The Internet of Things (IoT) is ubiquitous in our lives. However, the inherent vulnerability of IoT smart devices can lead to the destruction of networks in untrustworthy environments. Therefore, authentication is a necessary tool to ensure the legitimacy of nodes and protect data security. Naturally, the authentication factors always include various sensitive users’ information, such as passwords, ID cards, even biological information, etc. How to prevent privacy leakage has always been a problem faced by the IoT. Zero-knowledge authentication is a crucial cryptographic technology that uses authenticates nodes on the networks without revealing identity or any other data entered by users. However, zero-knowledge proof (ZKP) requires more complex data exchange protocols and more data transmission compared to traditional cryptography technologies. To understand how zero-knowledge authentication works in IoT, we produce a survey on zero-knowledge authentication in privacy-preserving IoT in the paper. First, we overview the IoT architecture and privacy, including security challenges and open question in different IoT layers. Next, we overview zero-knowledge authentication and provide a comprehensive analysis of designing zero-knowledge authentication protocols in various IoT networks. We summarize the advantages of ZKP-based authentication in IoT. Finally, it summarizes the potential problems and future directions of ZKP in IoT.

Since the first fully homomorphic encryption scheme was published in 2009, many papers have been published on fully homomorphic encryption and its applications. Machine learning is one of the most interesting applications and has drawn a lot of attention from researchers. To better represent and understand the field of Homomorphic Encryption in Machine Learning (HEML), this paper utilizes automated citation and topic analysis to characterize the HEML research literature over the years and provide the bibliometrics assessments for this burgeoning field. This is conducted by using a bibliometric statistical analysis approach. We make use of web-based literature databases and automated tools to present the development of HEML. This allows us to target several popular topics for in-depth discussion. To achieve these goals, we have chosen the well-established Scopus literature database and analyzed them through keyword counts and Scopus relevance searches. The results show a relative increase in the number of papers published each year that involve both homomorphic cryptography and machine learning. Using text mining of articles titles, we have found that cloud computing is a popular topic in this field, which also includes neural networks, big data, and the Internet of Things. The analysis results show that China, the US, and India have generated almost half of all the research contributions in HEML. The citation statistics, keyword statistics, and topic analyses give us a quick overview of the development of the field, which can be of great help to new researchers. It is also possible to apply our methodology to other research areas, and we see great value in this approach.

This paper investigates whether ChatGPT, a large language model, can assist in the implementation of lattice-based cryptography and fully homomorphic encryption algorithms, specifically the Ring Learning-with-Errors encryption scheme and the Brakerski–Fan–Vercauteren FHE scheme. To the best of our knowledge, this study represents the first systematic exploration of ChatGPT’s ability to implement these cryptographic algorithms. Fully homomorphic encryption, despite its theoretical and practical significance, poses significant challenges due to its computational complexity and efficiency requirements. This study evaluates ChatGPT’s capability as a development tool from both algorithmic and implementation perspectives. At the algorithmic level, ChatGPT demonstrates a solid understanding of the Rring Learning-with-Errors lattice encryption scheme but faces limitations in comprehending the intricate structure of the Brakerski–Fan–Vercauteren FHE scheme. At the code level, ChatGPT can generate functional C++ implementations of both encryption schemes, significantly reducing manual coding effort. However, debugging and corrections remain necessary, particularly for the more complex Brakerski–Fan–Vercauteren scheme, where additional effort is required to ensure correctness. The findings highlight ChatGPT’s potential and limitations in supporting cryptographic algorithm development, offering insights into its application for advancing implementations of complex cryptographic systems.

Deploying neural networks on encrypted data requires efficient evaluation of nonlinear activations, especially the ReLU function, without decryption. While the CKKS homomorphic encryption scheme supports packed arithmetic over approximate numbers efficiently, its approximate semantics make direct nonlinear evaluation difficult, and polynomial surrogates often introduce approximation error and non-discrete outputs. In this work, we present a task-specific, non-interactive construction for discrete ReLU evaluation in CKKS by combining modulus-switch-based discretization with interpolation-driven lookup-table (LUT) evaluation. We instantiate this design in two complementary schemes. The first uses trigonometric Hermite interpolation and functional bootstrapping to compute a discrete sign indicator, which is then combined with the encrypted input through conditional multiplication to obtain the ReLU output; this variant is compact and suitable for lightweight settings. The second uses iterative most-significant-bit (MSB) bootstrapping to support larger plaintext moduli and higher-precision regimes through repeated digit extraction. A common enabler of both schemes is a discretization step that maps approximate CKKS plaintexts to a finite integer representation; exactness in our setting therefore refers to exact evaluation over this discretized representation, while the deviation from the original CKKS plaintext is governed by the discretization error analyzed in Lemma 1. Experiments on encrypted MNIST inference and the accompanying LUT/storage analysis indicate that the proposed schemes preserve competitive accuracy relative to polynomial-approximation baselines while maintaining manageable auxiliary storage under the reported parameter settings. These results suggest that interpolation-based discrete activation is a promising alternative to polynomial approximation for selected CKKS-based encrypted inference tasks.

Encrypted recurrent inference must preserve both ciphertext depth and the numerical behavior of a feedback model. We develop OneBoot GRU, which couples the validation-locked selection of degree-three Sigmoid and degree-seven Tanh domains with a CKKS GRU cell that refreshes one hidden-state ciphertext after each step. On TwoPatterns, the locked polynomial model completed finite official-test trajectories with 92.431% macro accuracy, versus 98.114% for exact activations, and 0.830% mean domain violations. On SyntheticControl, polynomial and exact macro accuracies were 89.067% and 90.133%. Direct state-error comparisons show that improved domain coverage does not always reduce recurrent error; in a separate exploratory domain extension, screening reduced qualification tail error by 74.1% and 94.6% on ECG200 and ItalyPowerDemand. A parameter profile audited against pinned 128-bit sparse-secret references completed four encrypted recurrent steps, prefix pooling, and the trained head with maximum logit error 2.91 × 10⁻⁶ relative to the plaintext polynomial circuit. In three matched four-step runs, GRU median circuit latency was 226.343 s versus 336.981 s for an implemented polynomial LSTM. Twelve additional distinct 128-step inputs were completed under an intentionally insecure structural profile, with 12/12 prediction agreement against the plaintext polynomial reference. These experiments provide measured calibration, arithmetic-fidelity, and system-cost operating points within their stated parameter and sampling scopes.