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.

翻译：我们研究安全功能,这些功能可以用来为信息理论安全的两个核心问题建立语义安全:窃听频道和秘密钥匙生成过程中的隐私放大。安全功能是组合设计(更准确地说,组合可变设计和平衡的不完整区块设计)的功能形式。每个成员都与独特的颜色有关,每个颜色对应一个独特的信息或关键价值。由于应用这种安全功能需要两个可信任的通信方共享一个公共种子,我们希望尽可能减少混合组合组合组合设计所给出的种子。我们给出了明确的例子,这些例子对种子长度和颜色(即信息或钥匙)的比率有着最佳或近乎最佳的交换。我们还从设计组合组合组合组合组合组合组合组合组合组合组合组合中获取安全功能的安全性功能的界限。我们还从设计组合组合的功能形式中获得安全性功能的界限。