In this paper the linear multi-secret sharing schemes are studied by using monotone span programs. A relation between computing monotone Boolean functions by using monotone span programs and realizing multi-access str...In this paper the linear multi-secret sharing schemes are studied by using monotone span programs. A relation between computing monotone Boolean functions by using monotone span programs and realizing multi-access structures by using linear multi-secret sharing schemes is shown. Furthermore, the concept of optimal linear multi-secret sharing scheme is presented and the several schemes are proved to be optimal.展开更多
In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi- secret ...In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi- secret sharing scheme is measured by means of the complexity a and the randomness . Informally, the com- plexity a is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness is the ratio between the amount of information distributed to the set of users U = {1, …, n} and the minimum of information corresponding to every key. In this paper, we discuss a and of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make a and to be the minimum, respectively. That is, they are optimal.展开更多
主动秘密共享机制是在保持被共享的秘密不变的情况下,定期地对各参与者的秘密份额进行更新。许春香等人提出了一种定期更新防欺诈的秘密共享方案,该方案在秘密共享过程中仅支持共享单个秘密。在许春香等人方案的基础上,结合YCH(C C Yang...主动秘密共享机制是在保持被共享的秘密不变的情况下,定期地对各参与者的秘密份额进行更新。许春香等人提出了一种定期更新防欺诈的秘密共享方案,该方案在秘密共享过程中仅支持共享单个秘密。在许春香等人方案的基础上,结合YCH(C C Yang,T Y Chang和M S Hwang)多秘密共享机制提出了一种主动多秘密共享方案。在方案中,秘密份额能够在不改变秘密的前提下定期进行刷新,一次秘密共享过程可以同时共享多个秘密,并且每个参与者可以对其他参与者提供的秘密份额进行验证。方案的安全性基于Shamir门限机制和离散对数问题。展开更多
To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (...To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (n1+n2, m1+m2)-threshold multi-secret sharing scheme which combined cryptography and hypersphere geometry. In this scheme, we introduced a bivariate function and a coordinate function over finite field Zp to calculate the derived points of secret share, which can reconstruct the shared secrets by producing the intersection point of hypernormal plane and normal line on the hypertangent plane. At the initial stage the secret dealer distributes to each participant a secret share that can be kept secret based on the intractability of discrete logarithm problem and need not be changed with updating the shared secrets.Each cooperative participant only needs to submit a derived point calculated from the secret share without exposing this secret share during the process of reconstructing the shared secret. Analyses indicate that the proposed scheme is not only sound and secure because of hypersphere geometric properties and the difficulty of discrete logarithm problem, but also efficient because of its well dynamic behavior and the invariant secret share. Therefore, this bipartite threshold multi-secret sharing scheme is easy to implement and is applicable in practical settings.展开更多
A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange＇s interpolation formula. A secret sharing scheme has one key...A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange＇s interpolation formula. A secret sharing scheme has one key. On the other hand, a multi-secret sharing scheme has more than one key, that is, a multi-secret sharing scheme has p （〉_ 2） keys. Dealer distribute shares of keys among n participants. Gathering t （〈 n） participants, keys can be reconstructed. Yang et al. （2004） gave a scheme of a （t, n） multi-secret sharing based on Lagrange＇s interpolation. Zhao et al. （2007） gave a scheme of a （t, n） verifiable multi-secret sharing based on Lagrange＇s interpolation. Recently, Adachi and Okazaki give a scheme of a （t, n） multi-secret sharing based on Hermite interpolation, in the case ofp 〈 t. In this paper, we give a scheme ofa （t, n） verifiable multi-secret sharing based on Hermite interpolation.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.60083002,90304012,2004CB318000).
