Benchmark Performance of Homomorphic Polynomial Public Key Cryptography for Key Encapsulation and Digital Signature Schemes

TL;DR

The paper benchmarks two novel post-quantum schemes, HPPK KEM and HPPK DS, which rely on symmetric homomorphic encryption over two hidden rings and integrate asymmetry, symmetry, and homomorphism. By evaluating key generation, encapsulation/decapsulation, signing, and verification with SUPERCOP on multi-core hardware, it demonstrates that HPPK KEM achieves very compact key and ciphertext sizes and strong efficiency, while HPPK DS delivers compact public/private keys and signatures with highly efficient signing and verification. The results, benchmarked against NIST finalists and round-4 candidates, indicate competitive performance and smaller memory footprints, making these schemes attractive for post-quantum deployments in blockchain, digital currency, and IoT contexts. The work also discusses security considerations, including optimized DS attacks and the impact of single versus dual hidden rings, highlighting the practical viability and potential of HPPK for real-world security needs.

Abstract

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.