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进行了全面的基准性能分析：近期由Kuang等人提出的同态多项式公钥（HPPK）-密钥封装机制（KEM）与数字签名（DS）。这些方案突破了传统密码学范式，HPPK利用两个隐藏环上的同态对称加密安全性，不依赖于NP困难问题。HPPK可视为多变量公钥密码（MPKC）的一种特殊变体，其精妙地关联两个向量空间：用于秘密交换的多项式向量空间与用于随机化封装的多变量向量空间。HPPK中非对称、对称与同态密码学的独特融合，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、签名与验签）中的全面基准测试。结果表明HPPK具有卓越效率，其特征为紧凑的密钥尺寸、密文尺寸与签名尺寸。HPPK中对称加密的应用进一步提升了其整体性能。核心发现凸显了HPPK KEM与DS在不同安全等级下的出色表现，强调了其在关键密码操作中的优越性。本研究将HPPK定位为后量子密码应用（包括区块链、数字货币与物联网设备等广泛领域）中具有前景且富有竞争力的解决方案。