  With the rapid growth of cloud storage and cloud computing services, many
organisations and users choose to store the data on a cloud server for saving
costs. However, due to security concerns, data of users would be encrypted
before sending to the cloud. However, this hinders a problem of computation on
encrypted data in the cloud, especially in the case of performing data matching
in various medical scenarios. Public key encryption with equality test (PKEET)
is a powerful tool that allows the authorized cloud server to check whether two
ciphertexts are generated by the same message. PKEET has then become a
promising candidate for many practical applications like efficient data
management on encrypted databases. Lee et al. (Information Sciences 2020)
proposed a generic construction of PKEET schemes in the standard model and
hence it is possible to yield the first instantiation of post-quantum PKEET
schemes based on lattices. At ACISP 2019, Duong et al. proposed a direct
construction of PKEET over integer lattices in the standard model. However,
their scheme does not reach the CCA2-security. In this paper, we propose an
efficient CCA2-secure PKEET scheme based on ideal lattices. In addition, we
present a modification of the scheme by Duong et al. over integer lattices to
attain the CCA2-security. Both schemes are proven secure in the standard model,
and they enjoy the security in the upcoming quantum computer era.
