International Association
for Cryptologic Research

In this paper, we build a framework for constructing Constrained Pseudorandom Functions (CPRFs) with inner-product constraint predicates, using ideas from subtractive secret sharing and related-key-attack security.

Our framework can be instantiated using a random oracle or any suitable Related-Key-Attack (RKA) secure pseudorandom function. We provide three instantiations of our framework:

1. an adaptively-secure construction in the random oracle model; 2. a selectively-secure construction under the DDH assumption; and 3. a selectively-secure construction under the assumption that one-way functions exist.

All three instantiations are constraint-hiding and support inner-product predicates, leading to the first constructions of such expressive CPRFs under each corresponding assumption. Moreover, while the OWF-based construction is primarily of theoretical interest, the random oracle and DDH-based constructions are concretely efficient, which we show via an implementation.