A secret sharing scheme is one of cryptographies. 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 inter...A secret sharing scheme is one of cryptographies. 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 keys;that is, a multi-secret sharing scheme has p (≥2) keys. Dealers distribute shares of keys among n participants. Gathering t (≤n) participants, keys can be reconstructed. In this paper, we give a scheme of a (t,n) multi-secret sharing based on Hermite interpolation, in the case of p≤t.展开更多
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
文摘A secret sharing scheme is one of cryptographies. 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 keys;that is, a multi-secret sharing scheme has p (≥2) keys. Dealers distribute shares of keys among n participants. Gathering t (≤n) participants, keys can be reconstructed. In this paper, we give a scheme of a (t,n) multi-secret sharing based on Hermite interpolation, in the case of p≤t.
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
