Presentation	2001/3/15 (k,L,n) Ramp Secret Sharing Systems for Functions Yohei Kawamoto, Hirosuke Yamamoto,
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Abstract(in English)	Naor-Pinkas-Reingold's secret sharing system for a secret function S(.), that attains (k,n) threshold property for shares and l repeated uses of the system, must satisfy that H(V )〓H(S j) and H(W i)〓lmin j H(S j), where S j=S(X j) for input X j, V is a share of S j, and W i is a share of secret function S(・). Since the rates of shares, H(V ) and H(W i), are large, their scheme is inefficient from the viewpoint of coding rate. In this paper we propose a secret sharing system for functions with (k, L, n) ramp access structure proposed by Yamamoto. In the (k, L, n) scheme, k participants with V can recover secret S j, but k-L participants cannot recover S j and k-t participants, 1〓t〓L-1, have equivocation (t/L)H(S j). In this paper, we prove that any (k, L, n) scheme must satisfy that H(V )〓(1/L)H(S j) and H(W i)〓(l/L)min j H(S j). It is also shown that the lower bounds of the above inequalities can be attained by a linear (k, L, n) scheme. Furthermore, lower and upper bounds for the maximum of n and the number of X j are derived.
Keyword(in Japanese)	(See Japanese page)
Keyword(in English)	secret sharing system / secret sharing system for functions / (k, L, n) ramp scheme
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Conference Information
Committee	SST
Conference Date	2001/3/15(1days)
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Paper Information
Registration To	Spread Spectrum Technology (SST)
Language	JPN
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	(k,L,n) Ramp Secret Sharing Systems for Functions
Sub Title (in English)
Keyword(1)	secret sharing system
Keyword(2)	secret sharing system for functions
Keyword(3)	(k, L, n) ramp scheme
1st Author's Name	Yohei Kawamoto
1st Author's Affiliation	Department of Mathematical Engineering and Information Physics, University of Tokyo()
2nd Author's Name	Hirosuke Yamamoto
2nd Author's Affiliation	Department of Mathematical Engineering and Information Physics, University of Tokyo
Date	2001/3/15
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Volume (vol)	vol.100
Number (no)	693
Page	pp.pp.-
#Pages	8
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