A note on the error of optimized LFC Private Information Retrieval scheme

A number of low communication-cost private information retrieval (PIR) schemes have been proposed in recent years. In JWIS2006, Kwon et al. proposed a new scheme (optimized LFCPIR, or OLFCPIR), which aimed at reducing the communication cost of Lipmaa' s O(log
²
n) PIR(LFCPIR) to O(log n). However, in this paper, we demonstrate OLFCPIR' s fatal mistake of overflow contained, and show that it does not function as a PIR scheme.