Information-theoretical secure verifiable secret sharing with vector space access structures over bilinear groups and its applications

2015 ◽  
Vol 52 ◽  
pp. 109-115 ◽  
Author(s):  
Jie Zhang ◽  
Futai Zhang
Keyword(s):  
Vector Space ◽  
Secret Sharing ◽  
Verifiable Secret Sharing ◽  
Access Structures ◽  
Bilinear Groups

scholarly journals Span Programs and General Secure Multi-Party Computation

1997 ◽  
Vol 4 (28) ◽  
Author(s):  
Ronald Cramer ◽  
Ivan B. Damgård ◽  
Ueli Maurer
Keyword(s):  
Secret Sharing ◽  
Theoretic Model ◽  
Secret Sharing Schemes ◽  
Cryptographic Primitives ◽  
Information Theoretic ◽  
Verifiable Secret Sharing ◽  
Access Structures ◽  
Sharing Scheme ◽  
Multiplication Property ◽  
Span Programs

The contributions of this paper are three-fold. First, as an abstraction of previously proposed cryptographic protocols we propose two cryptographic primitives: homomorphic<br />shared commitments and linear secret sharing schemes with an additional multiplication property. We describe new constructions for general secure multi-party computation protocols, both in the cryptographic and the information-theoretic (or secure<br />channels) setting, based on any realizations of these primitives.<br />Second, span programs, a model of computation introduced by Karchmer and Wigderson, are used as the basis for constructing new linear secret sharing schemes, from which the two above-mentioned primitives as well as a novel verifiable secret sharing scheme can efficiently be realized. Third, note that linear secret sharing schemes can have arbitrary (as opposed to<br />threshold) access structures. If used in our construction, this yields multi-party protocols secure against general sets of active adversaries, as long as in the cryptographic (information-theoretic) model no two (no three) of these potentially misbehaving player sets cover the full player set. This is a strict generalization of the threshold-type adversaries and results previously considered in the literature. While this result is new for the cryptographic model, the result for the information-theoretic model was previously proved by Hirt and Maurer. However, in addition to providing an independent proof, our protocols are not recursive and have the potential of being more efficient.

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