Plaintext-Verifiably-Checkable Encryption and Its Extension in Dual-Server Setting

Plaintext-checkable encryption (PCE), first introduced by Canard et al., allows users searching on encrypted data through plaintexts. It provides a useful primitive in the cloud computing security. However, existing PCE schemes could not guarantee verifiability to prevent from malicious adversaries. To concentrate with, we provide the notion of plaintext-verifiably-checkable encryption (PVCE). Our PVCE scheme could check that if a ciphertext is valid, even though it could pass the check procedure, to avoid malicious ciphertexts. Furthermore, we extend the work in dual-server setting, called dual-server plaintext-verifiably-checkable encryption (DS-PVCE), to resist offline message recover attack. We also give the security definition IND-CCA-FS, IND-CCA-BS and IND-CCA-BS-II in standard model for DS-PVCE and prove that DS-PVCE is secure under these security notions. Then we give constructions of PVCE and DS-PVCE from pairing-friendly smooth projective hash function (PF-SPHF) and their instantiations based on k-MDDH assumption. At the end of this paper, we provide implementation to compare existing PCE schemes and our schemes, which shows that DS-PVCE has very high check efficiency compared with other PCE schemes.