文摘In this paper the linear multi-secret sharing schemes are studied by using monotone span programs. A relation between computing monotone Boolean functions by using monotone span programs and realizing multi-access structures by using linear multi-secret sharing schemes is shown. Furthermore, the concept of optimal linear multi-secret sharing scheme is presented and the several schemes are proved to be optimal.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11271003the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No.20134410110003+3 种基金High Level Talents Project of GuangdongGuangdong Provincial Natural Science Foundation under Grant No.S2012010009950the Project of Department of Education of Guangdong Province under Grant No 2013KJCX0146the Natural Science Foundation of Bureau of Education of Guangzhou under Grant No.2012A004
文摘In a linear multi-secret sharing scheme with non-threshold structures, several secret values are shared among n participants, and every secret value has a specified access structure. The efficiency of a multi- secret sharing scheme is measured by means of the complexity a and the randomness . Informally, the com- plexity a is the ratio between the maximum of information received by each participant and the minimum of information corresponding to every key. The randomness is the ratio between the amount of information distributed to the set of users U = {1, …, n} and the minimum of information corresponding to every key. In this paper, we discuss a and of any linear multi-secret sharing schemes realized by linear codes with non-threshold structures, and provide two algorithms to make a and to be the minimum, respectively. That is, they are optimal.
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.60573171)安徽省自然科学基金(the Natural Science Foundation of Anhui Province of China under Grant No.070412051)+2 种基金安徽高校省级重点自然科学研究项目(No.KJ2007A043No.2007JYXM020)安徽大学人才队伍建议经费
文摘主动秘密共享机制是在保持被共享的秘密不变的情况下,定期地对各参与者的秘密份额进行更新。许春香等人提出了一种定期更新防欺诈的秘密共享方案,该方案在秘密共享过程中仅支持共享单个秘密。在许春香等人方案的基础上,结合YCH(C C Yang,T Y Chang和M S Hwang)多秘密共享机制提出了一种主动多秘密共享方案。在方案中,秘密份额能够在不改变秘密的前提下定期进行刷新,一次秘密共享过程可以同时共享多个秘密,并且每个参与者可以对其他参与者提供的秘密份额进行验证。方案的安全性基于Shamir门限机制和离散对数问题。
文摘To address the problem that existing bipartite secret sharing scheme is short of dynamic characteristic, and to solve the problem that each participant can only use secret share once, this paper proposed a bipartite (n1+n2, m1+m2)-threshold multi-secret sharing scheme which combined cryptography and hypersphere geometry. In this scheme, we introduced a bivariate function and a coordinate function over finite field Zp to calculate the derived points of secret share, which can reconstruct the shared secrets by producing the intersection point of hypernormal plane and normal line on the hypertangent plane. At the initial stage the secret dealer distributes to each participant a secret share that can be kept secret based on the intractability of discrete logarithm problem and need not be changed with updating the shared secrets.Each cooperative participant only needs to submit a derived point calculated from the secret share without exposing this secret share during the process of reconstructing the shared secret. Analyses indicate that the proposed scheme is not only sound and secure because of hypersphere geometric properties and the difficulty of discrete logarithm problem, but also efficient because of its well dynamic behavior and the invariant secret share. Therefore, this bipartite threshold multi-secret sharing scheme is easy to implement and is applicable in practical settings.
文摘A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange＇s interpolation formula. A secret sharing scheme has one key. On the other hand, a multi-secret sharing scheme has more than one key, that is, a multi-secret sharing scheme has p （〉_ 2） keys. Dealer distribute shares of keys among n participants. Gathering t （〈 n） participants, keys can be reconstructed. Yang et al. （2004） gave a scheme of a （t, n） multi-secret sharing based on Lagrange＇s interpolation. Zhao et al. （2007） gave a scheme of a （t, n） verifiable multi-secret sharing based on Lagrange＇s interpolation. Recently, Adachi and Okazaki give a scheme of a （t, n） multi-secret sharing based on Hermite interpolation, in the case ofp 〈 t. In this paper, we give a scheme ofa （t, n） verifiable multi-secret sharing based on Hermite interpolation.
