Policy-based Signatures for Predicates

Policy-based Signatures (PBS), which were introduced by Bellare and Fuchsbauer, enable signers to sign messages that conform to some policy, yet privacy of the policy is maintained. Bellare et al. defined the policy in any NP language. In PBS schemes for NP language, one should have a valid witness for the policy checking and signing algorithms. In this work, we consider the case of PBS for P language which is a special case of NP language. In PBS schemes for P language, one can directly run the policy checking and signing algorithms without witness. We set policies as some boolean predicates and define the notion of PBS for predicates and its security. Next, for an important class of policy predicates described as (1dimensional) ranges (i.e., prefix predicate), we design a PBS scheme for such predicate based on tree-based signatures and analyze its application in some real-world scenarios. In addition, based on multilinear maps, we design three PBS schemes for more complex predicates, bit-fixing predicate, left/right predicate, and circuits predicate, respectively.