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

[0002] The present invention relates to an electronic payment system in electronic commerce of network, and especially to a system using an unbalanced binary tree structure to calculate. The network used includes an Internet, a telephone network, a dedicated network, a cable TV network, etc.

[0003] The basic structure of an electronic payment system 10 is illustrated in FIG. 1. A subscribe computer 1 and a merchant computer 2 perform data communication for completing a transaction through an Internet 3 (or other network). In general, the action of transferring account or verification for security is performed through an electronic payment service center 4 (for example, banks). In FIG. 2, the subscribe computer 1 purchases the total unit n by paying an amount of money to the electronic payment service center 4 and is awarded with an authority. Then, the total unit n is operated by a one-way function h to obtain a contrast data M. If the user desires to consume, the subscribe computer 1 firstly subtracts the unit spent, and uses the current unit k to calculate a value X_krepresenting current consumption state to the amount of money. These datum (M and X_k) is sent to the merchant computer 2 through the Internet 3. In a reprocessing procedure P, the merchant computer 2 calculates a second value X′_kusing identical one-way function h. In the conventional operating process of the subscribe computer 1 with respect to the values M and X_k, a payment chain of one-way hash function shown in FIG. 3 is used, which has the relation of a one-way function X_n−1=h(X_n). It means that the value X_nis substituted into a one-way hash function h to operate as a one-dimension function or obtaining the next value X_n−1. As shown in this figure, in the subscribe computer 1, starting from substituting the initial value of a random number X_ninto an one-way hash function h to perform n times for deriving a contrast data M or to perform n−k times for deriving X_k. Then, in the reprocessing procedure P of the merchant computer 2, by the same one-way hash function h, X_kis operated to generate X′_kand then the value X′_kis contrasted with data M. If X′_k=M, it identifies this transaction is successful, thus the merchant computer 2 provides services or merchandises to the subscriber and requests a transferring account to the electronic payment service center 4, thus storing current X_kas a contrast value M for being used in next consumption.

[0004] Since the one-way hash function is irreversible, any X_konly operates in a forward direction (the leftward direction in FIG. 3). Therefore, for each consumption. (with different k value, and value k is increased monotonically to value n), the subscribe computer 1 calculates from X_nto X_kfor n−k times. For example, assuming one unit of money is consumed each time, thus, n−1 times of function operation are necessary to calculate from X_nto X₁. In the next consumption, from X_nto X₂similarly, n−2 times of operation are necessary. In further next consumption, from X_nto X₃n−3 times of operation is necessary. And for X_n−1, only one time of operation from X_nis necessary. Thus, in the conventional calculation, totally, (n−1)+(n−2)+ . . . +1 times of functional operation are performed, and then this total value is divided by n to obtain an average of $\frac{\left(n-1\right)}{2}$

[0005] times for each consumption. For such a large amount of operations, the subscribe computer 1 with a finite ability of hardware (for example, an IC card) is insufficient. Therefore, the operation efficiency becomes low. The larger the unit of purchase, the lower the operation efficiency. Thus, the prior art only can be used in an electronic payment system with a smaller amount of money.

[0006] Accordingly, the primary object of the present invention is to provide an electronic payment device using an unbalanced binary tree for improving the calculating efficiency of an electronic payment system.

[0007] Another object of the present invention is to provide an electronic payment device using an unbalanced binary tree for reducing the operation times of an electronic payment system.

[0008] Another object of the present invention is to provide an article of manufacture comprising a medium contained a computer readable program, which can be used in the electronic payment device using an unbalanced binary tree of the present invention for improving the calculating efficiency.

