Electronic payment device using unbalanced binary tree and the method of the same

An electronic payment device and its method using an unbalanced binary tree are disclosed. The total unit n of the amount of money that user purchases is decomposed first into a Matrix of p rowsxq columns. Then, a first one-way function h1 and a second one-way function h2 serve to define the one-way function operation of the first row and each column, respectively. When two numbers of operation times a and b are calculated by their formulas respectively, they are substituted into formula Xk=h2b(h1a(Xpq)). Namely, by the first one-way function h1, a times of operation is performed, and then by the second one-way function h2, b times of operation is performed, thus, a first data Xk of current consumption can be derived rapidly. The present invention has only a few times of operation, thus the calculating efficiency is improved greatly.