In this paper we significantly extend the function privacy framework. First, we introduce the new notion of subspace-membership encryption, a generalization of inner-product encryption, and formalize a meaningful and realistic notion for capturing its function privacy. Then, we present a generic construction of a function-private subspace-membership encryption scheme based on any inner-product encryption scheme. This is the first generic construction that yields a function-private encryption scheme based on a non-function-private one.
Finally, we present various applications of function-private subspace-membership encryption. Among our applications, we significantly improve the function privacy of the identity-based encryption schemes of Boneh et al.: whereas their schemes are function private only for identities that are highly unpredictable (with min-entropy of at least $\lambda + \omega(\log \lambda)$ bits, where $\lambda$ is the security parameter), we obtain function-private schemes assuming only the minimal required unpredictability (i.e., min-entropy of only $\omega(\log \lambda)$ bits). This improvement offers a much more realistic function privacy guarantee.Category / Keywords: public-key cryptography / Function privacy, functional encryption. Date: received 19 Jun 2013 Contact author: segev at stanford edu Available format(s): PDF | BibTeX Citation Version: 20130620:111939 (All versions of this report) Discussion forum: Show discussion | Start new discussion