2023 Fiscal Year Final Research Report
Mathematical properties of multivariate polynomial cryptosystems and their application to security analysis
| Project/Area Number |
19K20270
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 60070:Information security-related
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| Research Institution | Meijo University (2022-2023)
Shimane University (2019-2021) |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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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 / 置換群 |
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| 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 subgroups of the polynomial automorphism groups over finite fields.
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| Free Research Field |
計算代数幾何学
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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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