Post-quantum secure ID-based encryption with equality test against insider attacks from isogeny

Abstract

With the rise of AI and smart computing, encryption with equality test has been shown useful in such applications. Compared to the standard ID-based encryption with equality test (IBEET), IBEET against insider attacks ($\mathrm{IBEETIA}$) allows one to check whether two ciphertexts encrypt the same message without using her private keys, and provides ciphertext indistinguishability against trapdoor holders. As a trade-off, a user needs to adopt a user-specific trapdoor to encryption messages. Unfortunately, we found that in the existing $\mathrm{IBEETIA}$ schemes actually fail to protect the information of the encrypted message, which should be the basic requirement for encryption. In this manuscript, therefore, an attack to the existing $\mathrm{IBEETIA}$ scheme is first demonstrated, and a potential solution by slightly modifying the definition of $\mathrm{IBEETIA}$ is given. Besides, a new generic construction for $\mathrm{IBEETIA}$ is also presented in this manuscript. To the best of our knowledge, the proposed construction is the only one achieving ciphertext indistinguishability and one-wayness simultaneously. Furthermore, by adopting Emura’s transformation, an ID-based encryption (IBE) from isogeny is further obtained, which may be the first quantum-resistant isogeny-based IBE scheme.