Method for deciding an efficient tree structure for logical key hierarchy and method for analyzing performance of a tree structure

A method for deciding an efficient tree structure for a logical key hierarchy and a method for analyzing performance of a tree structure are provided to compare performance of an entire tree by comparing only the number of average key updating messages for a partial tree. A method for deciding an efficient tree structure for a logical key hierarchy comprises the following steps of: performing a prime factorization for the number of all members, arranging each prime number according to the result of the prime factorization, and expressing the arrangement of the prime numbers in a tree structure(S101,S102); arranging each prime number of the tree structure in ascending order(S103); interchanging sequential two prime numbers of 2 with 4 and arranging the resultant prime numbers in ascending order if the prime number whose value is 2 is sequentially arranged among the prime numbers of the tree structure(S104,S105); and outputting the result as the effective tree structure(S106).