Study and development of advanced elliptic curve cryptosystem

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K11966
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 60070:Information security-related
• Research Institution: Future University-Hakodate
• Principal Investigator: Shirase Masaaki 公立はこだて未来大学, システム情報科学部, 教授 (70530757)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: 暗号 / 楕円曲線 / ペアリング / 同種写像 / 高速実装

Outline of Final Research Achievements

For elliptic curve cryptography, the principal investigator proposed an algorithm to search for an elliptic curve suitable for hardware implementation because the remainder is efficiently calculated, and implemented scalar multiplication of an elliptic curve using the curve found by the algorithm on FPGA. He also proposed quadratic and cubic characteristics on elliptic curves, and suggested efficient methods for determining the evenness of the order of points and the ploidy of 3 or 4 using these characteristics. For pairing cryptosystems, he improved the extension field construction method and final exponentiation calculation for pairing-friendly curves with various embedded degrees. For SIDH, which is one of post-quantum cryptography, he improved the composition of the extension field and the calculation method using the isomorphism. He proposed a pseudo-random number generation method using the Me operation, which is a new operation of elliptic curves.

Free Research Field

情報セキュリティ

Academic Significance and Societal Importance of the Research Achievements

電子署名ECDSAや鍵共有ECDHEを含む楕円曲線暗号は現在SSL/TLS通信やブロックチェーン等で広く普及している．IDベース暗号やグループ署名，属性ベース暗号などの機能性を有した暗号技術である高機能暗号は，その多くは楕円曲線上のペアリング写像を利用している．楕円曲線間の同種写像は，耐量子計算機の出現後も安全性が保たれる同種写像暗号の構成に利用される．このように楕円曲線は，様々なタイプの暗号技術の構成要素となっている．本研究はこれらの暗号の高速化や新しい演算Meの暗号技術への応用に対する成果を得ており，暗号技術や情報セキュリティ分野に貢献した．