Abstract Amid the rapid evolution of cloud computing, safeguarding data privacy has become a core priority for both academic and industrial communities. To protect user data from unauthorized access, vast volumes of sensitive information are encrypted before being transmitted to and stored on cloud platforms. Nevertheless, encryption inherently limits the platform’s ability to manipulate encrypted data, like direct search or matching on ciphertexts. Traditional Public Key Encryption with Equality Test (PKEET) schemes address this issue by enabling ciphertext equivalence verification without decryption, but they lack support for multi-ciphertext scenarios and fine-grained security. We propose a novel quantum-resistant Public Key Encryption with Multi-ciphertexts Equality Test (PKE-MET) scheme, the first to be constructed based on the Learning with Rounding (LWR) problem in lattice-based cryptography. We prove that the scheme achieves Chosen Ciphertext Attack (CCA2) security under the standard model, addressing the limitation of the existing Learning With Error (LWE)-based PKE-MET scheme which only reaches Chosen-Plaintext Attack (CPA) security. Compared with LWE-based solution, our scheme eliminates the need for complex discrete Gaussian sampling and adopts a smaller modulus. Theoretical analysis demonstrates that our proposed scheme exhibits good ciphertext scalability. Compared with the LWE-based solution, it requires only approximately 1/3 of the ciphertext storage. This reduces storage and communication resource consumption, thus lightening the operational load on cloud servers.

With the development of new computing models such as cloud computing, user’s data are at the risk of being leaked. Fully homomorphic encryption (FHE) provides a possible way to fundamentally solve the problem. It enables a third party who does not know anything about the secret key and plaintexts to homomorphically perform any computable functions on the corresponding ciphertexts. In 2009, Gentry proposed the first FHE scheme. After that, its inefficiency has always been a bottleneck of the development of practical schemes and applications. At TCC 2019, Gentry and Halevi proposed the first compressible FHE scheme that enables the ratio of plaintext size to the ciphertext size (i.e., the compression rate) to reach 1−ε for any small ε>0 under the standard learning with errors (LWE) assumption. However, it is only a single-key one, where the homomorphic evaluation can only be performed over ciphertexts encrypted under the same key. Compared with single-key FHE, multikey FHE is more practical. Multikey FHE enables ciphertexts encrypted under different public keys to be homomorphically computed without having to decrypt these ciphertexts using their own private keys. In addition, in a multi-identity FHE scheme, only identity information and public parameters are required when encrypting, which simplifies certificate-based key management in public key infrastructure. In this paper, a new compressible ciphertext expansion technique is proposed. Then, we use this technique to construct a compressible multikey FHE scheme and a compressible multi-identity FHE scheme to overcome the bottleneck of bandwidth inefficiency in the multikey and multi-identity settings. The two schemes proposed in this paper make it possible that the objects of homomorphic operation can be the ciphertexts encrypted under different keys or different identities before compression, thus solving the single-key defect of the work of Gentry and Halevi.