| Presentation | 2018-05-16 Hardness of Discrete Logarithm Problem Based on New Operation on Elliptic Curve over Finite Field and New Digital Signature Masaaki Shirase, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In the previous works, a new operation on elliptic curve over finite field $E(Fp)$, the Me operation $oplus$, is defined, and the Me scalar multiplication $P_{n,Z}$ for $P,Z in Fp$ and $n in N$ is defined. Moreover, the MeDLP (given $P,Z,P_{n,Z}$, compute $n$), the MeCDH (given $P_{n,Z}$ and $P_{m,Z}$, compute $(P_{n,Z})_{m,Z})$, and the modified MeCDH are defined. Although the MeCDH can be solved easily, the hardness of the MeDLP and the modified MeCDH were unknown. First, this report gives a solution of the modified MeCDH. Second, this report defines the MeDLP' as given $(P,z,P_{n,zP}) in E(Fp) times Z times E(Fp)$, compute $n in N$, and shows that the MeDLP' is as hard as, or harder than the ECDLP. Last, this report proposes a digital signature using the Me scalar multiplication. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | Elliptic curve cryptosystem / M operation / Me operation / Digital signature / Discrete logarithm problem |
| Paper # | ISEC2018-1 |
| Date of Issue | 2018-05-09 (ISEC) |
| Conference Information | |
| Committee | ISEC |
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| Conference Date | 2018/5/16(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Ookayama Campus, Tokyo Institute of Technology |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | Kazuto Ogawa(NHK) |
| Vice Chair | Atsushi Fujioka(Kanagawa Univ.) / Shiho Moriai(NICT) |
| Secretary | Atsushi Fujioka(Tohoku Univ.) / Shiho Moriai(Tokai Univ.) |
| Assistant | Keita Emura(NICT) / Yuichi Komano(TOSHIBA) / Yuuji Suga(IIJ) |
| 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) | Hardness of Discrete Logarithm Problem Based on New Operation on Elliptic Curve over Finite Field and New Digital Signature |
| Sub Title (in English) | |
| Keyword(1) | Elliptic curve cryptosystem |
| Keyword(2) | M operation |
| Keyword(3) | Me operation |
| Keyword(4) | Digital signature |
| Keyword(5) | Discrete logarithm problem |
| 1st Author's Name | Masaaki Shirase |
| 1st Author's Affiliation | Future University Hakodate(FUN) |
| Date | 2018-05-16 |
| Paper # | ISEC2018-1 |
| Volume (vol) | vol.118 |
| Number (no) | ISEC-30 |
| Page | pp.pp.1-8(ISEC), |
| #Pages | 8 |
| Date of Issue | 2018-05-09 (ISEC) |