Application and analysis of non-commutative structure to post-quantum cryptography

• Project/Area Number: 17K00197
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Information security
• Research Institution: Okayama University of Science
• Principal Investigator: Yasuda Takanori 岡山理科大学, 工学部, 准教授 (00464602)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 耐量子暗号 / 多変数多項式公開鍵暗号 / 格子ベース暗号 / 公開鍵暗号 / 多変数公開鍵暗号 / 暗号・認証等 / 応用数学 / 量子コンピュータ

Outline of Final Research Achievements

As a new mathematical problem which is resistant to quantum computer, I introduced the constrained MP problem. Compared with the mathematical problem, the usual MP problem which was often used, the constrained MP problem is easy to provide with encryption schemes on the multivariate public-key cryptosystems. In fact, I developed two encryption schemes using it. Such encryption scheme is possible to have non-commutative structure, therefore, it is highly secure. Moreover, since it has efficient encryption and decryption algorithm, it becomes practical.

Academic Significance and Societal Importance of the Research Achievements

提案した暗号方式が、量子コンピュータに耐性を持つ公開鍵暗号の１つとして標準化され、未来の暗号基盤を支える重要な要素として通信などの安全性を守っていく可能性がある。

Research Products

• [Journal Article] Multivariate Encryption Schemes Based on Polynomial Equations over Real Numbers (2020)
  • Author(s): Takanori Yasuda, Yacheng Wang, Tsuyoshi Takagi
  • Journal Title: Lecture Notes in Computer Science Volume: 12100 Pages: 402-421
  • DOI: 10.1007/978-3-030-44223-1_22
  • ISBN: 9783030442224, 9783030442231
  • Peer Reviewed / Open Access
• [Journal Article] Multivariate Encryption Schemes Based on the Constrained MQ Problem (2018)
  • Author(s): Takanori Yasuda
  • Journal Title: Lecture Notes in Computer Science Volume: 11192 Pages: 129-146
  • DOI: 10.1007/978-3-030-01446-9_8
  • ISBN: 9783030014452, 9783030014469
  • Peer Reviewed
• [Presentation] ノイズを利用した多変数公開鍵暗号 (2020)
  • Author(s): 安田貴徳
  • Organizer: Symposium on Cryptography and Information Security (SCIS2020)
• [Presentation] 制約付きMP問題に基づいた多変数公開鍵暗号方式 (2018)
  • Author(s): 安田貴徳
  • Organizer: Symposium on Cryptography and Information Security (SCIS2019)
• [Presentation] ペアリング高速計算に適した楕円曲線からその適切な部分群への効率的な写像 (2018)
  • Author(s): 安田貴徳
  • Organizer: 2018 Symposium on Cryptography and Information Security (SCIS2018)