Mosaics of combinatorial designs for privacy amplification

We study security functions which can serve to establish semantic security for 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 of a mosaic corresponds to a unique key value. We give explicit examples which have an optimal or nearly optimal tradeoff of seed size, given by the size of the block index set of the mosaics, versus key rate. We also derive bounds for the security performance in privacy amplification of security functions given by functional forms of mosaics of designs.