Security analysis on post-quantum cryptography based on multivariate quadratic polynomial problem

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K20266
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60070:Information security-related
• Research Institution: Kyushu University
• Principal Investigator: Ikematsu Yasuhiko 九州大学, マス・フォア・インダストリ研究所, 助教 (40833570)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 耐量子計算機暗号 / 多変数多項式暗号

Outline of Final Research Achievements

We studied the security analysis on multivariate public key cryptography (MPKC) based on the hardness of solving multivariate quadratic equations over finite fields. In particular, we analysed various multivariate cryptosystems, including schemes submitted to the NIST PQC standardization project, aiming at a precise estimation of the Groebner basis attacks and rank attacks. As a result, we found vulnerabilities in some schemes and proposed security estimations based on new attack methods. Moreover, using the results obtained in this study, we proposed a signature scheme and ID scheme.

Free Research Field

暗号理論

Academic Significance and Societal Importance of the Research Achievements

多変数多項式暗号は連立二次方程式の求解困難性を利用した耐量子計算機暗号の一つであり、量子コンピュータ時代における次世代暗号として必要不可欠な技術となっている。本研究課題で提案した方式や安全性解析手法により、安心・安全な耐量子計算機暗号の実用化に貢献できれば、量子コンピュータ時代の暗号基盤を支える重要な要素となり、社会に与えるインパクトは大きい。