Paper 2015/017

Simple Functional Encryption Schemes for Inner Products

Michel Abdalla, Florian Bourse, Angelo De Caro, and David Pointcheval

Abstract

Functional encryption is a new paradigm that allows users to finely control the amount of information that is revealed by a ciphertext to a given receiver. Recent papers have focused their attention on constructing schemes for general functionalities at expense of efficiency. Our goal, in this paper, is to construct functional encryption schemes for less general functionalities which are still expressive enough for practical scenarios. We propose a functional encryption scheme for the {\em inner-product} functionality, meaning that decrypting an encrypted vector x with a key for a vector y will reveal only <x,y> and nothing else, whose security is based on the DDH assumption. Despite the simplicity of this functionality, it is still useful in many contexts like descriptive statistics. In addition, we generalize our approach and present a generic scheme that can be instantiated, in addition, under the LWE assumption and offers various trade-offs in terms of expressiveness and efficiency.

Note: 2015-03-28: Revised the LWE instantiation, including change of parameters and additional proof details. Generic construction now has two security theorems associated with it, depending on the properties of the underlying public-key encryption scheme.