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 simply boho classroom 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 berkley power worm 100 pack 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.