Security Analysis of Elliptic Curve Cryptography using Groebner Basis

2015 Fiscal Year Final Research Report

• Project/Area Number: 25540047
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Information security
• Research Institution: Kyushu University
• Principal Investigator: Takagi Tsuyoshi 九州大学, マス・フォア・インダストリ研究所, 教授 (60404802)
• Co-Investigator(Kenkyū-buntansha): HAKUTA KEISUKE 島根大学, 総合理工学研究科, 助教 (90587099)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 暗号・認証等 / 公開鍵暗号 / 楕円曲線暗号 / 離散対数問題 / グレブナ基底

Outline of Final Research Achievements

In this research, we have investigated some algorithms using Groebner basis for solving the discrete logarithm problem over elliptic curve of characteristic 2. From the symmetric structure of Semaev polynomial we proposed an efficient algorithm that reduces the complexity and memory during the computation of Groebner basis. The proposed algorithm enables us to solve the discrete logarithm problem over elliptic curve of finite field of extension degree 29 in about 34 days using computer algebra software Magma on AMD Opteron 6276 with 512GB memory. From this cryptanalysis data we are able to estimate the computational over-limit of the expected attackers more precisely.

Free Research Field

暗号理論