Criteria of aptitude of a key-management tree for a frequency distribution of communication

Recently there are many opportunities for a private individual to send information to specific majority because of the spread of the Internet. In order to meet this demand, 1-to-k encryption (k ges 2) has been studied as a method to send the same message to authorized k persons safely and effectively. Algorithms of 1-to-k encryption consist of the following steps. Let U be the whole set of the n users.