| Presentation | 2007-11-22 Reduction Optimal Polynomials over GF(3) with Four Terms Toshiya NAKAJIMA, Tetsuya IZU, Tsuyoshi TAKAGI, |
|---|---|
| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In [10] we proposed to use the "Reduction Optimal Trinomials (ROTs)" which make reduction in GF(3^m) multiplication efficient for software implementation of the ηT pairing. We also showed examples of ROTs which are suitable to enough security levels for the ηT pairing. This time we search "Reduction Optimal Polynomials with Four Terms (ROP-4's)" (which are extension of ROTs to four terms) for m's with which no irreducible trinomials (including ROTs) exist. We call such m's "non-trinomial degrees". To avoid exhaustive search in every non-trinomial degree, we add another condition regarding characteristic of the finite field to ROP-4's and derive necessary conditions of m for existence of such "restricted" ROP-4's by calculating discriminants of them. Searching in non-trinomial degrees which satisfy the necessary conditions with m≦512, we found restricted ROP-4's for m=98, 311 and 397. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | finite field / characteristic three / ηT pairing / software implementation / reduction / ROT / restricted ROP-4 / discriminant / resultant |
| Paper # | ISEC2007-103,OIS2007-75 |
| Date of Issue |
| Conference Information | |
| Committee | ISEC |
|---|---|
| Conference Date | 2007/11/15(1days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | |
| Chair | |
| Vice Chair | |
| Secretary | |
| Assistant | |
| Paper Information | |
| Registration To | Information Security (ISEC) |
|---|---|
| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Reduction Optimal Polynomials over GF(3) with Four Terms |
| Sub Title (in English) | |
| Keyword(1) | finite field |
| Keyword(2) | characteristic three |
| Keyword(3) | ηT pairing |
| Keyword(4) | software implementation |
| Keyword(5) | reduction |
| Keyword(6) | ROT |
| Keyword(7) | restricted ROP-4 |
| Keyword(8) | discriminant |
| Keyword(9) | resultant |
| 1st Author's Name | Toshiya NAKAJIMA |
| 1st Author's Affiliation | Fujitsu Ltd.() |
| 2nd Author's Name | Tetsuya IZU |
| 2nd Author's Affiliation | Fujitsu Laboratories Ltd. |
| 3rd Author's Name | Tsuyoshi TAKAGI |
| 3rd Author's Affiliation | Future University-Hakodate School of Systems Information Science |
| Date | 2007-11-22 |
| Paper # | ISEC2007-103,OIS2007-75 |
| Volume (vol) | vol.107 |
| Number (no) | 346 |
| Page | pp.pp.- |
| #Pages | 6 |
| Date of Issue | |