Public key encryption with keyword search secure against keyword guessing attacks without random oracle

The notion of public key encryption with keyword search (PEKS) was put forth by Boneh et al. to enable a server to search from a collection of encrypted emails given a “trapdoor” (i.e., an encrypted keyword) provided by the receiver. The nice property in this scheme allows the server to search for a keyword, given the trapdoor. Hence, the verifier can merely use an untrusted server, which makes this notion very practical. Following Boneh et al.’s work, there have been subsequent works that have been proposed to enhance this notion. Two important notions include the so-called keyword guessing attack and secure channel free, proposed by Byun et al. and Baek et al., respectively. The former realizes the fact that in practice, the space of the keywords used is very limited, while the latter considers the removal of secure channel between the receiver and the server to make PEKS practical. Unfortunately, the existing construction of PEKS secure against keyword guessing attack is only secure under the random oracle model, which does not reflect its security in the real world. Furthermore, there is no complete definition that captures secure channel free PEKS schemes that are secure against chosen keyword attack, chosen ciphertext attack, and against keyword guessing attacks, even though these notions seem to be the most practical application of PEKS primitives. In this paper, we make the following contributions. First, we define the strongest model of PEKS which is secure channel free and secure against chosen keyword attack, chosen ciphertext attack, and keyword guessing attack. In particular, we present two important security notions namely IND-SCF-CKCA and IND-KGA. The former is to capture an inside adversary, while the latter is to capture an outside adversary. Intuitively, it should be clear that IND-SCF-CKCA captures a more stringent attack compared to IND-KGA. Second, we present a secure channel free PEKS scheme secure without random oracle under the well known assumptions, namely DLP, DBDH, SXDH and truncated q-ABDHE assumption. Our contributions fill the gap in the literature and hence, making the notion of PEKS