On the bound for anonymous secret sharing schemes

Kishimoto, Wataru; Okada, Koji; Kurosawa, Kaoru; Ogata, Wakaha

doi:10.1016/s0166-218x(01)00236-0

Cited by 8 publications

(8 citation statements)

References 6 publications

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“…In [4], the authors proved that, if t ≥ 3, the equality in Theorem 4.5 does not hold. For t = 2, [4] proved a weak inverse of Theorem 3.2.…”

Section: Theorem 48mentioning

confidence: 99%

“…For the clearness of the proof, we first repeat the proof of Theorem 4.5 in [4]. We only consider the case t = 2.…”

Section: Theorem 48mentioning

confidence: 99%

“…For anonymous (t, w) threshold schemes, if 1 < t < w, Kishimoto, Okada, Kurosawa, Ogata [4] gave a lower bound of |S|, which is optimal for some cases. In this paper we will prove that this bound is not optimal under the condition |K| = |P| + 1.…”

Section: Introductionmentioning

confidence: 99%

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Constructions for Anonymous Secret Sharing Schemes Using Combinatorial Designs

Deng

Guo

Liu

2007

Acta Mathematicae Applicatae Sinica, English Series

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In an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In this paper some constructions of anonymous secret sharing schemes with 2 thresholds by using combinatorial designs are given. Let v(t, w, q) denote the minimum size of the set of shares of a perfect anonymous (t, w) threshold secret sharing scheme with q secrets. In this paper we prove that v(t, w, q) = Θ(q) if t and w are fixed and that the lower bound of the size of the set of shares in [4] is not optimal under certain condition.

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“…In [4], the authors proved that, if t ≥ 3, the equality in Theorem 4.5 does not hold. For t = 2, [4] proved a weak inverse of Theorem 3.2.…”

Section: Theorem 48mentioning

confidence: 99%

“…For the clearness of the proof, we first repeat the proof of Theorem 4.5 in [4]. We only consider the case t = 2.…”

Section: Theorem 48mentioning

confidence: 99%

See 1 more Smart Citation

Constructions for Anonymous Secret Sharing Schemes Using Combinatorial Designs

Deng

Guo

Liu

2007

Acta Mathematicae Applicatae Sinica, English Series

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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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“…A typical application is anonymous sharing of the secret key corresponding to a certain public key. Unfortunately, the constructions of anonymous secret sharing schemes in the literature are not very efficient (in terms of the number of shares that every participant must hold) and existing bounds [4,16] do not leave much hope for forthcoming efficient constructions.…”

Section: Introductionmentioning

confidence: 99%

On Partial Anonymity in Secret Sharing

Daza

Domingo‐Ferrer

Public Key Infrastructure

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Anonymous secret sharing schemes allow a secret to be recovered from shares regardless of the identity of shareholders. Besides being interesting in its own right, this property is especially appealing to guarantee the anonymity of participants when secret sharing is used as a building block of more general distributed protocols (e.g. to anonymously share the secret key corresponding to a public key). However, current constructions of anonymous secret sharing schemes are not very efficient (because of the number of shares that every participant must hold) and existing bounds do not leave much room for optimism. In this paper we propose to weaken the anonymity condition to partial anonymity, where by partial anonymity we mean that the identity of the participant is not made public, but he is known to belong to some subset. That is, the search for a participant narrows down to one in a set of possible candidates. Furthermore, we propose a general construction of partial anonymous secret sharing schemes.

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On the bound for anonymous secret sharing schemes

Cited by 8 publications

References 6 publications

Constructions for Anonymous Secret Sharing Schemes Using Combinatorial Designs

Constructions for Anonymous Secret Sharing Schemes Using Combinatorial Designs

Weakly-Private Secret Sharing Schemes

On Partial Anonymity in Secret Sharing

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