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On the Power of Pair Encodings: Frameworks for Predicate Cryptographic Primitives

Recently Attrapadung (Eurocrypt 2014) proposed a generic framework for fully (adaptively) secure predicate encryption (PE) based on a new primitive, called pair encodings. The authors 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 for predicate signature (PS) from the pair encoding schemes. Our construction provides the signer privacy, and unforgeability in the adaptive-predicate model. Thereafter, we instantiate many PS schemes with new results, e.g., the first PS schemes for regular languages, the first attribute-based signature (ABS) scheme with constant-size signature in adaptive-predicate model, the unbounded ABS with large universes in key-policy flavor etc. Following the CCA conversions of Yamada et al. (PKC 2011, 2012) and Nandi et al. (ePrint Archive: 2015/457), one can have CCA secure PE from CPA-secure PE if the primitive PE has either verifiability or delegation. We show that the fully secure CPA-construction of Attrapadung holds the verifiability if we assume a very simple condition on the underlying pair encoding scheme. The aforesaid approach degrades the performance of the resultant CCA-secure PE scheme. As an alternative, we provide a direct fully secure CCA-construction for PE from the pair encoding schemes. This costs an extra computation of group element in encryption and an extra pairing computation in decryption as compared to CPAconstruction of Attrapadung. The predicate signcryption (PSC) is a super class of the existing class, attribute-based signcryption (ABSC), where the confidentiality, unforgeability and signer privacy are well preserved. By combining the proposed frameworks for PS and PE, we provide a generic construction for PSC from the pair encodings. It achieves the perfect privacy, and the strong unforgeability and CCA security in the adaptive-predicates model. The construction has the support of “combined-setup”, where the distribution of public parameters and keys in the (implicit) signature and encryption schemes are identical. The instantiations of the proposed PSC, provide many new schemes, e.g., the first PSC schemes for regular languages, the first ABSC with either constant-size signatures or constant-size keys, the unbounded ABSC with large universes in adaptive-predicates model etc.