Date Added: Jan 2012
This paper is concerned with several security notions for information theoretically secure encryptions defined by the variational (statistical) distance. To ensure the Perfect Secrecy (PS), the mutual information is often used to evaluate the statistical independence between a message and a cryptogram. On the other hand, in order to recognize the information theoretically secure encryptions and computationally secure ones comprehensively, it is necessary to reconsider the notion of PS in terms of the variational distance. However, based on the variational distance, three kinds of definitions for PS are naturally introduced, but their relations are not known.