Public-key encryption with keyword search (PEKS) is a cryptographic primitive that allows us to search for particular keywords over ciphertexts without recovering plaintexts. By using PEKS in cloud services, users can outsource their data in encrypted form without sacrificing search functionality. Concerning PEKS that can specify logical disjunctions and logical conjunctions as a search condition, it is known that such PEKS can be (generically) constructed from anonymous attribute-based encryption (ABE). However, it is not clear whether it is possible to construct this types of PEKS without using ABE which may require large computational/communication costs and strong mathematical assumptions. In this paper, we show that ABE is crucial for constructing PEKS with the above functionality. More specifically, we give a generic construction of anonymous key-policy ABE from PEKS whose search condition is specified by logical disjunctions and logical conjunctions. Our result implies such PEKS always requires large computational/communication costs and strong mathematical assumptions corresponding to those of ABE.

Replayable chosen ciphertext (RCCA) security was introduced by Canetti, Krawczyk, and Nielsen (CRYPTO'03) in order to handle an encryption scheme that is “non-malleable except tampering which preserves the plaintext.” RCCA security is a relaxation of CCA security and a useful security notion for many practical applications such as authentication and key exchange. Canetti et al. defined non-malleability against RCCA (NM-RCCA), indistinguishability against RCCA (IND-RCCA), and universal composability against RCCA (UC-RCCA). Moreover, they proved that these three security notions are equivalent when considering a PKE scheme whose plaintext space is super-polynomially large. Among these three security notions, NM-RCCA seems to play the central role since RCCA security was introduced in order to capture “non-malleability except tampering which preserves the plaintext.” However, their definition of NM-RCCA is not a natural extension of that of original non-malleability, and it is not clear whether their NM-RCCA captures the requirement of original non-malleability. In this paper, we propose definitions of indistinguishability-based and simulation-based non-malleability against RCCA by extending definitions of original non-malleability. We then prove that these two notions of non-malleability and IND-RCCA are equivalent regardless of the size of plaintext space of PKE schemes.