Smart grids integrate modern Internet of Things technologies with the traditional grid systems, aiming to achieve effective and reliable electricity distribution as well as promote clean energy development. Nowadays, it is an indispensable infrastructure for smart homes, wisdom medical, intelligent transportation, and various other services. However, when smart meters transmit users’ power consumption data to the control center, sensitive information may be leaked or tampered. Moreover, distributed architecture, fine-grained access control, and user anonymity are also desirable in real-world applications. In this paper, we propose a privacy-preserving data aggregation scheme for a smart grid with user anonymity and designated recipients. Smart meters collect users’ power consumption data, encrypt it using homomorphic re-encryption, and then transmit the ciphertexts anonymously. Afterward, proxies re-encrypt the aggregated data in a distributed fashion so that only the designated recipients can decrypt it. Therefore, our proposed scheme provides a more secure and flexible solution for privacy-preserving data aggregation in smart grids. Security analyses prove that our scheme achieves all the above-mentioned security requirements, and efficiency analyses demonstrate that it is efficient and suitable for real-world applications.

In the last decade, E-voting has received great attention due to its advantages in efficiency and accuracy. Fan et al. presented a novel E-voting system named HSE-Voting by utilizing homomorphic signcryption. The HSE-Voting system was claimed to gain a provable security goal under the standard proof. In this paper, we illustrate that their scheme may suffer from some potential security issues. On the one hand, the voting information could be recovered by the authentication center (AC). On the other hand, any malicious voter could disrupt the voting system undetected by locally modifying his ballot. In order to increase the resilience of the voting system to risks, an improvement of the HSE-Voting system is developed. Our improved system fixes the above security weaknesses but increases the computation cost on the AC side by a small amount. In addition, the proposed scheme satisfies voter anonymity, ballot privacy, and verifiability of election results.

Cloud-edge collaborative learning has received considerable attention recently, which is an emerging distributed machine learning (ML) architecture for improving the performance of model training among cloud center and edge nodes. However, existing cloud-edge collaborative learning schemes cannot efficiently train high-performance models on large-scale sparse samples, and have the potential risk of revealing the privacy of sensitive data. In this paper, adopting homomorphic encryption (HE) cryptographic technique, we present a privacy-preserving cloud-edge collaborative learning over vertically partitioned data, which allows cloud center and edge node to securely train a shared model without a third-party coordinator, and thus greatly reduces the system complexity. Furthermore, the proposed scheme adopts the batching technique and single instruction multiple data (SIMD) to achieve parallel processing. Finally, the evaluation results show that the proposed scheme improves the model performance and reduces the training time compared with the existing methods; the security analysis indicates that our scheme can guarantee the security in semi-honest model.

Collaborative learning is an emerging distributed learning paradigm, which enables multiple parties to jointly train a shared machine learning (ML) model without causing the disclosure of the raw data of each party. As one of the fundamental collaborative learning algorithms, privacy-preserving collaborative logistic regression has recently gained attention from industry and academia, which utilizes cryptographic techniques to securely train joint logistic regression models across data from multiple parties. However, existing schemes have high communication and computational overhead, lose the ability to deal with high-dimensional sparse samples, cut down the accuracy of the model, or exist the risk of leaking private information. To overcome these issues, considering vertically distributed data, we propose a privacy-preserving vertical collaborative logistic regression ( VCLR) based on approximate homomorphic encryption (HE), which enables two parties to jointly train a shared model without a trusted third-party coordinator. Our scheme utilizes batching method in approximate HE to encrypt multiple data into a single ciphertext and enable a parallel processing through single instruction multiple data (SIMD) manner. We evaluate our scheme by using three publicly available datasets, the experimental results indicate that our scheme outperforms existing schemes in terms of training time and model performance.

Let $p$ be a prime. In this paper, we present a detailed $p$ -adic analysis on factorials and double factorials and their congruences. We give good bounds for the $p$ -adic sizes of the coefficients of the divided universal Bernoulli number ${B}_{n} / n$ when $n$ is divisible by $p- 1$ . Using these, we then establish the universal Kummer congruences modulo powers of a prime $p$ for the divided universal Bernoulli numbers ${B}_{n} / n$ when $n$ is divisible by $p- 1$ .

Logistic regression is a data statistical technique, which is used to predict the probability that an event occurs. For some scenarios where the storage capabilities and computing resources of the data owner are limited, the data owner wants to train the logistic regression model on the cloud service provider, while the high sensitivity of training data requires effective privacy protection methods that enable efficient model training without exposing information about the training data to untrusted cloud service providers. Recently, several works have used cryptographic techniques to implement privacy-preserving logistic regression in such application scenarios. However, on large-scale training datasets, the existing works still have the problems of long model training time and poor model performance. To solve these problems, based on the homomorphic encryption (HE), we propose an efficient privacy-preserving outsourced logistic regression (P²OLR) on encrypted training data, which enables data owners to utilize the powerful storage and computing resources of cloud service providers for logistic regression analysis without exposing data privacy. Furthermore, the proposed scheme can pack multiple messages into one ciphertext and perform the same arithmetic evaluations on multiple plaintext slots by using the batching technique and single instruction multiple data (SIMD) mechanism in HE. On three public training datasets, the experimental results show that, compared with the existing schemes, the proposed scheme has better performance in terms of the encryption and decryption time of the data owner, the storage of encrypted training data, and the training time and accuracy of the model.