Short integrated PKE+PEKS in standard model

Abstract

At SeCrypt 2015, Buccafurri et al. [BLSS15] presented an integrated public-key encryption (PKE) and public-key encryption with keyword search (PEKS) scheme (PKE+PEKS) whose security relies on the Symmetric eXternal Diffie-Hellman (SXDH) assumption but they did not provide a security proof. We present a construction of PKE+PEKS and prove its security in the standard model under the SXDH assumption. We prove that our scheme is both IND-PKE-CCA secure, that is, it provides message confidentiality against an adaptive chosen ciphertext adversary, and IND-PEKS-CCA secure, that is, it provides keyword privacy against an adaptive chosen ciphertext adversary. Ours is the first secure PKE+PEKS construction to use asymmetric pairings which enable an extremely fast implementation useful for practical applications. Our scheme has much shorter ciphertexts than the scheme in [BLSS15] and all other publicly known PKE+PEKS schemes. Finally, we compare our scheme with other proposed PEKS and integrated PKE+PEKS schemes and provide a relative analysis of various parameters including assumption, security and efficiency.