  We study security functions which can serve to establish semantic security
for the two central problems of information-theoretic security: the wiretap
channel, and privacy amplification for secret key generation. The security
functions are functional forms of mosaics of combinatorial designs, more
precisely, of group divisible designs and balanced incomplete block designs.
Every member of a mosaic is associated with a unique color, and each color
corresponds to a unique message or key value. Every block index of the mosaic
corresponds to a public seed shared between the two trusted communicating
parties. The seed set should be as small as possible. We give explicit examples
which have an optimal or nearly optimal trade-off of seed length versus color
(i.e., message or key) rate. We also derive bounds for the security performance
of security functions given by functional forms of mosaics of designs.
