Abstract

To defend against quantum computer attacks, the National Institute of Standards and Technology (NIST) has been exploring post-quantum cryptography (PQC). Now, NIST has standardized only two PQC algorithms, one of which is the Leighton-Micali signature (LMS). However, the performance of LMS limits its practical application. In this paper, we propose a parallel LMS implementation on multiple nodes. Considering different application scenarios, we provide two parallel schemes: algorithmic parallelism and data parallelism. The main part of our work is the two-tier parallel structure for the LMS tree. Targeting the x86/64 multiple nodes, our work introduces vectorization to present the three-tier parallel structure. We also design communication optimization, including the selection of communication primitives and the creation of communicators for multi-node running. Experimental evidence shows that our code effectively reduces the latency, and is 19.04 \(\times\) faster than the fastest implementation on the same platform when running key pair generation for LMS_SHA256_M32_H20(20).

中文翻译：

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后量子leighton-Micali签名在多个节点上的并行实现

摘要

为了防御量子计算机攻击，美国国家标准与技术研究院 (NIST) 一直在探索后量子密码学 (PQC)。现在，NIST 仅标准化了两种 PQC 算法，其中之一是 Leighton-Micali 签名 (LMS)。然而，LMS的性能限制了它的实际应用。在本文中，我们提出了在多个节点上并行 LMS 实现。考虑到不同的应用场景，我们提供了两种并行方案：算法并行和数据并行。我们工作的主要部分是 LMS 树的两层并行结构。针对x86/64多节点，我们的工作引入向量化来呈现三层并行结构。我们还设计了通信优化，包括通信原语的选择和多节点运行的通信器的创建。实验证据表明，我们的代码有效降低了延迟，并且在运行 LMS_SHA256_M32_H20(20) 密钥对生成时，比同一平台上最快的实现快19.04 倍。