| Presentation | 2016-05-19 On the Possibility of Recovering Short Generators over Ideal Lattices for Cyclotomic Fields Shinya Okumura, Masaya Yasuda, Tsuyoshi Takagi, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | Recently, next-generation high-performance cryptography, e.g. post-quantum cryptography, fully homomorphic encryption schemes and cryptographic multilinear maps, using short generators over ideal lattices have attracted a lot of attention. Some of such cryptosystems use integral bases of principal ideals of cyclotomic fields as public keys and use short generators of the principal ideals as secret keys. Therefore, one can recover short generators (secret keys) by solving the principal ideal problem and the recovering short generators problem (RSGP). In this paper, we consider RSGP over $2^k$-th cyclotomic fields which are important for cryptographic applications, and we show efficient methods for extending an applicable range of a known efficient attack against RSGP and for constructing short generators having resistance to the known attack. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | ideal lattice / cyclotomic field / short generator / fast fourier transform |
| Paper # | ISEC2016-6 |
| Date of Issue | 2016-05-12 (ISEC) |
| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2016/5/19(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Kikai-Shinko-Kaikan Bldg. |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Yukiyasu Tsunoo(NEC) |
| Vice Chair | Masahiro Mambo(Kanazawa Univ.) / Kazuto Ogawa(NHK) |
| Secretary | Masahiro Mambo(AIST) / Kazuto Ogawa(Toshiba) |
| Assistant | Tetsuya Izu(Fujitsu Lab.) / Takaaki Mizuki(Tohoku Univ.) / Noritaka Yamashita(NEC) |
| Paper Information | |
| Registration To | Technical Committee on Information Security |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | On the Possibility of Recovering Short Generators over Ideal Lattices for Cyclotomic Fields |
| Sub Title (in English) | |
| Keyword(1) | ideal lattice |
| Keyword(2) | cyclotomic field |
| Keyword(3) | short generator |
| Keyword(4) | fast fourier transform |
| 1st Author's Name | Shinya Okumura |
| 1st Author's Affiliation | Kyushu University(Kyushu Univ.) |
| 2nd Author's Name | Masaya Yasuda |
| 2nd Author's Affiliation | Kyushu University(Kyushu Univ.) |
| 3rd Author's Name | Tsuyoshi Takagi |
| 3rd Author's Affiliation | Kyushu University(Kyushu Univ.) |
| Date | 2016-05-19 |
| Paper # | ISEC2016-6 |
| Volume (vol) | vol.116 |
| Number (no) | ISEC-35 |
| Page | pp.pp.25-32(ISEC), |
| #Pages | 8 |
| Date of Issue | 2016-05-12 (ISEC) |