Natural Generalizations of Threshold Secret Sharing

Farràs, Oriol; Padrö, Carles; Xing, Chaoping; An, Yang

doi:10.1109/tit.2014.2300113

Cited by 25 publications

(41 citation statements)

References 32 publications

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“…It is easy to see that these access structures greatly generalize the threshold cases. Several types of multipartite access structures have been in-depth studied in recent years such as compartmented access structures [44,48,47,9,18,16], weighted access structures [42,34,4,3], multilevel (hierarchical) access structures [44,9,6,18,17,16], partially hierarchical access structures [18,50], etc. And linear and efficient secret sharing schemes have been designed [42,9,44,48,47] for some of them.…”

Section: Extensionsmentioning

confidence: 99%

“…To showcase our basic scheme can be effectively extended to support multipartite access structures, we present an extension specifically for compartmented access structure with upper bounds [48,18]. For this type of access structures, there is a threshold for the whole participant set, and an upper bound for each separate group.…”

Section: Extensionsmentioning

confidence: 99%

“…The second extension focuses on a distributed signature scheme for compartmented access structures with upper bounds [48,18] which can be defined as follows…”

Section: Distributed Signature Scheme For Multipartite Access Structuresmentioning

confidence: 99%

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Practical (fully) distributed signatures provably secure in the standard model

Wang

Wong

et al. 2015

Theoretical Computer Science

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Please cite this article in press as: Y. Wang et al., Practical (fully) distributed signatures provably secure in the standard model, Theoret. Comput. Sci. (2015), http://dx. Highlights• We propose a CDH-based distributed signature scheme in the standard model. • We provide two extensions of the basic distributed signature scheme.• We propose a distributed key generation protocol over bilinear group.• We provide a CDH-based fully distributed signature scheme in the standard model. AbstractA distributed signature scheme allows participants in a qualified set to jointly generate a signature which cannot be forged even when any unqualified set of participants collude together. In this paper, we propose an efficient scheme that supports any monotone access structures and show its unforgeability and robustness under the computational Diffie-Hellman (CDH) assumption in the standard model. For 192-bit security, its secret key shares and signature fragments are as short as 511 bits and 1022 bits, which are shorter than existing schemes assuming random oracle. We then propose two extensions. The first one allows new participants to dynamically join the system without any help from the dealer. The second one supports a type of multipartite access structures, where the participant set is divided into multiple disjoint groups, and each group is bounded so that a distributed signature cannot be generated unless a pre-defined number of participants from multiple groups work together. Finally, we present a fully distributed signature scheme such that the centralized trusted dealer can be removed from the system, and the secret keys (shares) can be jointly computed by the involved participants.

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Section: Extensionsmentioning

confidence: 99%

Section: Extensionsmentioning

confidence: 99%

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Practical (fully) distributed signatures provably secure in the standard model

Wang

Wong

et al. 2015

Theoretical Computer Science

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“…They proved that every ideal hierarchical access structure is induced by a representable matroid. This connection of polymatroids and the associated access structures have been studied in [29]: Recently, by using the reduced discrete polymatroids, [30] obtained a sufficient condition for a multipartite access structure to be ideal and further give a new proof that all access structures related to bipartite and tripartite matroids coincide with the ideal ones. All these families of multipartite access structures described above are related to representable matroids, and hence, they are the ideal ones.…”

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confidence: 99%

New Results on Ideal Multipartite Secret Sharing and its Applications to Group Communications

Hsu

Harn

2014

Wireless Pers Commun

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With the rapid development of various group-oriented services, multipartite group communications occur frequently in a single network, where a multipartite access structure is defined to be a collection of the subsets of users who may come from different parts of the network such that only users in an authorized subset of users can use their shares to build up a group key for a secure group communication. Most existing group key establishment schemes based on a secret sharing target on building up a group key for a threshold access structure, and need to compute a t-degree interpolating polynomial in order to encrypt and decrypt the secret group key. This approach is not suitable and inefficient in terms of computational complexity for multipartite group environments which need to realize the multipartite access structures. In 1991, Brickell et al. proved that an ideal access structure is induced by a matroid and furthermore, an access structure is ideal if it is induced by a representable matroid. In this paper, we study the characterization of representable matroids. By using the connection between ideal secret sharing and matroids and, in particular, the recent results on ideal multipartite access structures and the connection between multipartite matroids and discrete polymatroids, we introduce a new concept on R-tuple, which is determined by the rank function of the associated discrete polymatroid. Using this new concept, we come up a new and simple sufficient condition for a multipartite matroid to be representable (in fact, every matroid and every access structure are multipartite). In other words, we have developed a sufficient condition for an access structure to be ideal. These new results can be applied to establish multipartite group keys efficiently in secure group communications.

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“…In this chapter, we will give some new and useful families of access structures, which are mainly included in our paper [44]. This line of research was initiated by Kothari [60], who presented some ideas to construct ideal linear secret sharing schemes with hierarchical properties.…”

Section: Chapter 3 New Families Of Ideal Access Structures 31 Introdmentioning

confidence: 99%

Secret sharing schemes and polymatroids

An¹

Self Cite

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Secret sharing, which refers to methods of distributing a secret value among a group of participants, is a very important primitive in cryptology. This thesis contains some contribution to this topic. The results that are presented herein deal with two of the main open problems in secret sharing: the characterization of the ideal access structures and the optimization of the length of the shares. For both open problems, polymatroids are a powerful tool. On one hand, ideal multipartite secret sharing schemes are strongly connected to polymatroids. On the other hand, the entropies of shares of a scheme determine a polymatroid, and because of that, they are fundamental in the search of lower bounds of the length of the shares. For the first open problem, some new and useful families of ideal multipartite access structures are found by using integer polymatroids. As a result the proofs for the existence of ideal secret sharing schemes for them are simplified in great measure. Regarding the second open problem, we present positive and negative results about the only known technique to find lower bounds: linear programming. The positive result are obtained by strengthening this method. The negative ones show the limitation of this method trying to improve the asymptotic lower bounds. vii

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Natural Generalizations of Threshold Secret Sharing

Cited by 25 publications

References 32 publications

Practical (fully) distributed signatures provably secure in the standard model

Practical (fully) distributed signatures provably secure in the standard model

New Results on Ideal Multipartite Secret Sharing and its Applications to Group Communications

Secret sharing schemes and polymatroids

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