E. F. Brickell. Some ideal secret sharing schemes. Journal of Combin. Math. and Combin. Comput., 6:105--113, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....realizing non threshold access structures, were introduced by Ito, Saito, and Nishizeki [42] where it was shown that every monotone access structure can be (inefficiently) realized by a secret sharing scheme. More efficient schemes for specific types of access structures were presented, e.g. in [11, 51, 19, 43]. We refer the reader to [50, 53] for extensive surveys on secret sharing literature. # A preliminary version of this paper appeared in the proceedings of the 16th Annu. IEEE Conf. on Computational Complexity, pages 188 202, 2001. Similarly to almost all of the vast literature on ....

....the shares are obtained by applying a linear mapping to the secret and several independent random field elements. Linear schemes may be equivalently defined by requiring that each authorized set reconstructs the secret by applying a linear function to its shares [8] For example, the schemes of [49, 15, 42, 11, 51, 19, 14, 43, 32] are all linear. The share size in linear schemes over F realizing a monotone function f is proportional to the monotone span program size of f over F . Span programs are a linear algebraic model of computation introduced in [43] In fact, there is a one to one correspondence between linear ....

E. F. Brickell. Some ideal secret sharing schemes. Journal of Combin. Math. and Combin. Comput., 6:105-- 113, 1989.

....under project BFM2001 2251. Second author partially supported by the Junta de Castilla y Le on under Projet VA56 00B. The problems of characterizing ideal access structures and nding ideal schemes for them are important and they have received great attention in the literature (see for example [3, 4]) A particular interesting class of secret sharing schemes is the class of threshold schemes, which were the rst secret sharing schemes introduced independently by Blakley [1] and Shamir [8] in 1979. The access structure of a (t; n) threshold scheme consists of all subsets of P with at least t ....

E.F. Brickell, Some Ideal Secret Sharing Schemes, Journal of Combinatorial Mathematics and Combinatorial Computing, 9 (1989), 105-113.

....in real life participants are, in a natural way, in a hierarchy and not on equal terms. Then, structures in which participants are divided in several classes abound in the literature: Simmons multilevel multipart schemes, 9] sums and products, bipartite structures, 7] compartmented schemes, [2], etc. In this paper we present a very general construction of this type. Participants are divided in several groups, each of them having its own family of authorized coalitions. As a particular case of this construction we introduce the class of iterated threshold schemes. We show that all ....

....vector space construction. Let us remember that a structure on P admits a vector space construction over the nite eld F p if there is a map : P F p (d large enough) and a vector v 2 F p ; v 6= 0, such that for all A P we have v 2 h (P i ) j P i 2 Ai if and only if A 2 (see [2, 11]) Such a construction directly provides an ideal PS( p) Unfortunately no criteria is known to decide when a structure admits a vector space construction. In the above construction usually one takes v = e 1 = 1; 0; 0) However it is clear that the particular choice of v is not ....

E.F. Brickell, Some Ideal Secret Sharing Schemes, Lecture Notes in Computer Science: Eurocrypt'89, (Springer Verlag, 1989), 468-475.

....unconditionally secure threshold VSS, b n 3. In [16] Stinson and Wei proposed more e#cient unconditionally secure VSS with threshold t and with b n 4 1. In this section we provide an unconditionally secure VSS which will be used in the proactive scheme later. 3. 1 LSSS and MSP Brickell [4] points out how the linear algebraic view leads to a natural extension to a wider class of secret sharing schemes that are not necessarily of the threshold type. These have later been generalized to all possible so called monotone access structures by Krachmer and Wigderson [13] based on a linear ....

E.F.Brickell, Some ideal secret sharing schemes, J. of Comb. Math. and Comb. Computing 9, 1989, 105-113.

....by all subsets with exactly t participants from a set of n participants. Further works considered the problem of nding secret sharing schemes for more general access structures. Ito, Saito and Nishizeki [10] proved that there exists a secret sharing scheme for any access structure, and Brickell [5] introduced the vector space construction which provides secret sharing schemes for a wide family of access structures, the vector space access structures. While in the threshold schemes proposed by Blakley [1] and Shamir [15] and in the vector space schemes given by Brickell [5] the shares have ....

