Searchable symmetric encryption refers to a system whereby clients store encrypted documents in a server that can be searched by keywords without revealing private information. In this paper, we demonstrate that the UC-secure SSE scheme proposed by Kurosawa and Ohtaki is inefficient under certain scenarios, and we propose a modified scheme. Our scheme has reliability and privacy, where privacy is slightly weaker than the original Kurosawa-Ohtaki scheme. Therefore, our scheme offers UC-security with slightly weaker privacy. More precisely, the additional information our scheme leaks is only the size of a set of keywords. On the other hand, the index size for our scheme is much smaller than the original scheme when the set of keywords is a very sparse subset of l-bit strings for some l. The UC-secure Kurosawa-Ohtaki scheme is improved with the proposed scheme by introducing a new tag for proving ``non-existence." The proposal is an example of how an SSE scheme can be effectively converted into a verifiable SSE scheme.
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