An infinite perfect-secrecy system with non-uniformly distributed keys

Based on some recent results derived from the Shannon theory of secrecy systems, this paper develops a new mathematical model for an infinite cryptosystem with perfect secrecy, and establishes a sufficient condition for a cryptosystem of perfect secrecy with non-uniformly distributed keys based on several groups of orthogonal Latin squares. The new model has the following features and advantages. First, the model with non-uniformly distributed keys, where the number of keys can be many more than the number of messages in a secrecy system, greatly improves the common one with finite perfect secrecy based on modulo additions in the current literature. Second, the model can be regraded as a theoretical base for designing practical block cipher algorithms. Third, since the number of basic cryptosystems in the new model is many more than that of the basic cryptosystems available in the current literature, it helps design new stream and block cipher algorithms with practical security and better resistance to known plaintext attacks. Finally, the present research on infinite secrecy systems of the new model is theoretically valuable and practically useful, as illustrated by an example of designing new basic cryptosystems under the conditions of the new model.