Succinct non-interactive zero-knowledge proofs (zk-SNARKs) are a powerful cryptographic primitive that allow a prover to convince a verifier of the truth of a statement without revealing any additional information. Due to the high computational cost associated with proof generation in existing zk-SNARKs, distributed zero-knowledge proving has emerged as a promising outsourcing approach, where the prover delegates heavy computation to multiple servers across different locations, as seen in systems like Siniel and zkSaaS. However, existing distributed zkSNARKs still rely on large prime fields, which increase computational overhead, and they often suffer from unavoidable network bandwidth bottlenecks. In this paper, we propose FDzkS, a flexible and efficient collaborative proving distributed protocol constructed using group signatures and binary fields. Our protocol allows the prover to delegate computation to multiple workers without revealing any part of the witness. Most importantly, compared with existing distributed zkSNARK schemes, FDzkS enables both the prover and the workers to perform their tasks almost entirely offline, and it avoids complex interactions among the workers. We benchmark FDzkS against the most advanced protocols such as Siniel, Eos, zkSaaS, and Pianist, covering both semi-honest and malicious worker settings. Experimental results show that under low bandwidth conditions (64 Mbps), FDzkS reduces total proving time by up to 300 under high bandwidth conditions (4 Gbps), it still achieves up to 200% improvement in efficiency.

Federated learning is a machine learning framework that enables multiple participants to collaboratively train a shared model on local data without having to exchange data directly. This helps maintain data privacy, reduces storage requirements in the data center, and lowers communication costs. In traditional federated learning, participants need to share their local data for model training. This sharing may lead to privacy leakage and security risks. The group signature protocol ensures the anonymity and unlinkability of the participants' identities during the model update process. Additionally, it provides a way to verify whether the model parameters updated by the participants are valid, helping to prevent malicious behavior. In this framework, the user's own information privacy is protected, and a three-layer structure is adopted to further ensure the security and credibility of the model training process.

In federated learning, multiple parties may use their data to cooperatively train a model without exchanging raw data. Federated learning protects the privacy of users to a certain extent. However, model parameters may still expose private information. Moreover, existing encrypted federated learning systems need a trusted third party to generate and distribute key pairs to connected participants, making them unsuitable for federated learning and vulnerable to security risks. To mitigate these issues, we propose a privacy-preserving oriented no trusted third party federated learning system based on blockchain (NttpFL). The initiator of the federated learning task and the partners negotiate keys through the conference key agreement and do not need to distribute keys through a trusted third party. We design a double-layer encryption mechanism to ensure privacy. Partners cannot obtain any private information other than their information. The decentralized nature of blockchain suits our system. In addition, blockchain makes the entire process transparent and traceable and avoids the single node failure problem. Experimental results confirm that the proposed method significantly reduces the communication costs and computational complexity compared to existing encrypted federated learning without compromising the performance and security.

With the advance of cloud computing technology, increasingly more documents are encrypted before being outsourced to the cloud for great convenience and economic savings. Thus, how to design a fast and accurate multi-keyword ranked search scheme over encrypted cloud data is of paramount importance. In this article, we propose a fast and accurate searchable encryption (FASE) scheme that supports accurate top-k multi-keyword retrieval. We utilize a homomorphic order-preserving encryption algorithm to encrypt the index and query vectors. The encryption method supports homomorphic addition, homomorphic multiplication, and order comparison over encrypted data, and it implements the secure calculation of relevance score between encrypted index and query vectors. The encryption method can not only ensure that the calculation of relevance score ($SI_i * T$) is not exposed to the cloud server, but also protect the privacy of ranking operator. Compared to the traditional method, there are no dummy keywords added to the query vector and document vector, and the top-k search precision of the FASE scheme is 100 percent. To improve the search efficiency, a large number of irrelevant documents are effectively filtered by matching the document mark vector and query mark vector, and the time cost for calculating the relevance score and ranking is greatly reduced. Furthermore, according to the two-round ranking of the keyword matching degree and the relevance score, not only more accurate search result is returned, but the search efficiency is also further improved. The theoretical analysis and experimental results show that the FASE scheme can achieve fast and accurate multi-keyword ranking search. In addition to ensuring data privacy and security, it can also effectively improve the search efficiency and reduce the time cost of creating an index, and it can return ranking results which more satisfy the user needs.

With the widespread application of big data, privacy-preserving data analysis has become a topic of increasing significance. The current research studies mainly focus on privacy-preserving classification and regression. However, principal component analysis (PCA) is also an effective data analysis method which can be used to reduce the data dimensionality, commonly used in data processing, machine learning, and data mining. In order to implement approximate PCA while preserving data privacy, we apply the Laplace mechanism to propose two differential privacy principal component analysis algorithms: Laplace input perturbation (LIP) and Laplace output perturbation (LOP). We evaluate the performance of LIP and LOP in terms of noise magnitude and approximation error theoretically and experimentally. In addition, we explore the variation of performance of the two algorithms with different parameters such as number of samples, target dimension, and privacy parameter. Theoretical and experimental results show that algorithm LIP adds less noise and has lower approximation error than LOP. To verify the effectiveness of algorithm LIP, we compare our LIP with other algorithms. The experimental results show that algorithm LIP can provide strong privacy guarantee and good data utility.

The issue of the privacy-preserving of information has become more prominent, especially regarding the privacy-preserving problem in a cloud environment. Homomorphic encryption can be operated directly on the ciphertext; this encryption provides a new method for privacy-preserving. However, we face a challenge in understanding how to construct a practical fully homomorphic encryption on non-integer data types. This paper proposes a revised floating-point fully homomorphic encryption scheme (FFHE) that achieves the goal of floating-point numbers operation without privacy leakage to unauthorized parties. We encrypt a matrix of plaintext bits as a single ciphertext to reduce the ciphertext expansion ratio and reduce the public key size by encrypting with a quadratic form in three types of public key elements and pseudo-random number generators. Additionally, we make the FFHE scheme more applicable by generalizing the homomorphism of addition and multiplication of floating-point numbers to analytic functions using the Taylor formula. We prove that the FFHE scheme for ciphertext operation may limit an additional loss of accuracy. Specifically, the precision of the ciphertext operation’s result is similar to unencrypted floating-point number computation. Compared to other schemes, our FFHE scheme is more practical for privacy-preserving in the cloud environment with its low ciphertext expansion ratio and public key size, supporting multiple operation types and high precision.