  S. S. Magliveras et al. have described symmetric and public key cryptosystems
based on logarithmic signatures (also known as group bases) for finite
permutation groups.
  In this paper we show that if $G$ is a nontrivial finite group which is not
cyclic of order a prime, or the square of a prime, then the round (or
encryption) functions of these systems, that are the permutations of $G$
induced by the exact-transversal logarithmic signatures (also known as
transversal group bases), generate the full symmetric group on $G$.
  This answers a question of S. S. Magliveras, D.R. Stinson and Tran van Trung.
