Generalised Cumulative Arrays in Secret Sharing

Long, Shoulun; Pieprzyk, Josef; Wang, Huaxiong; Wong, Duncan S.

doi:10.1007/s10623-006-0007-5

Cited by 8 publications

(9 citation statements)

References 31 publications

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“…Cumulative schemes were first introduced by Ito et al [23] and then used by several authors to construct a general scheme for arbitrary access structures.Simmons [41] proposed cumulative map, Jackson [24] proposed a notion of cumulative array.Ghodosi et al [17] introduced simpler and more efficient scheme and also introduced capabilities to detect cheaters. Generalized cumulative arrays in secret sharing is introduced by Long [29].…”

Section: Generalized Secret Sharingmentioning

confidence: 99%

Efficient Multi Secret Sharing with Generalized Access Structures

Binu¹,

Sreekumar²

2014

IJCA

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Multi secret sharing is an extension of secret sharing technique where several secrets are shared between the participants, each according to a specified access structure.The secrets can be reconstructed according to the access structure by participants using their private shares.Each participant has to hold a single share, additional information are made available in a public bulletin board.The scheme is computationally efficient and also each participant can verify the shares of the other participants and also the reconstructed secret.The scheme doesn't need any secure channel also. General Terms:secret sharing, multi secret sharing

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Section: Generalized Secret Sharingmentioning

confidence: 99%

Efficient Multi Secret Sharing with Generalized Access Structures

Binu¹,

Sreekumar²

2014

IJCA

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“…In addition to shared block ciphers and MACs, schemes using generalized cumulative arrays have been used in secret sharing [8] and for sharing pseudo random functions [18]. A GCA is defined below.…”

Section: Introductionmentioning

confidence: 99%

“…Long et al explore GCAs in the context of secret sharing and give upper and lower bounds for existence of GCAs [8]. Martin and Ng [11] also give constructions of GCAs and metrics to describe the efficiency of GCAs.…”

Section: Introductionmentioning

confidence: 99%

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Anonymity in shared symmetric key primitives

Zaverucha

Stinson

2010

Des. Codes Cryptogr.

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We provide a stronger definition of anonymity in the context of shared symmetric key primitives, and show that existing schemes do not provide this level of anonymity. A new scheme is presented to share symmetric key operations amongst a set of participants according to a (t, n)-threshold access structure. We quantify the amount of information the output of the shared operation provides about the group of participants which collaborated to produce it.

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“…Cumulative arrays were formally defined in [102]. The definitions and results in this subsection are taken from [74].…”

Section: Secret Sharing Schemes From Cumulative Arraysmentioning

confidence: 99%

On secret sharing schemes and linear codes

Cruz.¹

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A secret sharing scheme is a method of distributing a secret among a group of participants in such a way that only certain subgroups are authorized to know the secret. Secret sharing schemes have been used in many areas of cryptography such as secure information storage, threshold cryptographic protocols, secure message transmission, secure multiparty computation, and generalized oblivious transfer. This thesis deals with secret sharing schemes constructed using linear codes. First, we consider the secret sharing schemes based on linear codes constructed using the approach by Karnin, Greene and Hellman, by Bertilsson and Ingemarsson and by Massey. In this approach, the minimal authorized groups correspond to certain minimal codewords of the dual of the underlying code. We study three topics related to secret sharing schemes based on linear codes. The first topic is on the access structure and multiplicativity of linear secret sharing schemes based on codes from complete graphs. Multiplicative linear secret sharing schemes are used in the construction of secure multiparty computation protocols. The characterization of access structures of ideal multiplicative schemes has not been solved completely. We describe the access structure of the schemes based on cut-set and cycle codes and show that these schemes cannot be multiplicative. We then show v that the class of access structures based on odd cycles cannot be realized by ideal multiplicative linear secret sharing schemes over any finite field. This can be seen as a contribution to the characterization of access structures of ideal multiplicative schemes. The access structure based on odd cycles corresponds to the scheme based on the dual of the extended cycle code. Finally, we show that we can obtain ideal multiplicative linear secret sharing scheme based on the dual of an augmented extended cycle code. The second topic is a generalization of secret sharing schemes based on linear codes. In this generalization, the secret consists of multiple field elements. We give a characterization of the groups in the access structure using the dual code. We then use a generalized joint weight enumerator to describe the access structure. The third topic is on the maximum number of minimal codewords in binary linear codes. This subject has been studied before but in the setting of cycles in graphs and of circuits in matroids. We prove several upper and lower bounds on the maximum number of minimal codewords in binary linear codes given the length and dimension. We make the bounds explicit for code of small length and dimension. Exact values are given for small cycle codes of graphs. Some asymptotic results are presented including the asymptotic behavior for cycle codes of graphs. We also consider another type of secret sharing schemes constructed using linear codes. These are the so-called cheating-immune secret sharing schemes. A secret sharing scheme that is cheating-immune prevents a cheater, who submits a corrupted share, from gaining an advantage in knowing the secret ove...

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Generalised Cumulative Arrays in Secret Sharing

Cited by 8 publications

References 31 publications

Efficient Multi Secret Sharing with Generalized Access Structures

Efficient Multi Secret Sharing with Generalized Access Structures

Anonymity in shared symmetric key primitives

On secret sharing schemes and linear codes

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