Searchable encryption revisited: consistency properties, relation to anonymous IBE, and extensions
Ref: Michel Abdalla, Mihir Bellare, Dario Catalano, Eike Kiltz, Tadayoshi Kohno, Tanja Lange, John Malone-Lee, Gregory Neven, Pascal Paillier and Haixia Shi. Journal of Cryptology 21(3), pages 350-391, 2008. Preliminary version appeared in V. Shoup, editor, Advances in Cryptology - CRYPTO 2005, volume 3621 of Lecture Notes in Computer Science, pages 205-222. Springer-Verlag, 2005.
Abstract: We identify and fill some gaps with regard to consistency (the extent to which false positives are produced) for public-key encryption with keyword search (PEKS). We define computational and statistical relaxations of the existing notion of perfect consistency, show that the scheme of  is computationally consistent, and provide a new scheme that is statistically consistent. We also provide a transform of an anonymous IBE scheme to a secure PEKS scheme that, unlike the previous one, guarantees consistency. Finally we suggest three extensions of the basic notions considered here, namely anonymous HIBE, public-key encryption with temporary keyword search, and identity-based encryption with keyword search.