We give several efficient transformations for manipulating the statistical difference (variation distance) between a pair of probability distributions. The effects achieved include increasing the statistical difference, decreasing the statistical difference, "polarizing" the statistical relationship, and "reversing" the statistical relationship. We also show that a boolean formula whose atoms are statements about statistical difference can be transformed into a single statement about statistical difference. All of these transformations can be performed in polynomial time, in the sense that, given circuits which sample from the input distributions, it only takes polynomial time to compute circuits which sample from the output distributions.

By our prior work (see FOCS 97), such transformations for manipulating statistical difference are closely connected to results about SZK, the class of languages possessing statistical zero-knowledge proofs. In particular, some of the transformations given in this paper are equivalent to the closure of SZK under complement and under certain types of Turing reductions. This connection is also discussed briefly in this paper.

This report contains a discussion of the difficult problem of key management for multicast communication sessions.  It focuses on two main areas of concern with respect to key management, which are, initializing the multicast group with a common net key and rekeying the multicast group.  A rekey may be necessary upon the compromise of a user or for other reasons (e.g., periodic rekey).  In particular, this report identifies a technique which allows for secure compromise recovery, while also being robust against collusion of excluded users.  This is one important feature of multicast key management which has not been addressed in detail by most other multicast key management proposals [1,2,4].  The benefits of this proposed technique are that it minimizes the number of transmissions required to rekey the multicast group and it imposes minimal storage requirements on the multicast group.