  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 in 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 is associated with a unique color, and each color corresponds to a
unique message or key value. Since the application of such security functions
requires a public seed shared between the two trusted communicating parties, we
want to minimize the seed set given by the common block index set of the
designs in the mosaic. 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.
