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.
ramp schemes randomness cryptography data security secret sharing schemes