2023 Fiscal Year Final Research Report

Large-scale experiments for cryptanalysis of lattice-based cryptography and evaluation of the computational complexity

Research Project

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Project/Area Number	20H04142
Research Category	Grant-in-Aid for Scientific Research (B)
Allocation Type	Single-year Grants
Section	一般
Review Section	Basic Section 60010:Theory of informatics-related
Research Institution	Rikkyo University
Principal Investigator	Yasuda Masaya 立教大学, 理学部, 教授 (30536313)
Co-Investigator(Kenkyū-buntansha)	鍛冶静雄九州大学, マス・フォア・インダストリ研究所, 教授 (00509656) 藤澤克樹九州大学, マス・フォア・インダストリ研究所, 教授 (40303854) 青野良範国立研究開発法人情報通信研究機構, サイバーセキュリティ研究所, 主任研究員 (50611125)
Project Period (FY)	2020-04-01 – 2024-03-31
Keywords	格子問題 / 最短ベクトル問題 / 格子アルゴリズム / 格子基底簡約 / 大規模並列化 / 列挙法 / 篩法
Outline of Final Research Achievements	Lattice-based cryptography is a next-generation cryptographic technology that is resistant to cryptanalysis by quantum computers and applicable to the construction of high-functional cryptography such as fully homomorphic encryption. The purpose of this research is to design and parallelize the best algorithms for solving lattice problems such as the shortest vector problem (SVP) that support the security of lattice-based cryptography. We also conduct large-scale solving experiments to estimate the time complexity precisely.In this research, we succeeded in developing the world's first distributed, asynchronous, and large-scale parallelization system for lattice basis reduction, which is essential for solving lattice problems. With the parallelization system, we conducted large-scale experiments for solving instances in the SVP challenge to estimate the average solving time.
Free Research Field	暗号数理
Academic Significance and Societal Importance of the Research Achievements	本研究では、耐量子性と高機能性の両方を併せ持つ格子暗号の安全性を支える数学問題に対して、実際の計算機上での解読実験を通して、その解読計算量を評価した。本研究で得られた格子暗号に対する解読技術や解析法は、高性能計算や暗号解析の分野における国際会議や学術雑誌で多数発表した。また、本研究の解読評価により、格子暗号の安全なパラメータ抽出が可能となるため、今後の格子暗号の標準化等の社会活動への貢献が期待できる。