| Presentation | 2022-03-10 A New Necessary and Sufficient Condition for the Existence of a one-bit Secret Sharing Scheme and Its Applications Ryo Okamura, Hiroki Koga, |
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| PDF Download Page |  PDF download Page Link |
| Abstract(in Japanese) | (See Japanese page) |
| Abstract(in English) | In a secret sharing scheme, a dealer generates $n$ shares from a secret and distributes the $n$ shares to respective participants. Recently, Bogdanov et al. clarified the conditions of the function $f$ that is equivalent to the existence of a secret sharing scheme for a 1-bit secret. They also obtained a lower bound of the share size by using the discrete Fourier transform. In this paper, we give other conditions, the decodability condition and the security condition, of the function $f$. We show that these conditions are equivalent to Bogdanov's conditions. We also show that the security condition can be expressed in a simple form by using the discrete Fourier transform. In particular, the functions that are equivalent to the $(n,n)$- and the $(n-1,n)$- thresholds scheme for a 1-bit secret are expressed in simple forms in the frequency domain. We discuss the conditions which are equivalent to the existence of a secret sharing scheme of a multiple-valued secret as well. |
| Keyword(in Japanese) | (See Japanese page) |
| Keyword(in English) | secret sharing scheme / general access structure / threshold scheme |
| Paper # | IT2021-83,ISEC2021-48,WBS2021-51,RCC2021-58 |
| Date of Issue | 2022-03-03 (IT, ISEC, WBS, RCC) |
| Conference Information | |
| Committee | IT / ISEC / RCC / WBS |
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| Conference Date | 2022/3/10(2days) |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Online |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Joint Meeting of ISEC, IT, RCC, and WBS |
| Chair | Tadashi Wadayama(Nagoya Inst. of Tech.) / Tetsuya Izu(Fujitsu Labs.) / HUAN-BANG LI(NICT) / Masanori Hamamura(Kochi Univ. of Tech.) |
| Vice Chair | Tetsuya Kojima(Tokyo Kosen) / Noboru Kunihiro(Tsukuba Univ.) / Goichiro Hanaoka(AIST) / Shunichi Azuma(Nagoya Univ.) / Koji Ishii(Kagawa Univ.) / Takashi Shono(INTEL) / Masahiro Fujii(Utsunomiya Univ.) |
| Secretary | Tetsuya Kojima(Saitamai Univ.) / Noboru Kunihiro(Yamaguchi Univ.) / Goichiro Hanaoka(Fujitsu Labs.) / Shunichi Azuma(Ibaraki Univ.) / Koji Ishii(CRIEPI) / Takashi Shono(Osaka Univ.) / Masahiro Fujii(National Defence Academy) |
| Assistant | Masanori Hirotomo(Saga Univ.) / Takahiro Matsuda(AIST) / SHAN LIN(NICT) / Masaki Ogura(Osaka Univ.) / Masayuki Kinoshita(Chiba Univ. of Tech.) / Sun Ran(Ibaraki Univ.) |
| Paper Information | |
| Registration To | Technical Committee on Information Theory / Technical Committee on Information Security / Technical Committee on Reliable Communication and Control / Technical Committee on Wideband System |
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| Language | JPN |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | A New Necessary and Sufficient Condition for the Existence of a one-bit Secret Sharing Scheme and Its Applications |
| Sub Title (in English) | |
| Keyword(1) | secret sharing scheme |
| Keyword(2) | general access structure |
| Keyword(3) | threshold scheme |
| 1st Author's Name | Ryo Okamura |
| 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 | 2022-03-10 |
| Paper # | IT2021-83,ISEC2021-48,WBS2021-51,RCC2021-58 |
| Volume (vol) | vol.121 |
| Number (no) | IT-428,ISEC-429,WBS-430,RCC-431 |
| Page | pp.pp.1-6(IT), pp.1-6(ISEC), pp.1-6(WBS), pp.1-6(RCC), |
| #Pages | 6 |
| Date of Issue | 2022-03-03 (IT, ISEC, WBS, RCC) |