| Project/Area Number |
16K16066
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Information security
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| Research Institution | Shimane University |
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Principal Investigator |
Hakuta Keisuke 島根大学, 学術研究院理工学系, 助教 (90587099)
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| Research Collaborator |
TAKAGI Tsuyoshi
DING Jintai
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | アフィン代数幾何学 / 多変数多項式暗号 / 耐量子計算機暗号 / 有限体 / 置換 / アフィン代数幾何 / 暗号・認証等 / 代数一般 / 応用数学 |
|---|
| Outline of Final Research Achievements |
The multivariate polynomial cryptosystems have emerged as one of the candidates of post-quantum cryptography. Most of the multivariate polynomial cryptosystems make use of the fact that solving a random multivariate polynomial system over a finite field is an NP-complete problem. However, multivariate polynomials with special properties are used to construct public key encryption schemes and digital signature schemes. For this reason, we need a detailed understanding of mathematical properties of multivariate polynomial cryptosystems. In this research, we showed some mathematical properties of multivariate polynomial cryptosystems. In addition, we proved relations between computational problems within the multivariate polynomial cryptosystems (so-called the Tame automorphism Decomposition Problem, TDP for short). These results may be able to provide a better understanding of the security of the multivariate polynomial cryptosystems.
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| Academic Significance and Societal Importance of the Research Achievements |
従来の公開鍵暗号は量子計算機によって多項式時間で解読可能であることが知られており、現在、量子計算機に耐性を持つ暗号技術（耐量子計算機暗号）の標準化が進められている。上記の標準化活動における安全性評価のみならず、ウェブブラウザのセキュアプロトコルであるSSL/TLSなどインフラとして利用されている暗号技術の高安全化に貢献できる可能性があるため、本研究成果は、学術的意義だけでなく、社会的意義も高いと考えられる。
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