# Sillcom: A Communication-Efficient Privacy-Preserving Scheme for Indoor Localization
## 8 Evaluation Results
### Comparison with FAPRIL [14]  
In this section, we provide a detailed comparison between Sillcom and FAPRIL, which currently achieves the optimal end-to-end query time, covering aspects from online and offline communication overhead to query time.  
We begin by comparing the offline communication of \(\text{Sillcom}_{3R}\), \(\text{Sillcom}_{trd}\), and FAPRIL in Figure 15. Due to the need for single-layer \(\text{Sillcom}_{3R}\) to distribute \(O(m^{2})\) DDCF keys, its communication grows quadratically with \(m\), eventually surpassing the linear growth in communication overhead of FAPRIL. \(\text{Sillcom}_{trd}\) effectively addresses this issue; by adopting a two-layer structure, the communication overhead of the first layer is reduced by a factor of \(\frac{m}{m^{\prime}}\), and further optimization can be achieved by adjusting the value of \(m^{\prime}\) to balance the number of DDCF keys in the first and second layers, thereby minimizing offline communication cost. Additionally, it is noteworthy that the offline communication in FAPRIL is proportional to \(n\), whereas our two schemes are much less affected by \(n\), with the difference solely arising from the number of bits required to represent the \(n\) dimensions.  
Compared to the expensive offline communication caused by the distribution of DDCF keys, the communication advantage of FSS in the preprocessing model method during the online phase is significantly larger, as shown in Figure 16. FAPRIL has already made attempts to optimize online communication: by utilizing ABY2.0's delta-sharing [28], they effectively reduce the online communication of the distance computation module. However, to save communication rounds, FAPRIL employs garbled circuits, resulting in still considerable online communication cost. The increased online bandwidth consumption directly impacts the throughput of their scheme. On the other hand, \(\text{Sillcom}_{3R}\), which has undergone various online communication optimizations, is optimal on this metric, with its online communication volume being about 5.6% that of FAPRIL. While the online communication of \(\text{Sillcom}_{trd}\) is slightly higher than \(\text{Sillcom}_{3R}\), the tradeoff is valuable, as it achieves a significant reduction in both offline communication and online computation cost with such a small increase in online communication.  
Figure 14: \(\text{Sillcom}_{trd}^{mt}\).  
Figure 15: Comparison of offline communication with FAPRIL.  
Finally, we compare the schemes based on end-to-end query time. Table 4 lists the comparison between our schemes and FAPRIL with a set of commonly used parameters, \(n=241\) and \(m=505\). The results show that our two-layer \(\text{Silcom}_{trd}\), even in single thread, has a smaller online runtime than FAPRIL. Under 8-threaded execution, the user query time of \(\text{Silcom}_{trd}^{8t}\) is less than a quarter of FAPRIL, server computation time is even less than the network latency for sending the user's query and receiving the result. \(\text{Silcom}_{3R}\) is online faster than FAPRIL only in the 8 threads case. Furthermore, our offline runtime also outperforms FAPRIL. Although \(\text{Silcom}_{3R}\) has a higher offline communication volume, this may be due to the simpler network distribution task of DDCF keys, while FAPRIL's offline phase requires more complex multiplication triple generation using oblivious transfer.