2016 Fiscal Year Research-status Report
格子最短ベクトル問題と準同型暗号の安全性に関する研究
| Project/Area Number |
16K17644
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| Research Institution | Kyushu University |
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Principal Investigator |
Duong Hoang・Dung 九州大学, マス・フォア・インダストリ研究所, 助教 (40770970)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | Lattice cryptography / MPKC |
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| Outline of Annual Research Achievements |
In the academic year H28, we investigated lattice and multivariate cryptography.
In lattice cryptography, we investigate fully homomorphic encryption schemes and applications. We first investigated the somewhat homomorphic encryption (SHE) scheme proposed by Brakerski and Vaikuntanathan and proposed efficient methods for matrix multiplications using RLWE-based homomorphic encryption. Our methods are every efficient and outperform previous methods for secure matrix multiplication. One journal paper was published in this topic, its extended abstract was accepted and presented at an international conference.
In multivariate cryptography (MPKC), we first investigated the SRP encryption scheme and proposed an efficient way to reduce the its public key size - one of the main problems in MPKC. Next we revisited the Cubic UOV (CUOV) signature scheme and analysed the reason why CUOV is not secure against the Hashimoto's attack. We then propose a new efficient cubic signature scheme secure against Hashimoto's attack. Next we revisited the key generation algorithm of the ZHFE encryption scheme proposed an efficient key generation algorithm for ZHFE scheme. There papers in this area were published in international conferences.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The research is going fine and smoothly. Multivariate cryptography was not planned in the research proposal but has now come as a part of it. For Lattice Cryptography, it is a bit slower than planned, but it is now getting more smoothly with the research and we hope to obtain more results in lattice cryptography in next year.
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| Strategy for Future Research Activity |
For lattice cryptography, we will work on proposing some improving variants of lattice reduction algorithms (such as DeepLLL and algorithm for solving CVP by using voronoi cells) and we will work on designing efficient fully homomorphic encryption schemes.
For multivariate cryptography, we will work on security evaluation of existing multivariate encryption and signature schemes.
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| Causes of Carryover |
We need money for travels/visits and hiring students for doing implementation as well as buying some more books and devices.
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| Expenditure Plan for Carryover Budget |
I plan to visit abroad for conferences or joint research and hire some students for joint research and implementation
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