....and Brickell [5] introduced the vector space construction which provides secret sharing schemes for a wide family of access structures, the vector space access structures. While in the threshold schemes proposed by Blakley [1] and Shamir [15] and in the vector space schemes given by Brickell [5] the shares have the same size as the secret, in the schemes constructed in [10] for general access structures the shares are, in general, much larger than the secret. Since the security of a system depends on the amount of information that must be kept secret, the size of the shares given to the ....

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E.F. Brickell. Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989), 105-113.

....4 secret sharing were proposed independently by Shamir [17] and Blakley [4] The first secret sharing schemes have been (r, k) threshold schemes, were only groups of more than a certain number of participants r (where k and k is the number of all players) can reconstruct the secret. Brickell [6] points out how the linear algebraic view leads to a natural extension to a wider class of secret sharing schemes that are not necessarily of threshold type. This have later been generalized to all possible so called monotone access structures by Karchmer and Wigderson [12] based on a linear ....

E. F. Brickell, Some Ideal Secret Sharing Schemes, J. of Comb. Math. and Comb. Computing 9, 1989, pp.105-113.

....by Shamir [21] and Blakley [4] in 1979. Shamir proposed a threshold scheme, i.e. subsets that can recover the secret are those with at least t members (t is the threshold) Other works have proposed schemes realizing more general structures, such as vector space secret sharing schemes [7]. An access structure is realizable by such a scheme de ned in a nite eld Z q , for some prime q, if there exists a positive integer r and a function : P [ fDg (Z q ) such that W 2 if and only if (D) 2 h (P i )i P i 2W . Here D denotes a special entity (real or not) outside the set P . ....

E.F. Brickell. Some ideal secret sharing schemes. J.Combin. Math. and Combin. Comput. 9 p. 105-113 (1989).

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E. F. Brickell. Some ideal secret sharing schemes. Journal of Combin. Math. and Combin. Comput., 6:105--113, 1989.

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E. F. Brickell. Some ideal secret sharing schemes. Journal of Combin. Math. and Combin. Comput., 6:105--113, 1989.

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E. F. Brickell. Some ideal secret sharing schemes. Journal of Combinatorial Mathematics and Combinatorial Computing, 6:105--113, 1989.

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E.F. Brickell. Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989) 105--113.

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E.F. Brickell. Some ideal secret sharing schemes. Journal of Combinatorial Mathematics and Combinatorial Computing, 9, pp. 105-113 (1989).

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E.F. Brickell. Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989) 105--113.

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E.F. Brickell. Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989) 105--113.

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E. F. Brickell. Some ideal secret sharing schemes. In J.-J. Quisquater and J. Vandewalle, editors, Advances in Cryptology - EUROCRYPT '89, volume 434 of Lecture Notes in Computer Science, pages 468--475. Springer-Verlag, 1990.

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E. F. Brickell, Some ideal secret sharing schemes, J. Combin. Maths. & Combin. Comp. 9 (1989), pp. 105--113.

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E. Brickell. Some ideal secret sharing schemes, J. of Comb. Math. and Comb. Computing 9, 1989, pp. 105-113.

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E.F. Brickell, Some ideal secret sharing schemes. Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 9: 105-113 (1989).

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E.F. Brickell. Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989) 105--113.

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Ernest F. Brickell. Some ideal secret sharing schemes. In Advances in Cryptology---EUROCRYPT '89, volume 434 of Lecture Notes in Computer Science. Springer, 1989.

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E. Brickell. Some ideal secret sharing schemes, J. of Comb. Math. and Comb. Computing 9, 1989, pp. 105-113.

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E. F. Brickell. Some ideal secret sharing scheme. Journal of combinatorial mathematics and combinatorial computing 9, 105-113, 1989.

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E. F. Brickell. Some ideal secret sharing scheme. Journl of combinatorial mathematics and combinatorial computing, Vol. 9, 105-113, 1989.

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E. F. Brickell. Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989), 105--113.

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E. F. Brickell. Some ideal secret sharing schemes. Journal of Combinatorial Mathematics and Combinatorial Computing, 9:105--113, 1989.

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