Abstract:

The construction of ideal access structure has an important role for designing secret sharing scheme with high information rate. The access structures corresponding to Shamir(k,n)’s type scheme( different from Shamir’s threshold type scheme) are ideal, but how to get these access structures which are not mutually isomorphic is a problem needed to be solved. First of all, the definition that the tracks are mutually equivalent is proposed, and then the problem for judging whether two minimal access structures are isomorphic in Shamir(k,n)’s type scheme is converted into the problem for judging whether their corresponding tracks are equivalent. This paper designs an algorithm which can be used to calculate all minimal privileged arrays that exist in the Shamir(k,n)’s type scheme and can be used to calculate all the tracks existing in the Shamir(k,n)’s type scheme that are not mutually equivalent. So this paper perfectly solves the problem that how to construct all ideal access structures which are not mutually isomorphic in the Shamir(k,n)’s type scheme. Particularly, this paper gives all the minimal privileged arrays with 7 participants in finite field F₁₃ and obtains all the tracks that are not mutually equivalent, and thus gives all the ideal minimal access structures with 7 participants that are not mutually isomorphic by the above judgment.

Key words: Shamir(k, n)’s type scheme, tracks, minimal privileged arrays, minimal access structure, ideal access structure