[0009] In order to attain the aforementioned objects, in the electronic payment system of the present invention, an operation device is installed in a computer comprising a data providing device for providing datum including the total unit n of the amount of money that user purchases, a first one-way function h₁, a second one-way function h₂, and the current unit k of the amount of money after current consumption; and a microprocessor. The microprocessor includes a first processing device for selecting two positive integers p and q which conforming the relation p×q=n; a random number generator for generating a random number and setting the random number as an initial value X_pq; a second processing device to calculate the number a of times of the first one-way function h₁by formula $a=q-\lceil \frac{k}{p}\rceil ;$

[0010] a third processing device to calculate the number b of times of the second one-way function h₂by formula b=[p−(k mod p)] mod p; and a fourth processing device to derive a first data X_kby formula X_k=h₂^b(h₁^a(X_pq)). Thereby, the first data X_kof current consumption, or a plurality of contrast values M_qare calculated. After the first data X_kand the contrast values M_qbeing sent to a merchant computer through a network, the merchant computer performs a reprocess procedure to the first data X_kto form with a second data X′_k, and checking whether the respective contrast value M_qis equal to the second data X′_k, so as to determine whether this transaction is successful.

[0011] The data providing device of the present invention is a storing device (such as ROM, hard disk), or an input device (such as a modem) reading data from a network.

[0012] It is suggested that the first one-way function h₁and the second one-way function h₂of the present invention are one-way Hash functions, for example, a MD-5 algorithm, a RIPE-MD algorithm, a SHA-1 algorithm, a MDC2 algorithm, or a MDC4 algorithm, etc. It is preferred that the first and second one-way functions h₁, h₂are RIPE-MD algorithm, SHA-1 algorithm, respectively. They have the advantages of short data length and preferred reliability.

[0013] In the present invention, the operating device can be installed within the subscriber's computer or the merchant computer. The operating device can be made as an IC card itself (such as a Smart IC card), or the device can be modularized as a chip. Preferably, the procedure of the method of the present invention can be encoded in a medium to serve as a computer readable program to perform the calculation with the unbalanced binary tree. Of course, it can be used in a reprocessing procedure of the merchant computer for reducing operation times and thus improving the operating efficiency.

[0014] FIG. 1 shows a basic structure of an electronic payment system.

[0015] FIG. 2 shows the flow chart about the transaction of an electronic payment system.

[0016] FIG. 3 is a schematic view showing the operating process of an one dimensional one-way hash function.

[0017] FIG. 4 shows the structure of the operating device according to the present invention.

[0018] FIG. 5 shows the flow chart of the calculating method in the present invention,

[0019] FIG. 6 is a schematic view showing the operating process of two dimensional one-way hash functions in the unbalanced binary tree structure.

[0020] FIG. 7 is a schematic view showing the operating process of two embodiments.

[0021] With reference to FIG. 4, the operating device of the present invention is installed at subscriber's computer 1, and includes a data providing device 12 and a microprocessor 1. The data providing device 12 may be a memory, such as ROM, hard disk, or a modem connected to an Internet 3 for providing data. In this embodiment, an Internet 3 serves to exchange data (it also can be sent by a telephone network, a dedicated network, a cable TV network, or other equivalent network).

[0022] Referring to FIG. 5, step S1 to S3 are initialization operations, and step S4 to S6 shows the operating process of the present invention. The microprocessor 11 reads or receives datum including the total unit n of the amount of money that user purchases, first one-way function h₁and second one-way function h₂(step S1). Selecting two positive integers p and q so as to conform the relation p×q=n (step S2, the microprocessor 11 generates a random number and set as an initial value X_pq(step S3). Then, the current unit k of the amount of money after current consumption is read (step S4). Then formulas $a=q-\lceil \frac{k}{p}\rceil$

[0023] (formula A) and b=[p−(k mod p)] mod p (formula B) are served to calculate values a and b (step S5), and then they are substituted into formula X_k=h₂^b(h₁^a(X_pq)) (formula C) for obtaining a first data X_k(step S6) where $\lceil \frac{k}{p}\rceil$

[0024] represents that the value k dividing by p is carried by one in any condition; (k mod p) represents the residue of k dividing by p; h₁^a(X_pq) represents that by the first one-way function h₁, a times of operation to value X_pqis performed; h₂^b(h₁^a(X_pq)) represents by the second one-way function h₂, b times of operation is performed to h₁^a(X_pq). In next consumption, the next consumption unit k is read again, and the step S4 to S6 proceeds for deriving the next first data X_krepeatedly.

