A Combinatorial Approach to Threshold Schemes

Stinson, D. R.; Vanstone, Scott A.

doi:10.1137/0401024

Cited by 67 publications

(44 citation statements)

References 6 publications

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“…Stinson and Vanstone [28] proved that in any (t, k) anonymous threshold scheme, v > (k-t+ 1)ISl +t-1.…”

Section: Anonymous Threshold Schemesmentioning

confidence: 99%

“…We recall the following condition of regularity that in [20] and [28] was made on the distribution of shares of the participants.…”

Section: Anonymous Threshold Schemesmentioning

confidence: 99%

“…Following the characterization of [28] and [20] we can define anonymous threshold schemes as follows.…”

Section: Anonymous Threshold Schemesmentioning

confidence: 99%

“…Anonymous threshold schemes were first analyzed in [28]. Following the characterization of [28] and [20] we can define anonymous threshold schemes as follows.…”

Section: Anonymous Threshold Schemesmentioning

confidence: 99%

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On the dealer's randomness required in secret sharing schemes

Blundo

Gaggia

Stinson

1995

Advances in Cryptology — EUROCRYPT'94

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Abstract. The problem we deal with in this paper is the research of upper and lower bounds on the randomness required by the dealer to set up a secret sharing scheme. We give both lower and upper bounds for infinite classes of access structures. Lower bounds are obtained using entropy arguments. Upper bounds derive from a decomposition construction based on combinatorial designs (in particular, t-(v, k, )~) designs). We prove a general result on the randomness needed to construct a scheme for the cycle C,~; when n is odd our bound is tight. We study the access structures on at most four participants and the connected graphs on five vertices, obtaining exact values for the randomness for all them. Also, we analyze the number of random bits required to construct anonymous threshold schemes, giving upper bounds. (Informally, anonymous threshold schemes are schemes in which the secret can be reconstructed without knowledge of which participants hold which shares.)

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“…Stinson and Vanstone [28] proved that in any (t, k) anonymous threshold scheme, v > (k-t+ 1)ISl +t-1.…”

Section: Anonymous Threshold Schemesmentioning

confidence: 99%

“…We recall the following condition of regularity that in [20] and [28] was made on the distribution of shares of the participants.…”

Section: Anonymous Threshold Schemesmentioning

confidence: 99%

“…Following the characterization of [28] and [20] we can define anonymous threshold schemes as follows.…”

Section: Anonymous Threshold Schemesmentioning

confidence: 99%

“…Anonymous threshold schemes were first analyzed in [28]. Following the characterization of [28] and [20] we can define anonymous threshold schemes as follows.…”

Section: Anonymous Threshold Schemesmentioning

confidence: 99%

See 2 more Smart Citations

On the dealer's randomness required in secret sharing schemes

Blundo

Gaggia

Stinson

1995

Advances in Cryptology — EUROCRYPT'94

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“…In particular, our scheme improves the share size when t ≤ log n − 2 log log n. These schemes have the additional nice property that they are anonymous, that is, the reconstruction of the secret does not depend on the identity of the authorized set. Anonymous secret-sharing schemes were introduced by [47], and were further studied in [14,33,39].…”

Section: Our Resultsmentioning

confidence: 99%

Weakly-Private Secret Sharing Schemes

Beimel

Franklin

Theory of Cryptography

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Abstract. Secret-sharing schemes are an important tool in cryptography that is used in the construction of many secure protocols. However, the shares' size in the best known secret-sharing schemes realizing general access structures is exponential in the number of parties in the access structure, making them impractical. On the other hand, the best lower bound known for sharing of an -bit secret with respect to an access structure with n parties is Ω( n/ log n) (Csirmaz, EUROCRYPT 94). No major progress on closing this gap has been obtained in the last decade.Faced by our lack of understanding of the share complexity of secret sharing schemes, we investigate a weaker notion of privacy in secrets sharing schemes where each unauthorized set can never rule out any secret (rather than not learn any "probabilistic" information on the secret). Such schemes were used previously to prove lower bounds on the shares' size of perfect secret-sharing schemes. Our main results is somewhat surprising upper-bounds on the shares' size in weakly-private schemes.

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Completing the spectrum for LGDD (mv)

Lei¹

1997

J. Combin. Designs

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A Combinatorial Approach to Threshold Schemes

Cited by 67 publications

References 6 publications

On the dealer's randomness required in secret sharing schemes

On the dealer's randomness required in secret sharing schemes

Weakly-Private Secret Sharing Schemes

Completing the spectrum for LGDD (mv)

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