Based On The Vector Space Offers No Third Party Involved In The Study Of The Secret Sharing Scheme

Secret sharing scheme is a major subject of information security. It is proposed to solve the questions of the revelation and missing of the key in the key management. Based on the Lagrange interpolation polynomial and the theory of the projective geometry, the threshold secret sharing was independently introduced by Shamir and Blakley in1979. Later, secret sharing schemes based Matrix and Chinese Remainder Theorem etc are proposed. But, a lot of questions which are not taken into account in the basic secret scheme were appeared in the actual application. Such as the change of shareholders, the number of the secrets and the honesty of shareholders. So, in order to satisfy some special cases for secret sharing schemes of the real world, various kinds of schemes have been put forward. In this paper, we mainly discuss a class of the secret sharing scheme without the existence of a trusted party. It is used to solve the problem that there is no trust party or the trust party is more different to find in the real world. It was first proposed by Ingemarsson and Simmon in1990. Later, some scholars also give papers of this class. In the analysis of the deficiencies of the existing schemes, we propose a secret sharing scheme without the existence of a trusted party which is suited to the vector space access structure. Compared with the original schemes, the proposed scheme is more general and is applied more widelyMain contributions of this paper are summarized as follows:1、Based on the definition of the((?),(?))homomorphism property of (t/n) secret sharing scheme and the feature of secret sharing scheme in vector space, we define the (+,+) homomorphism property of secret sharing scheme in vector space.2、At first, we analyze the shortcoming of the original schemes. Then, based on the method of strong (n,t,n) secret sharing scheme, which was proposed by Harn and Lin, a secret sharing scheme without the existence of a trust party in vector space is proposed. The new scheme is suited to the vector space access structure, and has no dealer. Furthermore, its information rate is equal to one.3、We give a verifiable secret sharing scheme without the existence of a trust party in vector space. It can effectively solve the cheating between the shareholders when there is no dealer in the scheme. The security of the scheme is based on the intractability of discrete logarithm.4、Combined with the actual situation and the applications of secret sharing, two application examples are given. The examples show the practicality of the secret sharing scheme without the existence of a trusted party scheme.