Security Evaluation of Representative Post-quantum Cryptographic Scheme from Lattices

2018 Fiscal Year Final Research Report

• Project/Area Number: 17H06571
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Information security
• Research Institution: The University of Tokyo
• Principal Investigator: Takayasu Atsushi 東京大学, 大学院情報理工学系研究科, 助教 (00808082)
• Project Period (FY): 2017-08-25 – 2019-03-31
• Keywords: 耐量子暗号 / 格子 / learning with errors問題 / 最短ベクトル問題 / 安全性解析

Outline of Final Research Achievements

It is widely known that RSA/ECC is insecure in the presence of quantum computers. Thus, I work on the security estimation of post-quantum cryptography. In particular, I focus on lattice-based cryptography as the representative post-quantum scheme. Therefore, I study the hardness of the shortest vector problem and learning with errors problem in this project. I first find a necessary and sufficient condition when the LLL algorithm outputs the shortest non-zero lattice vector in small dimensions. Then, I further work on the learning with errors. I provide a generic framework to study the hardness of the learning with errors in general formulation.

Free Research Field

暗号理論

Academic Significance and Societal Importance of the Research Achievements

これまで、格子暗号の安全性を見積もるために、Kannanの埋め込み法とBai-Galbraithの埋め込み法の二つが広く用いられてきた。本研究は、格子暗号の安全性を見積もるためのLWE問題の一般的な定式化を捉え、従来よりもLWE問題の計算量解析をより統一的に行えるようになったという意味で学術的意義を持つ。さらに、本研究は、将来量子計算機が実用化された場合の情報社会の安全性を守るための耐量子公開鍵暗号の実用化へ向けて重要な社会的意義を持つ研究となった。