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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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
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
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)