Predicate signatures from pair encodings via dual system proof technique

Recently, Attrapadung (Eurocrypt 2014) proposed a generic framework for fully (adaptively) secure predicate encryption (PE) based on a new primitive, called pair encodings. The author shows that if the underlying pair encoding scheme is either perfectly secure or computationally (doubly-selectively) secure, then the PE scheme will be fully secure. Although the pair encodings were solely introduced for PE, we show that these can also be used to construct predicate signatures, a signature analogue of PE. More precisely, we propose a generic construction of predicate signature (PS) from pair encoding schemes. Our construction provides unconditional signer privacy, and unforgeability in the adaptive model. Thereafter, we instantiate many PS schemes with new results, e.g., the first practical PS schemes for regular languages, the first attribute-based signature (ABS) scheme with constant-size signatures in the adaptive model, unbounded ABS with large universes in key-policy flavor, etc.