This paper conducts a comprehensive benchmarking analysis of the performance of two innovative cryptographic schemes: Homomorphic Polynomial Public Key (HPPK)-Key Encapsulation Mechanism (KEM) and Digital Signature (DS), recently proposed by Kuang et al. These schemes represent a departure from traditional cryptographic paradigms, with HPPK leveraging the security of homomorphic symmetric encryption across two hidden rings without reliance on NP-hard problems. HPPK can be viewed as a specialized variant of Multivariate Public Key Cryptography (MPKC), intricately associated with two vector spaces: the polynomial vector space for the secret exchange and the multivariate vector space for randomized encapsulation. The unique integration of asymmetric, symmetric, and homomorphic cryptography within HPPK necessitates a careful examination of its performance metrics. This study focuses on the thorough benchmarking of HPPK KEM and DS across key cryptographic operations, encompassing key generation, encapsulation, decapsulation, signing, and verification. The results highlight the exceptional efficiency of HPPK, characterized by compact key sizes, cipher sizes, and signature sizes. The use of symmetric encryption in HPPK enhances its overall performance. Key findings underscore the outstanding performance of HPPK KEM and DS across various security levels, emphasizing their superiority in crucial cryptographic operations. This research positions HPPK as a promising and competitive solution for post-quantum cryptographic applications in a wide range of applications, including blockchain, digital currency, and Internet of Things (IoT) devices.

翻译：本文对两种创新密码方案——由Kuang等人近期提出的同态多项式公钥（HPPK）密钥封装机制（KEM）与数字签名（DS）——进行了全面的基准性能分析。这些方案突破了传统密码范式，HPPK通过两个隐藏环上的同态对称加密提供安全性，且不依赖NP困难问题。HPPK可视为多元公钥密码（MPKC）的特化变体，其机制紧密关联两个向量空间：用于秘密交换的多项式向量空间和用于随机化封装的多元向量空间。HPPK内部集成非对称、对称及同态密码技术的独特性，要求对其性能指标进行严谨评估。本研究聚焦于HPPK KEM与DS在关键密码操作（涵盖密钥生成、封装、解封装、签名及验签）中的深度基准测试。结果表明HPPK具有卓越效率，具体体现为紧凑的密钥尺寸、密文尺寸及签名尺寸。HPPK采用对称加密提升了整体性能。核心发现强调HPPK KEM与DS在不同安全等级下均表现优异，在关键密码操作中展现出显著优势。本研究将HPPK定位为后量子密码应用的可行且具有竞争力的解决方案，可广泛适用于区块链、数字货币及物联网（IoT）设备等场景。