A. Beimel and B. Chor. Universally ideal secret sharing schemes. IEEE Trans. on Information Theory, 40(3):786--794, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the parties is s. Therefore, every lower bound on the total size of shares in a secret sharing scheme is also a lower bound on the size of monotone span programs for the same function. On the other hand, lower bounds for monotone span programs imply lower bounds for linear secret sharing schemes [15, 16, 26]. 1.3.2. Branching programs A branching program is a directed acyclic graph with a source node called START, and two sinks called ACCEPT and REJECT. Every vertex that is not a sink has outdegree 2, and the two edges leaving a given vertex are labeled by complementary literals x i ; x i for some ....

A. Beimel and B. Chor, "Universally ideal secret sharing schemes", IEEE Transactions on Information Theory, IT-40, 3, 1994, pp. 786-794.

.... PW95] Secret sharing: Secret sharing was originally suggested for threshold access structures by Shamir and Blakely [Sha79, Bla79] It was extended to arbitrary access structures in [ISN87] The issue of efficiency (i.e. share sizes) of such schemes has been considered in several papers (cf. [BD90, BDGV92, BC92]) Schemes suggested in [BL88] for structures represented by monotone formulas turn out to be important for our quorum systems. The most general access structures for which efficient secret sharing schemes are known is that of span programs [KW93] All our schemes fall into this category. Krawczyk ....

A. Beimel and B. Chor. Universally ideal secret sharing schemes. In Advances in Cryptology - CRYPTO'92 , LNCS 740, pages 183--195. Springer-Verlag, 1992.

....minimal coalitions authorized to recover both bits of the secret correspond to supports of vectors 1013102; 1100123; 1033320 and those of their cyclic shifts that have 1 or 3 on the 1 st coordinate. We shall show that this access structure cannot be realized by a binary ideal scheme. It is known [5], 19] that every binary ideal scheme is either linear or affine, i.e. corresponds to a binary linear code or to a binary affine code (a binary code is affine if the sum of any three code vectors is a code vector) Suppose that the minimal coalitions in this scheme correspond to minimal vectors ....

A. Beimel and B. Chor, "Universally ideal secret-sharing schemes," IEEE Trans. Inf. Theory, IT-40 (1994), 786--794.

.... 36, 39] Secret sharing: Secret sharing (cf. 44] was originally suggested for threshold access structures by Shamir and Blakley [43, 5] It was extended to arbitrary access structures in [24] The issue of efficiency (i.e. share sizes) of such schemes has been considered in several papers (cf. [7, 6, 3]) Schemes suggested in [4] for structures represented by monotone formulas turn out to be important for our quorum systems. The most general access structures for which efficient secret sharing schemes are known is that of span programs [26] All our schemes fall into this category. Krawczyk [27] ....

A. Beimel and B. Chor. Universally ideal secret sharing schemes. In Advances in Cryptology -- CRYPTO'92, LNCS 740, pages 183--195. Springer-Verlag, 1992.

.... in [33, 37] Secret sharing: Secret sharing was originally suggested for threshold access structures by Shamir and Blakely [40, 4] It was extended to arbitrary access structures in [22] The issue of efficiency (i.e. share sizes) of such schemes has been considered in several papers (cf. [6, 5, 2]) Schemes suggested in [3] for structures represented by monotone formulas turn out to be important for our quorum systems. The most general access structures for which efficient secret sharing schemes are known is that of span programs [24] All our schemes fall into this category. Krawczyk [25] ....

A. Beimel and B. Chor. Universally ideal secret sharing schemes. In Advances in Cryptology - CRYPTO'92, LNCS 740, pages 183--195. Springer-Verlag, 1992.

....secret, were characterized by Brickell and Davenport [11] in terms of matroids. The uniqueness of the associated matroid is established by Martin in [26] Brickell constructed some classes of ideal schemes in [10] and an interesting non existence result was proved by Seymour [30] Beimel and Chor [1] investigate the access structures for which an ideal scheme can be constructed for every possible size of the set of secrets. Finally, equivalence of ideal threshold schemes and orthogonal arrays is shown independently in [17] and [23] We also mention some extended capabilities of secret ....

A. Beimel and B. Chor. Universally ideal secret sharing schemes. Lecture Notes in Computer Science 740 (1993), 185--197.

....threshold access structures. An (m; n) threshold access structure, Gamma m;n , has as its basis all the m subsets of an n set. The well known Shamir threshold scheme [37] is one way to obtain a Gamma m;n ISSS. Many other classes of ideal schemes have been constructed; see, for example, [17, 18, 4]. We give a short description of the Shamir threshold scheme, since we will be using it later. Let q n 1 be a prime power. Initially, the TA chooses n distinct non zero random numbers x i 2 GF (q) and gives x i to user i (1 i n) These values do not need to be secret. Then, the TA the ....

A. Beimel and B. Chor. Universally Ideal Secret Sharing Schemes. IEEE Transactions on Information Theory 40 (1994), 786--794.

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A. Beimel and B. Chor. Universally ideal secret sharing schemes. IEEE Trans. on Information Theory, 40(3):786--794, 1994.

....seems to be useful in the computation. It enables us to reduce the length of the shares by a factor of log n in our basic scheme for linear functions. We also study ideal threshold schemes. These are schemes in which the size of the shares equals the size of the secrets 4 (see, e.g. [12, 13, 4, 33, 25]) We deal with the characterization of the families of functions F which can be evaluated by an ideal threshold scheme. For the interactive private channel model, we prove that every boolean function that can be evaluated is a linear function. For the broadcast model, we prove that F cannot ....

A. Beimel and B. Chor, Universally ideal secret sharing schemes, IEEE Trans. on Information Theory, 40 (1994), pp. 786-794.

....s. Therefore, every lower bound on the total size of shares in a secret sharing scheme is also a lower bound on the size of monotone span programs for the same function. On the other hand, lower bounds for monotone span programs imply the same lower bounds for linear secret sharing schemes (see [3, 4, 18]) Most of the known secret sharing schemes are linear, e.g. those in [33, 25, 19, 7, 34, 36, 12] and all the schemes described in the survey [37] The Omega Gamma m 2 = log m) lower bound implied by [15, 16] for monotone span program size is the strongest previously known lower bound for an ....

A. Beimel and B. Chor. Universally ideal secret sharing schemes. IEEE Transactions on Information Theory, IT-40,3 (1994) 786--794.

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A. Beimel and B. Chor (1994) Universally ideal secret-sharing schemes. IEEE Trans. Information Theory 40 786794.

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A. Beimel and B. Chor. Universally ideal secret sharing schemes. Lecture Notes in Computer Science 740 (1993), 185--197.

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