| Presentation | 2018-03-08 Construction of Secret Sharing Schemes with Small Thresholds for Countably Infinite Participants Takashi Hisatome, Hiroki Koga, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In Shamir's (k, n)-threshold scheme, given a secret S a dealer generates n shares by using a random polynomial of degree k-1 over a finite field Fq. While S is recovered from arbitrary collection of more than or equal to k shares, no information about S is revealed from any collection of less than k shares. In Shamir's scheme the number of shares is at most q-1. Recently, Komargodski et al give a construction of a secret sharing scheme called the evolving k-THR in which for a given secret S a dealer can generate countably infinite shares with the property similar to Shamir's (k,n)-threshold scheme. In this paper, we propose new simple constructions of the evolving 3-THR and 4-THR and evaluate the sizes of the shares. In particular, we prove that the size of the share of the t-th participant can be reduced to O((log log t)^2) in the evolving 3-THR. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | secret sharing schemes / evolving k-THRs |
| Paper # | IT2017-108,ISEC2017-96,WBS2017-89 |
| Date of Issue | 2018-03-01 (IT, ISEC, WBS) |
| Conference Information | |
| Committee | WBS / IT / ISEC |
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| Conference Date | 2018/3/8(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Katsusika Campas, Tokyo University of Science |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | joint meeting of IT, ISEC, and WBS |
| Chair | Fumiaki Maehara(Waseda Univ.) / Masayoshi Ohashi(Fukuoka Univ.) / Kazuto Ogawa(NHK) |
| Vice Chair | Masanori Hamamura(Kochi Univ. of Tech.) / Fumie Ono(NICT) / Jun Muramatsu(NTT) / Atsushi Fujioka(Kanagawa Univ.) / Shiho Moriai(NICT) |
| Secretary | Masanori Hamamura(Mitsubishi Electric) / Fumie Ono(Ibaraki Univ.) / Jun Muramatsu(Yokohama College of Commerce) / Atsushi Fujioka(UEC) / Shiho Moriai(Tohoku Univ.) |
| Assistant | Akira Nakamura(Tokyo Univ. of Science) / Ryohei Nakamura(National Defense Academy) / Sigeaki Kuzuoka(wakayama univ.) / Keita Emura(NICT) / Yuichi Komano(TOSHIBA) / Yuuji Suga(IIJ) |
| Paper Information | |
| Registration To | Technical Committee on Wideband System / Technical Committee on Information Theory / 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) | Construction of Secret Sharing Schemes with Small Thresholds for Countably Infinite Participants |
| Sub Title (in English) | |
| Keyword(1) | secret sharing schemes |
| Keyword(2) | evolving k-THRs |
| 1st Author's Name | Takashi Hisatome |
| 1st Author's Affiliation | University of Tsukuba(Univ. Tsukuba) |
| 2nd Author's Name | Hiroki Koga |
| 2nd Author's Affiliation | University of Tsukuba(Univ. Tsukuba) |
| Date | 2018-03-08 |
| Paper # | IT2017-108,ISEC2017-96,WBS2017-89 |
| Volume (vol) | vol.117 |
| Number (no) | IT-487,ISEC-488,WBS-489 |
| Page | pp.pp.31-36(IT), pp.31-36(ISEC), pp.31-36(WBS), |
| #Pages | 6 |
| Date of Issue | 2018-03-01 (IT, ISEC, WBS) |