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.
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.
Abstract With the rise of cloud storage and the looming threat of quantum computing, traditional encryption methods are encountering significant challenges that hinder data manipulation without decryption. To counter quantum attacks while maintaining data manipulation capabilities, new architectures such as quantum-resistant public key encryption with equality test (PKEET) must be developed. Our study presents the initial PKEET that leverages the Learning with Rounding (LWR) problem, which provides security within standard model. We also introduce its variants, public key encryption with delegated equality test (PKE-DET) and PKEET supporting flexible authorization (PKEET-FA). Our proposals could achieve fine-grained delegation at the ciphertext-specified level compared to previous PKE-DET schemes. For example, our PKE-DET supports a delegated tester function while ensuring security against quantum computing threats. Our PKEET-FA could accord users even more controls over what ciphertexts they want to compare. Our schemes’ security is founded on the LWR problem which avoids the need for discrete Gaussian sampling, unlike the Learning with Errors (LWE) problem. This distinction renders our methods both simpler and more efficient compared to those based on LWE. Moreover, our schemes enjoy smaller-sized ciphertexts.
Data is typically encrypted before transmission to a cloud server to safeguard user privacy. However, such encryption prevents the server from performing searches on the data, necessitating the introduction of novel cryptographic primitives, such as public key encryption with multi-ciphertext equality test (PKEMET). PKEMET allows the cloud server to execute a single equality test on multiple ciphertexts, determining if the underlying messages are identical disclosing any extra information. Ciphertext-policy attribute-based encryption (CP-ABE) facilitates secure and efficient data sharing in cloud computing environments by supporting fine-grained access control and flexible encryption. In this work, we integrate the concepts of PKEMET and CP-ABE, introducing a novel cryptographic primitive of CP-ABE with multi-ciphertext equality test (CP-ABEMET). We present the first quantum-resistant CP-ABEMET scheme based on the learning with errors (LWE) problem. This scheme enables the receiver to delegate the cloud server to perform a single equality test among multiple messages encrypted under distinct access policies. Importantly, during the multi-ciphertexts equality test, the server gains no knowledge of the encrypted messages. Furthermore, our proposed scheme not only achieves traditional indistinguishability against chosen plaintext attack (IND-CPA) and one-way against chosen plaintext attack (OW-CPA) security but is also proven to be number secure and resilient against collusion attacks. Finally, a comparative performance analysis between our CP-ABEMET and existing equality test schemes demonstrates that our approach is more practical, efficient, and secure.
Cloud computing enables users to remove the necessity of the need of local hardware architecture, which removes the burden of the users from high computation costs. Therefore, it has attracted much attention and research has been conducted heavily on it. To protect users’ privacy, data is usually encrypted prior to being sent to the cloud server. As the resulting system is unusable, since the cloud can no longer search throughout the data, new cryptographic primitive such as public-key encryption with equality test (PKEET) has been introduced. In PKEET, users can test whether the underlying messages of two ciphertexts encrypted under different public keys are equal or not without the need to decrypt those ciphertexts. This is a very useful tool, especially for the cloud database, since PKEET mainly focuses on the equality test between two ciphertexts. However, in practice, the cloud server may need to verify the equivalence among more than two ciphertexts. This leads to disclosing unnecessary information of users and redundant computation cost will also occur when using traditional PKEET schemes. How to make this more efficient and practical remains an interesting research problem. In this article, to solve the aforementioned problems by providing a novel concept of public-key encryption with multi-ciphertext equality test (PKE-MET). In PKE-MET, each ciphertext can designate a numberssuch that the cloud server can only perform equality test on this ciphertext with others−1ciphertexts, where all their designated numbers ares. For PKE-MET, besides traditional OW-CPA and IND-CPA security, we specially define Number security. We instantiate PKE-MET to a concrete scheme and give its security proof. Furthermore, to enable the primitive to be more practical in applications, we extend it to the concept of PKE with flexible MET (PKE-FMET). In PKE-FMET, the cloud server can perform equality test on any number of ciphertexts as long as the maximum number of their designated numbers is less than or equal to the number of ciphertexts. We construct a PKE-FMET scheme based on our PKE-MET construction and prove its security under the defined security models. Besides, the performance analysis mainly of efficiency and security between our constructions and existing equality test schemes in cloud computing show that our proposed schemes are more efficient and secure in the multi-ciphertext scenario.
The rapid proliferation of cloud computing enables users to access computing resources and storage space over the internet, but it also presents challenges in terms of security and privacy. Ensuring the security and availability of data has become a focal point of current research when utilizing cloud computing for resource sharing, data storage, and querying. Public key encryption with equality test (PKEET) can perform an equality test on ciphertexts without decrypting them, even when those ciphertexts are encrypted under different public keys. That offers a practical approach to dividing up or searching for encrypted information directly. In order to deal with the threat raised by the rapid development of quantum computing, researchers have proposed post-quantum cryptography to guarantee the security of cloud services. However, it is challenging to implement these techniques efficiently. In this paper, a compact PKEET scheme is pro-posed. The new scheme does not encrypt the plaintext's hash value immediately but embeds it into the test trapdoor. We also demon-strated that our new construction is one-way secure under the quantum security model. With those efforts, our scheme can withstand the chosen ciphertext attacks as long as the learning with errors (LWE) assumption holds. Furthermore, we evaluated the new scheme's performance and found that it only costs approximately half the storage space compared with previous schemes. There is an almost half reduction in the computing cost throughout the encryption and decryption stages. In a nutshell, the new PKEET scheme is less costly, more compact, and applicable to cloud computing scenarios in a post-quantum environment.
Identity-based encryption with equality test (IBEET) provides a feasible way for cloud server partitioning or searching on ciphertexts in the cloud. In that case, the server can judge if two different ciphertexts encrypt the same plaintexts or not. In response to threats posed by quantum computers, lattice-based IBEET schemes have been proposed to make cloud service post-quantum secure. However, those schemes are inefficient and can hardly meet the needs of resource-constrained devices. In this article, an efficient post-quantum IBEET scheme is introduced, which achieves testability by embedding the hash value of plaintext into testing trapdoor instead of encrypting it directly and doubling the size of ciphertext. We also prove that, with the Learning With Errors (LWE) problem assumption, the new scheme is one-way secure against selective identity and chosen ciphertext attacks (OW-sID-CCA) in quantum secure model. Furthermore, we evaluate the performance of the new construction and demonstrate its efficiency by showing that it only costs about half storage comparing with other lattice-based IBEET schemes. The execution time of encryption and decryption phrases in the new scheme reduce by 50%, while the computational cost in test algorithm keeps the same. Therefore, the new proposed IBEET is much more practical for working in post-quantum cloud computing scenarios.
Public key encryption with equality test (PKEET) supports to check whether two ciphertexts encrypted under different public keys contain the same message or not. PKEET has many interesting applications such as keyword search on encrypted data, encrypted data partitioning for efficient encrypted data management, personal health record systems, spam filtering in encrypted email systems and so on. However, the PKEET scheme lacks an authorization mechanism for a user to control the comparison of its ciphertexts with others. In 2015, Ma et al. introduce the notion of PKEET with flexible authorization (PKEET-FA) which strengthens privacy protection. Since 2015, there are several follow-up works on PKEET-FA. But, all are secure in the random-oracle model. Moreover, all are vulnerable to quantum attacks. In this paper, we provide three constructions of quantum-safe PKEET-FA secure in the standard model. Proposed constructions are secure based on the hardness assumptions of integer lattices and ideal lattices. Finally, we implement the PKEET-FA scheme over ideal lattices.