2018 Fiscal Year Final Research Report
On constructions and analyses of public key cryptosystems based on diophantine problems and problems on ideal lattices of global fields
| Project/Area Number |
17K18450
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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 |
Foundations of mathematics/Applied mathematics
Theory of informatics
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2019-03-31
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| Keywords | 耐量子暗号 / 格子暗号 / Ring-LWE / ディオファントス方程式 / 複数のイデアルを用いた識別攻撃 / 代入攻撃 / 格子攻撃 / IE-LWE |
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| Outline of Final Research Achievements |
Attacks against cryptosystems based on Ring-Learning With Errors（LWE）problem are mainly divided to two types. One is lattice attacks, and the other is distinguish and search attacks. We compared the difficulty of Ring-LWE problems over cyclotomic fields, which are usually used, with that over decomposition fields w.r.t. some primes. As a result, we cocluded that decomposition fields do not decrease the difficulty of Ring-LWE problem. Also, we improved a known evaluation attack against a cryptosystem based on the IE-LWE problem, which is a polynomial analogue of LWE. Our improved evaluation attack is efficient and effective against recommended parameters.
We presented our results at four internal workshops (including one invited talk) and an international conference.
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| Free Research Field |
数論アルゴリズム、暗号理論、耐量子暗号、高機能暗号
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| Academic Significance and Societal Importance of the Research Achievements |
公開鍵暗号の設計には、計算困難な数学的問題が利用される。また、現在の公開鍵暗号基盤を崩壊させることができる量子計算機が十数年以内に完成すると言われている。本研究では、量子計算機完成後も安全な暗号（耐量子暗号）の設計に利用されるRing-LWE問題と利用が期待できるディオファントス問題に着目した。特に、特殊なRing-LWE問題とある種のディオファントス問題に基づく耐量子準同型暗号の候補の安全性を、既存攻撃やその改良により検証し、今後の関数体上のRing-LWE及び有理整数環上のディオファントス問題に基づく暗号の構成と安全性解析の手法の研究において、有益な知見を与える結果であると考える。
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