Abstract Fully homomorphic encryption (FHE) has emerged as a prominent area of cryptographic research in recent years, offering the capability to perform computations on ciphertext without compromising data privacy. Among various FHE schemes, the Cheon–Kim–Kim–Song (CKKS) algorithm for approximate homomorphic encryption has gained prominence due to its efficient handling of floating-point operations. Bootstrapping, a critical technique that enables unlimited homomorphic operations by refreshing noisy ciphertexts, represents both the most complex and essential component of practical FHE implementations. This survey provides a comprehensive analysis of bootstrapping techniques in CKKS, examining their evolution from the original proposal to current state-of-the-art methods. Recent literature has witnessed a proliferation of novel bootstrapping schemes for CKKS, these diverse approaches often emphasize different performance aspects, leading to a lack of a unified quantitative framework for comparative analysis. To address this gap, we systematically categorize existing approaches into three main directions: optimization of homomorphic modular reduction, optimization of encoding/decoding operations, and development of alternative constructions using blind rotation techniques. Through detailed comparative analysis, we identify that current schemes can achieve either high throughput (processing over 1000 ciphertexts per second) or high precision (up to 400 bits), but exhibit limitations in concurrent optimization of both parameters. Furthermore, potential directions for future optimizations are explored and discussed, contributing to the ongoing development of efficient and practical FHE systems.

Private data alignment, as the prerequisite for multiparty collaborative computation, attracts more attention in recent years, and some existing researches achieve the intersection sharing through two-party private set intersection (PSI) protocol based on various cryptographic techniques. However, they focus on the correctness and confidentiality of the protocol in the two-party scenario, while ignoring the efficiency and scalability in multiparty scenario. Additionally, the multiparty PSI protocol is difficult to be compatible with two parties simultaneously. To this end, we propose an oblivious pseudorandom function-based PSI scheme to achieve the data alignment, which is suitable for two parties and multiple parties. Specifically, to avoid frequent interactions among multiple parties, an efficient filtering algorithm is designed with the assistance of a server. The security proof for semi-honest and corrupted parties is provided, meanwhile, the computation and communication overhead analysis is given in detail. To evaluate the performance, we deploy the proposed scheme in two-party and multiparty scenario, and compare it with the existing protocols to discuss the execution complexity and overhead, which shows the efficiency and scalability of the proposed scheme in the multiparty scenario.

Private set intersection (PSI) has emerged as a key cryptographic protocol, enabling secure data sharing and facilitating collaborative computing among distributed data providers in recent years. However, it remains challenging to achieve efficient multiparty private set intersection (MPSI) for large-scale data and numerous participants in an open environment. To this end, we propose EL-MPSI, an Efficient and Lightweight MPSI scheme based on Vector Oblivious Linear Evaluation (VOLE) and Oblivious Key-Value Store (OKVS), which enables secure data sharing in settings with millions of datasets and dozens of participants. By simplifying the interaction process among multiple participants, the proposed scheme achieves constant-level round complexity and provides resistance against malicious adversaries, as well as collusion attack. Through theoretical analysis and experiments, we demonstrate that the security, efficiency and scalability of our scheme perform better than existing state-of-the-art (SOTA) works. For millions of datasets and dozens of participants, EL-MPSI achieves second-level latency while keeping client communication overhead to approximately 10 MB. Moreover, in scenarios of malicious adversary setting, the extra execution overhead is negligible, which effectively facilitates large-scale data sharing.

Federated Learning (FL) has attracted increasing attention from both academia and industry due to its merit of securely constructing AI models across multiple entities while preserving the privacy of local training data. However, recent research shows two persisting problems in FL that have yet to be solved: (1) limited practical adaptation of federated learning because of time-consuming conventional privacy-preserving methods, and (2) the absence of quantum-computing resistance in these methods. To address these problems, we propose a novel vertical federated learning strategy, HQsFL, which relies on Fully Homomorphic Encryption (FHE) and Matrix Vector Product basing on Coefficient Encoding. The proposed method can be widely applied to FL algorithms such as logistic regression and XGBoost, etc. We fully implement our approach and evaluate its utility and efficiency through extensive experiments performed on four synthetic datasets. The experimental results demonstrate that our proposed methods for vertical LR and XGBoost achieve comparable levels of AUC to conventional methods, while significantly improving training efficiency and achieving security property of quantum-computing resistance.

Blockchain can be utilized to enhance both security and efficiency for location-based service (LBS) in vehicular social networks (VSNs), due to its inherent decentralization, anonymity, and trust properties. Unfortunately, the existing approaches either lack effective authentication, which is vulnerable to the man-in-the-middle attack, or require an online certificate authority (CA) where frequent interactions with resource-constrained vehicles are required. To address these challenging issues, in this article, a lightweight threshold CA for consortium blockchain along with a privacy-preserving LBS protocol in blockchain enforced VSNs is proposed. First, a lightweight threshold CA framework LTCA is proposed by devising a threshold proxy signature, where the proxy signing key is issued by a coalition of threshold number of CAs playing the roles of authorized nodes in the consortium blockchain. Without the intervene of an online CA, each vehicle in the online phase can authenticate its identity by itself each time its blockchain address (i.e., account address) is updated. Then, based on the proposed LTCA, an efficient privacy-preserving LBS protocol PPVC is contrived to protect each vehicle’s conditional identity privacy with a moderate cost. Finally, both security analysis and performance evaluation demonstrate the effectiveness and efficiency of our proposed LTCA and PPVC in blockchain enforced VSNs.