Low-Rate denial of service (LDoS) attacks degrade the quality of service with less traffic than ordinary DoS attacks. LDoS attacks can easily evade conventional counter-DoS detection mechanisms because their time-averaged flow is small and, therefore, become a serious problem. With the recent spread of IoT devices, Zigbee has attracted much attention. Zigbee is a low-power wireless communication protocol that sacrifices transfer range and bandwidth. Since Zigbee consumes very low power, it is widely adopted for small inexpensive IoT devices. The advantage of the low power consumption of Zigbee is due to the indirect transmission. We have already pointed out LDoS attack methods exploiting the characteristics of the indirect transmission, proposed algorithms detecting attackers, and evaluated the accuracy of the algorithms. In this paper, we focus on memory efficient implementation of the algorithm. First, we found that straightforward implementation of the algorithm needs large memory. Then, we propose an improved implementation which requires much less memory. Furthermore, we implement it on a resource-constrained single-board computer and confirm that our proposed algorithm can work correctly with much less memory space and shorter execution time than our previously proposed method. These results prove that the proposed detection algorithm is feasible for a wider range of IoT devices.