems under different secure conditions over a network with multiple source nodes and a single sink node which desires a function of all source messages without error. A wiretapper has access to some edges of the network. Based on different practical requirements, we consider two secure conditions named as secure and user secure respectively. The main parameter concerned here is the computing rate, which is the average times of the target function that can be computed securely or user securely without error for one use of the network. In the secure case, a new upper bound which is tighter than the previous one is provided for arithmetic sum functions and arbitrary networks. Moreover, we show that the improved upper bound is strictly tight for tree-like networks. In the user secure case, we give a sufficient and necessary condition for the existence of user secure network codes and obtain an upper bound for the computation capacity.

翻译：在本文中, 我们调查多源节点和单一汇节点的网络在不同的安全条件下的函数计算问题。 窃听器可以进入网络的某些边缘。 根据不同的实际要求, 我们认为两个安全条件分别被命名为安全和用户安全。 这里涉及的主要参数是计算率, 即目标函数的平均时间, 可以安全地或用户安全地为网络的某一用途而安全地计算。 在安全的情况下, 一个比前一个更紧的新上限为计算总和功能和任意网络。 此外, 我们显示, 改进后的上限对于类似树的网络是严格紧紧的。 在用户安全的情况下, 我们给用户安全网络代码的存在提供了足够和必要的条件, 并获得计算能力的上限 。