Digital Signature Performance of a New Quantum Safe Multivariate Polynomial Public Key Algorithm

Abstract

This paper presents a comprehensive benchmarking analysis of the Homomorphic Polynomial Public Key (HPPK) Key Encapsulation Mechanism (KEM) and Digital Signature (DS), recently introduced by Kuang et al. Departing from traditional cryptographic approaches, these schemes leverage the security of homomorphic symmetric encryption across two hidden rings without relying on NP-hard problems. HPPK can be considered a specialized variant of Multivariate Public Key Cryptography (MPKC), intricately associated with two vector spaces: the polynomial vector space for secret exchange and the multivariate vector space for randomized encapsulation.Given the unique integration of asymmetric, symmetric, and homomorphic cryptography within HPPK, a meticulous examination of its performance metrics is imperative. This study focuses on a comprehensive benchmarking of HPPK KEM and DS, spanning key cryptographic operations, including key generation, encapsulation, decapsulation, signing, and verification. The results underscore the exceptional efficiency of HPPK, characterized by compact key sizes, cipher sizes, and signature sizes. The incorporation of symmetric encryption enhances overall performance. Key findings highlight the outstanding performance of HPPK KEM and DS across various security levels, emphasizing their superiority in critical cryptographic operations. This research positions HPPK as a promising and competitive solution for post-quantum cryptographic applications across diverse domains such as blockchain, digital currency, and Internet of Things (IoT) devices.

A Comparative Study on Post-Quantum Cryptographic Digital Signature Algorithms: Network Performance, Key Robustness, and Energy Consumption.

“…To crack MPPK/DS, attackers need to produce a fake signature for a message that can pass verification. This requires universal or selective forgery of signatures, which can be achieved by cracking public keys or signatures to obtain private keys, or by consistently brute-forcing the values A, B, C, D, and E in the verification relationship [55]. MPPK/DS is categorized by 3 main algorithms:…”

“…This technique is comparable to the encryption known-plaintext attack. In the key-only attack, it is assumed that everyone has access to the signer's public key [55]. Utilizing this information, the adversary attempts to replicate the signer's signature and digitally sign messages that the signer does not intend to.…”