NEW BOUNDS ON THE INFORMATION RATE OF SECRET SHARING SCHEMES

A secret sharing scheme permits a secret to be shared among participan ts in such a way that only qualified subsets of participants can recov er the secret, but any nonqualified subset has absolutely no informati on on the secret. In this correspondence we derive new limitations on the information rate of secret sharing schemes, that measures how much information is being distributed as shares as compared to the size of the secret key, and the average information rate, that is the ratio b etween the secret size and the arithmetic mean of the size of the shar es. By applying the substitution technique, we are able to construct m any new examples of access structures where the information rate is bo unded away from 1. The substitution technique is a method to obtain a new access structure by replacing a participant in a previous structur e with a new access structure.