The query complexity of order-finding

We consider the problem here pi is an unknown permutation on {0, 1,...,2(n) - 1}, y(0) is an element of {0, 1,..., 2(n) - 1), and the goal is to determine the minimum r > 0 such that pi(r)(y(0)) = y(0). Information about pi is available only via queries that yield pi(x)(y) from any x is an element of {0, 1,...,2(n) - 1} and y is an element of {0, 1,...,2(n) - 1) (where m is polynomial in n). The resource under consideration is the number of these queries (hence our model of computation is the decision tree). We show that the number of queries necessary to solve the problem in the classical probabilistic bounded-error model is exponential in n. This contrasts sharply with the quantum bounded-error model, where a constant number of queries suffices.