Authors:
Changlu Lin
1
;
Lein Harn
2
and
Dingfeng Ye
3
Affiliations:
1
Graduate University of Chinese Academy of Sciences / Fujian Normal University / Beijing Municipal Commission of Education, China
;
2
University of Missouri-Kansas City, United States
;
3
Graduate University of Chinese Academy of Sciences, China
Keyword(s):
Secret sharing, Verifiable secret sharing, Secret sharing homomorphism, t-consistency, Informationtheoretically secure.
Related
Ontology
Subjects/Areas/Topics:
Cryptographic Techniques and Key Management
;
Information and Systems Security
;
Public Key Crypto Applications
Abstract:
In a (t,n) secret sharing scheme, a mutually trusted dealer divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret, but fewer than t shares cannot reconstruct the secret. When there is no mutually trusted dealer, a (n, t,n) secret sharing scheme can be used to set up a (t,n) secret sharing because each shareholder also acts as a dealer to decide a master secret jointly and divide each selected secret for others. A verifiable secret sharing (VSS) allows each shareholder to verify that all shares are t-consistent (i.e. every subset of t of the n shares defines the same secret). In this paper, we show that (t,n)-VSS and (n, t,n)-VSS proposed by Pedersen can only ensure that all shares are t-consistent; but shares may not satisfy the security requirements of secret sharing scheme. Then, we introduce a new notion of strong VSS. A strong VSS scheme can ensure that (a) all shares are t-consistent, and (b) all shares satisfy the security requ
irements of secret sharing scheme. We propose two simple ways to convert Pedersen’s VSS schemes into strong VSS schemes, which are information-theoretically secure. We also prove that our proposed VSS schemes satisfy the strong verifiable property.
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