In recent years, the research on ciphertext-policy attribute-based encryption (CP-ABE) scheme design based on learning with errors (LWE) has been a challenging problem, and many researchers have made a lot of attempts at it. At EUROCRYPT 2021, Datta, Komargodski, and Waters proposed the first provably secure direct CP-ABE construction that supports NC${}^1$ circuit access structures. Improving on their work, we propose a CP-ABE scheme. Technically, we use the new lattice two-stage sampling technique of Lai, Liu, and Wang (EUROCRYPT 2021) in the key generation phase instead of the extended trapdoor sampling technique. In this way, we obtain a CP-ABE scheme, which is at least as secure as the original scheme under the same conditions, and has a shorter ciphertext; we provide an innovative design idea for designing CP-ABE schemes only based on LWE, although this is only a partial theoretical work.

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.

The idea of multi-keyword ranked search over encrypted cloud data has attracted considerable attention in recent studies, as it allows users to securely and efficiently retrieve highly relevant results. Traditional methods improve search efficiency by incorporating the K-means clustering algorithm. However, when applied to large-scale datasets, K-means can become computationally expensive. This paper introduces a multi-keyword ranked search method, SAO-KRS, which leverages the snow ablation optimizer (SAO) to enhance clustering performance. The approach begins with principal component analysis (PCA) to reduce the dimensionality of high-dimensional data, followed by clustering the reduced data using SAO, which reduces clustering overhead massively. By incorporating a heuristic best-first search algorithm over index trees, the scheme achieves reduced computational cost with high retrieval accuracy. In the best-case scenario, the proposed method achieves up to 21 times faster clustering and 2.7 times faster searching compared to the traditional K-means approach. Extensive experimental results verify that this method significantly improves clustering efficiency while ensuring both search speed and accuracy.

Middle-product learning with errors (MP-LWE) was proposed in 2017 by Rosa et al., it is considered to be a method that combines the high efficiency of the R-LWE with the security guarantee of the ordinary LWE. Following the idea of this problem, in the TCC 2019, Alex Lombardi et al. further studied the method of constructing identity-based encryption (IBE) scheme on the premise of the MP-LWE. They introduced several major technologies, these include the introduction of a new leftover hash lemma and the instan-tiation of a brand-new variant of lattice trapdoor corresponding to MP-LWE. The idea of instantiation of trapdoor is very novel, but the equation can not be solved correctly by using the trapdoor. In the current work, we have improved the research results of the Lombardi et al., that is, we re-instantiate the trapdoor matching MP-LWE and use it to construct a new IBE scheme. Further, we also use the classical transformation of Abdalla et al. to transform the constructed IBE scheme into a MP-LWE-based public key search encryption scheme (PEKS). Compared to IBE and PEKS schemes from LWE, our scheme is more effective, and their ciphertexts and keys size are only O˜(n) in size (for identities of size n bits). Compared to IBE and PEKS schemes from ring-LWE, our schemes have similar efficiency