[0025] The arithmetic meaning of the aforementioned steps is illustrated in FIG. 6. The datum including the total unit n of amount of money that user purchases is decomposed first into a matrix of p rows×q columns in step S2. Each node is represented by a general form X_p(q−a)−b, where “a” represents the line distance between the node and the initial value X_pq, and “b” represents the line distance between the node X_p(q−a)−b, and the initial value X_pq. The “a” and “b” can be calculated from the formula A and B in step S5 in this embodiment. The first one-way function h₁defines as a function of a leftward operation one-way function for each node X_p(q−a)in the first row (b=0), which may be a one-way hash function of RIPE-MD algorithm with an irreversible property of h₁(X_p(q−a))=X_p[q−(a+1)]. The second one-way function h₂defines as a function of a downward operation one-way function for each node X_p(q−a)−b, which may be a one-way hash function of SHA-1 algorithm with an irreversible property of h₂(X_p(q−a)−b)=X_{p(q−a)−(b+1)}. Therefore, in step 6, each node X_k(with a general form X_p(q−a)−b) can be derived easily by a times of first one-way function h₁operations and b times of second one-way function h₂operations to the initial value X_pq. Thus, each node X_{p(q−a)−(p−1)}in the last row (b=p−1) of the matrix can be operated easily so as to form a root sequence R. If each value in root sequence R is operated by one times of second one-way function h₂operation, then q contrast values M_qare obtained, where q=1,2,3 . . .

[0026] Since each node in the first row (b=0) except the leftmost node, having a longer left string than its right string, that's why it is named as an “Unbalanced Binary-Tree”.

[0027] When consumption is occurred in Internet 3, the first data X_kand contrast value M_qare calculated and transferred to the merchant computer 2 through the Internet 3. The merchant computer 2 re-processes X_kto become a second data X′_kand check whether X′_k=M_q. The merchant computer 2 may store the first data X_kas its contrast value M_qfor later use. Wherein, in the reprocess procedure P, the merchant computer 2 also can use the present invention to calculate the second data X′_kfrom the first data X_krapidly.

[0028] FIG. 7 is two real embodiment illustrating the operation of the present invention. The first one-way function h₁and the second one-way function h₂are one-way hash function of RIPE-MD algorithm and SHA-1 algorithm respectively. In the first embodiment, assume that user purchases $11.2 for n=56 units (1 unit=$0.2). By the present invention above mentioned, the two positive integers p=7 rows, q=8 columns are selected (the closer the p and q, the better the operation efficiency). If the user consumes 10 units (K=10) at the first time, by the aforementioned formulas A and B, we obtains that a=6 times, b=4 times, these values are substituted into formula C for deriving X₁₀. Namely, totally, 10 times of operation are performed including 6 times of first one-way function h₁operations and 4 times of second one-way function h₂operations. However, this is more efficient than that in the prior art in which by the operation of a single one-way function, from X₅₆to X₁₀, totally 56−10=46 times of operations are necessary. If in next time, 22 units are consumed, then, K=32, by the present invention, a=3 times, and b=3 times. Thus, only six times of operation is necessary for obtaining X₃₂. This is more efficient than that in the prior art in which by the operation of a single one-way function, from X₅₆to X₃₂, totally 56−32=24 times of operations are necessary.

[0029] In practical, in the case that one unit of money consumed each time, the total operation times T of FIG. 6 is $T=\sum _{a=0}^{q-1}\sum _{b=0}^{p-1}\left(a+b\right)=\mathrm{pq}\left(\frac{p+q}{2}-1\right).$

[0030] Thus, the average operating efficiency is T divided by n which is equal to $\left(\frac{p+q}{2}\right)-1.$

[0031] This value is less than the prior art in which $\frac{\left(p·q-1\right)}{2}$

[0032] times of operations is necessary. Therefore. the present invention has greatly improved the operating efficiency.

[0033] Although the present invention has been described using specified embodiment, the examples are meant to be illustrative and not restrictive. It is clear that many other variations would be possible without departing from the basic approach, demonstrated in the present invention. Therefore, all such variations are intended to be embraced within the scope of the invention as defined in the appended claims.