Multiple ramp schemes

A (t,k,n,S) ramp scheme is a protocol to distribute a secret s chosen in S among a set P of n participants in such a way that: (1) sets of participants of cardinality greater than or equal to k can reconstruct the secret s; (2) sets of participants of cardinality less than or equal to t have no information on s, whereas (3) sets of participants of cardinality greater than t and less than k might have "some" information on s. In this correspondence we analyze multiple ramp schemes, which are protocols to share many secrets among a set P of participants, using different ramp schemes. In particular, we prove a tight lower bound on the size of the shares held by each participant and on the dealer's randomness in multiple ramp schemes.