| Presentation | 2012-11-22 A note on subgroup decision problem and pairing inversion problem Naoki KANAYAMA, Shigenori UCHIYAMA, Eiji OKAMOTO, |
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| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In the present paper, we treat hardness of the subgroup decision problem. In 2005, Boneh et al. proposed a homomorphic encryption scheme whose security is based on hardness of the subgroup decision problem. The subgroup decision problem is stated as follows. Given a group G of composite order N=l_1l_2, where l_1 and l_2 are distinct primes, and generators g of G and gl_1 of the subgroup of order l_1, distinguish between whether an element T is a random member of the subgroup or a random element of the full group G. They also proposed to use elliptic curves which have subgroups whose group orders are large composite integers. If the factorization of the group order is known, the subgroup decision problem on such elliptic curves are efficiently solved. Therefore, we must choose composite integers such as RSA-modulus to construct groups in which the subgroup decision problem is hard. In the present paper, we show that the subgroup decision problem on bilinear group is reduced to pairing inversion problem when the group order is of the form N=l_1l_2. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | elliptic curves / bilinear groups / subgroup decision problem / pairing inversion problem |
| Paper # | ISEC2012-70,LOIS2012-45 |
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| Committee | LOIS |
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| Conference Date | 2012/11/14(1days) |
| Place (in Japanese) | (See Japanese page) |
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| Topics (in Japanese) | (See Japanese page) |
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| Registration To | Life Intelligence and Office Information Systems (LOIS) |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A note on subgroup decision problem and pairing inversion problem |
| Sub Title (in English) | |
| Keyword(1) | elliptic curves |
| Keyword(2) | bilinear groups |
| Keyword(3) | subgroup decision problem |
| Keyword(4) | pairing inversion problem |
| 1st Author's Name | Naoki KANAYAMA |
| 1st Author's Affiliation | Graduate School of Systems and Information Engineering, University of Tsukuba() |
| 2nd Author's Name | Shigenori UCHIYAMA |
| 2nd Author's Affiliation | Graduate School of Science and Engineering, Tokyo Metropolitan University |
| 3rd Author's Name | Eiji OKAMOTO |
| 3rd Author's Affiliation | Graduate School of Systems and Information Engineering, University of Tsukuba |
| Date | 2012-11-22 |
| Paper # | ISEC2012-70,LOIS2012-45 |
| Volume (vol) | vol.112 |
| Number (no) | 306 |
| Page | pp.pp.- |
| #Pages | 4 |
| Date of Issue | |