Elliptic Curve Cryptography (ECC) is an encryption method that provides security comparable to traditional techniques like Rivest–Shamir–Adleman (RSA) but with lower computational complexity and smaller key sizes, making it a competitive option for applications such as blockchain, secure multi-party computation, and database security. However, the throughput of ECC is still hindered by the significant performance overhead associated with elliptic curve (EC) operations, which can affect their efficiency in real-world scenarios. This article presents gECC , a versatile framework for ECC optimized for GPU architectures, specifically engineered to achieve high-throughput performance in EC operations. To maximize throughput, gECC incorporates batch-based execution of EC operations and microarchitecture-level optimization of modular arithmetic. It employs Montgomery’s trick [ 40 ] to enable batch EC computation and incorporates novel computation parallelization and memory management techniques to maximize the computation parallelism and minimize the access overhead of GPU global memory. Furthermore, we analyze the primary bottleneck in modular multiplication by investigating how the user codes of modular multiplication are compiled into hardware instructions and what these instructions’ issuance rates are. We identify that the efficiency of modular multiplication is highly dependent on the number of Integer Multiply-Add (IMAD) instructions. To eliminate this bottleneck, we propose novel techniques to minimize the number of IMAD instructions by leveraging predicate registers to pass the carry information and using addition and subtraction instructions (IADD3) to replace IMAD instructions. Our experimental results show that, for ECDSA and ECDH, the two commonly used ECC algorithms, gECC can achieve performance improvements of 5.56 × and 4.94 ×, respectively, compared to the state-of-the-art GPU-based system. In a real-world blockchain application, we can achieve performance improvements of 1.56 ×, compared to the state-of-the-art CPU-based system. gECC is completely and freely available at https://github.com/CGCL-codes/gECC .

This is a corrigendum for the article “gECC: A GPU-based high-throughput framework for Elliptic Curve Cryptography” published in ACM Trans. Arch. Code Optim. 22, 3, Article 84 (September 2025), 27 pages.

Data stream clustering is a critical operation in various real-world applications, ranging from the Internet of Things (IoT) to social media and financial systems. Existing data stream clustering algorithms often lack the flexibility and self-optimization capabilities needed to adapt to diverse workload characteristics such as outlier, cluster evolution and changing dimensions in data points. These limitations manifest in suboptimal clustering accuracy and computational inefficiency. In this paper, we introduce MOStream, a modular and self-optimizing data stream clustering algorithm to dynamically balance clustering accuracy and computational efficiency at runtime. MOStream distinguishes itself by its adaptivity, clearly demarcating four pivotal design dimensions: the summarizing data structure, the window model for handling data temporality, the outlier detection mechanism, and the refinement strategy for improving cluster quality. This clear separation facilitates flexible adaptation to varying design choices and enhances its adaptability to a wide array of application contexts. We conduct a rigorous performance evaluation of MOStream, employing diverse configurations and benchmarking it against 9 representative data stream clustering algorithms on 4 real-world datasets and 3 synthetic datasets. Our empirical results demonstrate that MOStream consistently surpasses competing algorithms in terms of clustering accuracy, processing throughput, and adaptability to varying data stream characteristics.

Data Stream Clustering (DSC) plays an important role in mining continuous and unlabeled data streams in real-world applications. Over the last decades, numerous DSC algorithms have been proposed with promising clustering accuracy and efficiency. Despite the significant differences among existing DSC algorithms, they are commonly built around four key design aspects: summarizing data structure, window model, outlier detection mechanism, and offline refinement strategy. However, there is a lack of empirical studies on these key design aspects in the same codebase using real-world workloads with distinct characteristics. As a result, it is difficult for researchers to improve upon the state-of-the-art. In this paper, we conduct such a study of DSC on its four key design aspects. We implemented state-of-the-art variants of all of these design choices in an open-sourced platform from scratch and evaluated them using both real-world and synthetic workloads. Our analysis identifies the fundamental issues and trade-offs of each design choice in terms of both accuracy and efficiency. We even find that combining flexible design choices led to the development of a new algorithm called Benne, which can be tuned to achieve either better accuracy or better efficiency compared to the state-of-the-art.