Hierarchical Threshold Secret Sharing

Tassa, Tamir

doi:10.1007/s00145-006-0334-8

Cited by 205 publications

(223 citation statements)

References 17 publications

Supporting

Mentioning

206

Contrasting

Unclassified

Order By: Relevance

“…We will show in this section that the Boolean circuits representing multilevel access structures [12,14] fulfill this property. For a compact representation of multilevel access structures we need Boolean circuits with threshold gates (as in [7]).…”

Section: Extensions and Applicationsmentioning

confidence: 88%

See 1 more Smart Citation

Key-Policy Attribute-Based Encryption for Boolean Circuits from Bilinear Maps

źIplea

DrăźGan

2015

Cryptography and Information Security in the Balkans

View full text Add to dashboard Cite

Abstract. We propose the first Key-policy Attribute-based Encryption (KP-ABE) scheme for (monotone) Boolean circuits based on bilinear maps. The construction is based on secret sharing and just one bilinear map, and can be viewed as an extension of the KP-ABE scheme in [7]. Selective security of the proposed scheme in the standard model is proved, and comparisons with the scheme in [5] based on leveled multilinear maps, are provided. Thus, for Boolean circuits representing multilevel access structures, our KP-ABE scheme is more efficient than the one in [5].

show abstract

Section: Extensions and Applicationsmentioning

confidence: 88%

“…we replace "∃" by "∀" in the above definition, we obtain the concept of conjunctive multilevel access structure [14]. It is well-known, and not difficult to prove (see Appendix 10), that disjunctive and conjunctive multilevel access structures cannot be represented by Boolean formulas.…”

Section: Extensions and Applicationsmentioning

confidence: 99%

Key-Policy Attribute-Based Encryption for Boolean Circuits from Bilinear Maps

źIplea

DrăźGan

2015

Cryptography and Information Security in the Balkans

View full text Add to dashboard Cite

show abstract

“…Another paradigmatic example of access structure realizable by a monotone span program is the threshold hierarchical one, see Tassa [26]. Although we did not include any example, recall that our construction is also for non-ideal sss, that is, the monotone span program might have more than one row with the same label (this is important since there are not that many known instances of ideal sss for interesting access structures).…”

Section: Ifmentioning

confidence: 99%

Stretching Groth-Sahai: NIZK Proofs of Partial Satisfiability

Ràfols

2015

Theory of Cryptography

View full text Add to dashboard Cite

Groth, Ostrovsky and Sahai constructed a non-interactive Zap for NP-languages by observing that the common reference string of their proof system for circuit satisfiability admits what they call correlated key generation. The latter means that it is possible to create from scratch two common reference strings in such a way that it can be publicly verified that at least one of them guarantees perfect soundness while it is computationally infeasible to tell which one. Their technique also implies that it is possible to have NIWI Groth-Sahai proofs for certain types of equations over bilinear groups in the plain model. We extend the result of Groth, Ostrovsky and Sahai in several directions. Given as input some predicate P computable by some monotone span program over a finite field, we show how to generate a set of common reference strings in such a way that it can be publicly verified that the subset of them which guarantees perfect soundness is accepted by the span program. We give several different flavors of the technique suitable for different applications scenarios and different equation types. We use this to stretch the expressivity of Groth-Sahai proofs and construct NIZK proofs of partial satisfiability of sets of equations in a bilinear group and more efficient Groth-Sahai NIWI proofs without common reference string for a larger class of equation types. Finally, we apply our results to significantly reduce the size of the signatures of the ring signature scheme of Chandran, Groth and Sahai or to have a more efficient proof in the standard model that a commitment opens to an element of a public list.

show abstract

“…These hierarchical structures are now called disjunctive, since only one of the m conditions must be satisfied for a coalition to be authorized. If all conditions must be satisfied, then the hierarchical access structure is called conjunctive (Tassa, 2007). A typical example of a conjunctive hierarchical game would be the United Nations Security Council where for the passage of a resolution all five permanent members must vote for it and also at least nine members in total.…”

Section: Introductionmentioning

confidence: 99%

“…Both disjunctive and conjunctive hierarchical access structures have been proved to be ideal (Brickell, 1990;Tassa, 2007) which means they can carry the most informationally efficient secret sharing scheme and be completely secure (i.e., not giving any information about the secret to unauthorized coalitions). Classification of ideal access structures proved to be extremely difficult problem and the focus of attention has moved to classification of ideal access structures in subclasses of access structures like weighted threshold access structures introduced by Shamir (1979).…”

Section: Introductionmentioning

confidence: 99%

Weightedness and structural characterization of hierarchical simple games

Gvozdeva

Hameed

Slinko

2013

Mathematical Social Sciences

View full text Add to dashboard Cite

In this paper we give structural charaterizations for disjunctive and conjunctive hierarchical simple games by characterizing them as complete games with a unique shift-maximal losing and, respectively, shift-minimal winning coalitions. We prove canonical representation theorems for both types of hierarchical games and establish duality between them. We characterize those disjunctive and conjunctive hierarchical games which are weighted majority games. This paper was inspired by Beimel et al. (2008) and Farràs and Padró (2010) characterizations of ideal weighted threshold access structures of secret sharing schemes.

show abstract

Hierarchical Threshold Secret Sharing

Cited by 205 publications

References 17 publications

Key-Policy Attribute-Based Encryption for Boolean Circuits from Bilinear Maps

Key-Policy Attribute-Based Encryption for Boolean Circuits from Bilinear Maps

Stretching Groth-Sahai: NIZK Proofs of Partial Satisfiability

Weightedness and structural characterization of hierarchical simple games

Contact Info

Product

Resources

About