Book ChapterDOI
On the Power of Computational Secret Sharing
V. Vinod,Arvind Narayanan,Kannan Srinathan,C. Pandu Rangan,Kwangjo Kim +4 more
- pp 162-176
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TLDR
This work considers computational secret sharing (CSS) which provably allows a smaller share size (and hence greater efficiency) than its information-theoretic counterparts and introduces the notion of secret sharing with a semi-trusted third party, and proves that in this relaxed model efficient CSS schemes exist for a wider class of access structures, namely monotone NP.Abstract:
Secret sharing is a very important primitive in cryptography and distributed computing. In this work, we consider computational secret sharing (CSS) which provably allows a smaller share size (and hence greater efficiency) than its information-theoretic counterparts. Extant CSS schemes result in succinct share-size and are in a few cases, like threshold access structures, optimal. However, in general, they are not efficient (share-size not polynomial in the number of players n), since they either assume efficient perfect schemes for the given access structure (as in [10]) or make use of exponential (in n) amount of public information (like in [5]). In this paper, our goal is to explore other classes of access structures that admit of efficient CSS, without making any other assumptions. We construct efficient CSS schemes for every access structure in monotone P. As of now, most of the efficient information-theoretic schemes known are for access structures in algebraic NC 2. Monotone P and algebraic NC 2 are not comparable in the sense one does not include other. Thus our work leads to secret sharing schemes for a new class of access structures. In the second part of the paper, we introduce the notion of secret sharing with a semi-trusted third party, and prove that in this relaxed model efficient CSS schemes exist for a wider class of access structures, namely monotone NP.read more
Citations
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Book ChapterDOI
Secret-sharing schemes: a survey
TL;DR: This survey describes the most important constructions of secret-sharing schemes and explains the connections between secret- sharing schemes and monotone formulae and monOTone span programs, and presents the known lower bounds on the share size.
Proceedings ArticleDOI
Robust computational secret sharing and a unified account of classical secret-sharing goals
Mihir Bellare,Phillip Rogaway +1 more
TL;DR: In this article, the authors give a unified account of classical secret sharing goals from a modern cryptographic vantage, including perfect, statistical, and computational secret sharing; static and dynamic adversaries; schemes with or without robustness; schemes where a participant recovers the secret and those where an external party does so.
Journal ArticleDOI
Space efficient secret sharing for implicit data security
Abhishek Parakh,Subhash Kak +1 more
TL;DR: This paper presents a k-threshold computational secret sharing technique that distributes a secret S into shares of size |S |k-1, where |S| denotes the secret size, and can be looked upon as a new information dispersal scheme that provides near optimal space efficiency.
Journal Article
Secret Sharing Schemes with Applications in Security Protocols.
TL;DR: It is proved, using the concept of entropy, that in any perfect threshold secret sharing scheme the shares must be at least as long as the secret and, later on, Capocelli, De Santis, Gargano, and Vaccaro have extended this result to the …
Journal ArticleDOI
Monotone circuits for monotone weighted threshold functions
Amos Beimel,Enav Weinreb +1 more
TL;DR: This work by-passes this addition step and construct a polynomial size logarithmic depth unbounded fan-in monotone circuit for every weighted threshold function, i.e., it is shown that weighted threshold functions are in mAC^1.
References
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Proceedings ArticleDOI
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Journal ArticleDOI
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Proceedings ArticleDOI
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Journal ArticleDOI
Secret sharing scheme realizing general access structure
TL;DR: This paper shows that by providing the trustees with several information data concerning the distributed information of the (k, n) threshold method, any access structure can be realized.