Bounded-Collusion Identity-Based Encryption from Semantically-Secure Public-Key Encryption: Generic Constructions with Short Ciphertexts

Identity-based encryption (IBE) is a special case of public-key encryption where user identities replace public keys. Every user is given a corresponding secret key for decryption, and encryptions for his or her identity must remain confidential even to attackers who learn the secret keys associated with other identities. Several IBE constructions are known to date, but their security relies on specific assumptions, such as quadratic residuosity, as well as different pairing-based and lattice-based assumptions. To circumvent the lack of generic constructions, Dodis et al. (EUROCRYPT ’02) introduced the notion of bounded-collusion IBE (BC-IBE), where attackers only learn secret keys of an a-priori bounded number t of identities. They provided a generic BC-IBE construction from any semantically-secure encryption scheme which, however, suffers from a ω(t) blow-up in ciphertext size. Goldwasser et al. (TCC 2012) recently presented a generic construction with no ciphertext-length blow-up. Their construction requires an underlying public-key scheme with a key homomorphism, as well as a hash-proof-style security definition that is strictly stronger than semantic security. This latter requirement in particular reduces the applicability of their construction to existing schemes. In this paper, we present the first generic constructions of BC-IBE from semantically-secure encryption schemes with no ciphertext-length blow-up. Our constructions require different degrees of key-homomorphism and malleability properties that are usually easy to verify. We provide concrete instantiations based on the DDH, QR, NTRU, and LWE assumptions. For all of these assumptions, our schemes present the smallest BC-IBE ciphertext size known to date. Our NTRU-based construction is particularly interesting, due to the lack of NTRUbased IBE constructions as well as the fact that it supports fully-homomorphic evaluation. Our results also yield new constructions of bounded CCA-secure cryptosystems.