Private, but restricted, access to databases

6 pages.-- Contributed to: X Spanish Meeting on Cryptology and Information Security (Salamanca, Spain, Sep 2-5, 2008).We consider the primitive of restricted oblivious transfer: the owner of a database wants to restrict the access of users to this data according to some policy, whereas a legitimate user wants to privately retrieve allowed parts of the data, without letting the owner know which part of the data is being obtained.We formally describe the protocols and required properties for restricted oblivious transfer, and we explain how the techniques of priced oblivious transfer can be used to solve the problem in the particular case where the family of restrictions is a weighted threshold one. We state a conjecture on a new characterization of these kind of families. Then we propose a generic solution for the problem of restricted oblivious transfer, which works for any possible monotone family of restrictions. The solution is right now of theoretical interest only, because it uses a cryptographic tool which has not been realized yet: cryptosystems which are both multiplicatively and additively homomorphic.Queremos dar las gracias a todos los patrocinadores y colaboradores por su apoyo moral y económico: CajaDuero, Realsec, Ericsson, El Corte Inglés Informática, Junta de Castilla y León, Universidad de Salamanca, Centro Criptológico Nacional, Fábrica Nacional de Moneda y Timbre, Consejo Superior de Investigaciones Científicas, Ministerio de Ciencia e Innovación (TIN2008-00637), Criptored, Red Temática de Matemáticas para la Sociedad de la Información y RENFE.Peer reviewe