Security analysis and development of post-quantum cryptography using optimization theory

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K03741
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Okayama University of Science
• Principal Investigator: Yasuda Takanori 岡山理科大学, 基盤教育センター, 准教授 (00464602)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 公開鍵暗号 / 耐量子暗号 / 多変数公開鍵暗号 / 最適化理論 / 格子ベース暗号

Outline of Final Research Achievements

We constructed a lattice-based cryptosystem as an analogue of a multivariate public-key cryptosystem. This is an application of the construction method using optimization theory. We also found a vulnerability in the secret key of MQ-sign, a signature scheme for multivariate public-key cryptosystems, and proposed an attack method using it. This made it impossible to use some parts of MQ-sign securely. We also proposed an attack method that can be used under certain conditions against public-key cryptosystems based on two-sided composition by linear transformation of multivariate polynomial systems.

Free Research Field

暗号理論

Academic Significance and Societal Importance of the Research Achievements

多変数公開鍵暗号では、様々な暗号方式や署名方式が提案されている。特に、UOVと呼ばれる署名方式は安全とされているが、その秘密鍵の鍵長削減などを行うと、必ずしも安全ではなくなくことを明らかにできた。また、これまであまり関連性がなかった多変数公開鍵暗号と格子ベース暗号であったが、どちらの特徴を持つ暗号方式を提案したことで、２つの中間の状態の公開鍵暗号が存在することを明らかにできた。