Sharing one secret vs. sharing many secrets: tight bounds on the average improvement ratio
Giovanni Di Crescenzo · Symposium on Discrete Algorithms · 2000
A secret sharing scheme is a method for distributing a secret among several parties in such a way that only qualified subsets of the parties can reconstruct it and unqualified subsets receive no information about the secret. A multi secret sharing scheme is the natural extension of a secret sharing scheme to the case in which many secrets need to be shared, each with respect to possibly different subsets of qualified parties. A multi secret sharing scheme can be trivially realized by realizing a secret sharing scheme for each of the secrets. A natural question in the area is whether this simple construction is the most efficient as well, and, if not, how much improvement is possible over it.