Abstract: Disclosed is an electronic payment device and its method using an balanced binary tree for calculating a first data Xk of current consumption or a plurality of root values Rq from an initial value Xn of the amount of money that user purchases. The first data Xk is correspondent to a position value j with a respective relation of j=n−k+1. The first data Xk is generated according to the value of the binary code dm−1dm−2 . . . d1d0 of the position value j being a 0 or 1, by formula Xk=hd0(. . . (hdm−2(hdm−1(Xn)))). If the binary code di=0, i=m−1, m−2, . . . , 1, 0, then the first one-way function h0 is used as an operating function. Otherwise, the second one-way function h1 is operated when the binary code di=1. Moreover, a function operating device for an electronic payment using an balanced binary tree is also disclosed. The present invention requires less calculation than that in the prior art, and thus is more effective.

Abstract: 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 rows×q 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.