Open Access

ARTICLE

Pareto-Based Multi-Objective Evaluation of Multivariate Signature Schemes in the NIST Standardization Process

Jian Zhang¹, Seong-Min Cho², Seung-Hyun Seo^3,*

1 Department of Electrical and Electronic Engineering, Graduate School, Hanyang University, Seoul, Republic of Korea
2 Electronics and Telecommunications Research Institute (ETRI), Daejeon, Republic of Korea
3 Division of Electrical Engineering, Hanyang University ERICA, Ansan, Republic of Korea

* Corresponding Author: Seung-Hyun Seo. Email:

Computers, Materials & Continua 2026, 89(1), 80 https://doi.org/10.32604/cmc.2026.084319

Received 20 April 2026; Accepted 02 July 2026; Issue published 13 August 2026

Abstract

Classical digital signature schemes such as RSA and ECDSA are threatened by the development of quantum computers, prompting the need for post-quantum cryptography (PQC). Among the various PQC candidates, multivariate quadratic (MQ) signature schemes have attracted significant attention due to their small signature size and efficient signing and verification. Evaluating these schemes is challenging because compactness, computational efficiency, and effective security are objectives that often conflict with one another and cannot usually be optimized simultaneously. In this work, we adapt a systematic multi-objective evaluation framework to MQ-based signature schemes in the NIST additional digital signature standardization process. The framework is based on Pareto optimality and enables a structured comparison of trade-offs among public key size, signature size, computational performance, and effective security without relying on subjective weighting. By representing each scheme in a multi-dimensional objective space, the Pareto-based framework used in this work identifies non-dominated schemes. Using this framework, we conduct a comparative analysis of four representative MQ-based signature schemes—UOV, MAYO, QR-UOV, and SNOVA. We analyze their design principles, parameter choices, performance characteristics, and security against known cryptanalytic attacks. To improve reproducibility and reduce hardware-related bias, all schemes are executed and evaluated on a unified platform, and performance metrics are obtained through repeated experiments. The results reveal that no single scheme simultaneously optimizes all criteria, highlighting inherent trade-offs among MQ-based designs. This Pareto-based evaluation framework provides a structured and reproducible approach for evaluating PQC schemes and offers practical insights for selecting appropriate schemes under different system and performance requirements.

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Keywords

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