t-Cheater Identifiable (k, n) Threshold Secret Sharing Schemes

Kurosawa, Kaoru; Obana, Satoshi; Ogata, Wakaha

doi:10.1007/3-540-44750-4_33

Cited by 54 publications

(47 citation statements)

References 10 publications

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“…While this condition is the same as that of Kurosawa et al [12], the share size is dramatically reduced compared to [12]. Namely, the share size of the first scheme satisfies |V i | = |S|/ and is only one bit longer than the bound of eq.…”

Section: Introductionmentioning

confidence: 82%

“…The size of share |V i | of their scheme is |V i | = |S| 3n−2 where |S| denotes the size of secret 1 . In [12], Kurosawa, Obana and Ogata showed that when the number of cheater t satisfies t ≤ (k − 1)/3 the share size is greatly reduced compared to that of [21]. The size of share of their scheme is |V i | = |S|/ t+2 , which until now has been the most efficient scheme, despite the fact that the bit length of their scheme is still linear to the number of cheaters.…”

Section: Introductionmentioning

confidence: 99%

“…The size of share of their scheme is |V i | = |S|/ t+2 , which until now has been the most efficient scheme, despite the fact that the bit length of their scheme is still linear to the number of cheaters. The lower bound of share size is given by Kurosawa et al as follows [12]:…”

Section: Introductionmentioning

confidence: 99%

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Almost Optimum t-Cheater Identifiable Secret Sharing Schemes

Obana¹

2011

Lecture Notes in Computer Science

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Abstract. In Crypto'95, Kurosawa, Obana and Ogata proposed a kout-of-n secret sharing scheme capable of identifying up to t cheaters with probability 1 − under the condition t ≤ (k − 1)/3 . The size of share |Vi| of the scheme satisfies |Vi| = |S|/ t+2 , which was the most efficient scheme known so far. In this paper, we propose new k-out-ofn secret sharing schemes capable of identifying cheaters. The proposed scheme possesses the same security parameters t, as those of Kurosawa et al.. The scheme is surprisingly simple and its size of share is |Vi| = |S|/ , which is much smaller than that of Kurosawa et al. and is almost optimum with respect to the size of share; that is, the size of share is only one bit longer than the existing bound. Further, this is the first scheme which can identify cheaters, and whose size of share is independent of any of n, k and t. We also present schemes which can identify up to (k − 2)/2 , and (k−1)/2 cheaters whose sizes of share can be approximately written by |Vi| ≈ (n · (t + 1) · 2 3t−1 · |S|)/ and |Vi| ≈ ((n · t · 2 3t ) 2 · |S|)/ 2 , respectively. The number of cheaters that the latter two schemes can identify meet the theoretical upper bound.

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Section: Introductionmentioning

confidence: 82%

Section: Introductionmentioning

confidence: 99%

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Almost Optimum t-Cheater Identifiable Secret Sharing Schemes

Obana¹

2011

Lecture Notes in Computer Science

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“…A framework for considering robust secret sharing is provided in [1], which includes schemes in both the information-theoretic and computationally secure settings. Secret-sharing schemes that either detect or identify participants who present incorrect shares during an attempted recovery have also been extensively studied, for example [17,21,22]. While such schemes make it apparent that cheating has occurred, they do not necessarily permit honest participants to recover the correct secret.…”

Section: Introductionmentioning

confidence: 99%

Error decodable secret sharing and one-round perfectly secure message transmission for general adversary structures

2010

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An error decodable secret-sharing scheme is a secret-sharing scheme with the additional property that the secret can be recovered from the set of all shares, even after a coalition of participants corrupts the shares they possess. In this paper we consider schemes that can tolerate corruption by sets of participants belonging to a monotone coalition structure, thus generalising both a related notion studied by Kurosawa, and the well-known error-correction properties of threshold schemes based on Reed-Solomon codes. We deduce a necessary and sufficient condition for the existence of such schemes, and we show how to reduce the storage requirements of a technique of Kurosawa for constructing error-decodable secret-sharing schemes with efficient decoding algorithms.In addition, we explore the connection between one-round perfectly secure message transmission (PSMT) schemes with general adversary structures and secret-sharing schemes, and we exploit this connection to investigate factors affecting the performance of one-round PSMT schemes such as the number of channels required, the communication overhead, and the efficiency of message recovery.

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“…Secret sharing is a fundamental building block for many cryptographic protocols and is often used in the general composition of secure multiparty computations. In recent, secret sharing has still been an active research area because of its importance in cryptography [2][3][4][5][6][7][8][9][10][13][14].…”

Section: Introductionmentioning

confidence: 99%