In private computation, a user wishes to retrieve a function evaluation of messages stored on a set of databases without revealing the function's identity to the databases. Obead \emph{et al.} introduced a capacity outer bound for private nonlinear computation, dependent on the order of the candidate functions. Focusing on private \emph{quadratic monomial} computation, we propose three methods for ordering candidate functions: a graph edge-coloring method, a graph-distance method, and an entropy-based greedy method. We confirm, via an exhaustive search, that all three methods yield an optimal ordering for $f < 6$ messages. For $6 \leq f \leq 12$ messages, we numerically evaluate the performance of the proposed methods compared with a directed random search. For almost all scenarios considered, the entropy-based greedy method gives the smallest gap to the best-found ordering.

翻译：在私有计算中，用户希望从一组数据库中检索消息的函数评估结果，同时不向数据库泄露函数的身份。Obead等人引入了一个依赖于候选函数顺序的私有非线性计算容量上界。针对私有*二次单项式*计算，我们提出了三种候选函数排序方法：图边着色法、图距离法和基于熵的贪心法。通过穷举搜索验证，对于$f < 6$个消息，这三种方法均能产生最优排序。对于$6 \leq f \leq 12$个消息，我们通过数值评估将所提方法的性能与有向随机搜索进行比较。在几乎所有考虑的场景中，基于熵的贪心法与最佳已知排序的差距最小。