NOT ALL PERFECT EXTRINSIC SECRET SHARING SCHEMES ARE IDEAL

Abstract. We construct a perfect extrinsic secret sharing scheme for any case in which a set of participants can gain access to the secret if and only if the set contains a pair of members from some given list of pairs. A secret sharing scheme is a way by which a dealer rnay distribute secret information to individuals (call participants). There is associated '-<U.lh'.lcH"""F- of subsets of a set of can if they constitute a member of the access structure. usual to demand that the access structure be monotone: If A contains a subset which to the structure, then A itself must also belong to the structure. A secret scheme is called perfect if a set of pa.rticipants can no information by their shares unless the set is member of the access structure. An structure is called extrinsic if each participant '8 share contains the same amount of information. Simmons [4] has pointed out the desirability of a scheme which is and the access structure of which extrinsic. Observ