Efficient Trapdoor Generation From Multiple Hashing In Searchable Symmetric Encryption

Searchable symmetric encryption (SSE) which can search encrypted data using encrypted keywords has been extremely studied. In Asiacrypt' 10, Chase and Kamara formalized structured encryption which is a generalization of SSE, and its concrete schemes were proposed. An efficient SSE scheme (hereafter, Chase-Kamara scheme) which has a very simple encrypted index is obtained by simplifying the concrete schemes, and its adaptive security can be proved, easily. In the Chase-Kamara scheme, a search result for a keyword is represented as a bit string in which the i-th bit is 1 when the i-th document contains the keyword, and the encrypted index is built by directly masking the search result with each bit of the output of a pseudo-random function. Therefore, the Chase-Kamara scheme requires pseudo-random functions whose output lengths are longer than the number of documents that users would like to store. As a result, the trapdoor size of the Chase-Kamara scheme depends on the number of stored documents. In this paper, we propose a modified scheme whose trapdoor size does not depend on the number of stored documents. The modified scheme is constructed by using our multiple hashing technique which can transform a trapdoor of short length to that of long length without any secret information. We also show that the modified scheme achieves the same adaptive security as the Chase-Kamara scheme in the random oracle model.