JP5220967B2 - Auction system and auction method - Google Patents

Description

  The present invention relates to an auction system for performing an auction using a network such as the Internet, an information processing apparatus, an auction bidding method, an auction winning bid amount determining method, an auction winning bidder determining method, and a program for causing a computer to execute these methods. The present invention relates to a recorded computer-readable recording medium.

  Conventionally, it is considered that information on who has paid which product at what price in an auction is very important information related to privacy. In a normal auction, a style in which bid values (amounts) are auctioned over time is adopted. In the meantime, since information such as who paid what price and who is competing is open to the public, it can be considered that personal information leakage continues in a sense.

  Even if the system displays only the bid value and membership number, the auction organizer who manages the membership number tells who is bidding and how much he wants what. It will be known. There is a risk that such information may be used for sending direct mail.

Problems to be solved by the invention

  However, in the above prior art, it is only necessary that the final winning bid value and information of the winning bidder are transmitted to the seller (hereinafter referred to as a seller), and other participants' Ideally, personal information and bid prices are not known.

  The present invention has been made in view of the above-described conventional technology, and only the seller can know the personal information of the successful bidder while ensuring the confidentiality of the bid information of bidders other than the successful bidder. The purpose is to provide an auction system.

Means for solving the problem

[Means for Solving the Problems]
In order to solve the above-described problems and achieve the object, an auction system according to the present invention is an auction system that performs an auction based on bid information transmitted from a terminal device connected to a network. Information on bidders is digitized using a public key issued by the seller, and the bid information including the digitized information on bidders is distributed to a plurality of servers connected to the network using a predetermined algorithm. In the state where the bid information is distributed and stored in the plurality of servers, the highest bidder who is the highest bidder is determined and the bid amount of a bidder other than the highest bidder is awarded. It is characterized by being determined as a forehead.

The auction system according to the present invention, in the above invention, generates a polynomial based on information related to a bid amount included in the bid information, and distributes information related to the bid amount using the generated polynomial. Features.

In the above invention, the auction system according to the present invention calculates the value of the other polynomial by reducing the degree of the other polynomial derived from the polynomial, and determines the winning bid amount based on the calculated value. It is characterized by determining.

In the auction system according to the present invention, in the above invention, the information about the bidder included in the bid information is digitized, a polynomial is generated based on the digitized information about the bidder, and the generated polynomial is The method is characterized in that information on the bidder is distributed.

In addition, an information processing apparatus according to the present invention is connected to a network, receives receiving information related to an auction from the network, displaying means displaying information related to an auction received by the receiving means, and the display means. Input means for inputting bid information including information regarding the bid amount and bidder with respect to the displayed information related to the auction, and distribution for distributing the bid information input by the input means to a predetermined number using a predetermined algorithm Processing means; and transmitting means for transmitting each bid information distributed by the distributed processing means to a server connected to the network, which is determined in advance for each target product of the auction, and to each separate server; It is provided with.

In the information processing apparatus according to the present invention, in the above invention, the distributed processing unit generates a polynomial based on information about a bid amount input by the input unit, and is a value predetermined for each server. Is substituted for the polynomial, and the value of the polynomial is calculated for each server, and the transmission means transmits the value of the polynomial calculated by the distributed processing means to the server. .

In the information processing apparatus according to the present invention, in the above invention, the distributed processing unit quantifies information about the bidder input by the input unit, and calculates a polynomial based on the digitized information about the bidder. Generating and substituting a predetermined value for each of the servers into the polynomial, thereby calculating the value of the polynomial for each of the servers, and the transmission means calculates the value of the polynomial calculated by the distributed processing means. And transmitting to each of the servers.

The information processing apparatus according to the present invention is characterized in that, in the above invention, the bidder information is digitized using a public key issued by a seller.

The bidding method for an auction according to the present invention relates to a receiving process for receiving information related to an auction through a network, a display process for displaying information related to an auction received by the receiving process, and an auction displayed by the display process. An input process for inputting bid information including information on a bid amount and a bidder for information, a distribution process for distributing the bid information input by the input process to a predetermined number using a predetermined algorithm, and the distribution Transmitting each bid information distributed by the process to a server connected to the network, which is predetermined for each target product of the auction, and transmitted to each separate server. To do.

Further, according to the bidding method for an auction according to the present invention, in the above invention, the distribution step generates a polynomial based on information on the bid amount input in the input step, A calculation step of calculating a value of the polynomial for each server by substituting a determined value into the polynomial generated by the polynomial generation step, and the transmission step is calculated by the calculation step. Each polynomial value is transmitted to the server.

In the auction bidding method according to the present invention, in the above invention, the distribution step is quantified by the quantification step for quantifying the information regarding the bidder input by the input step, and the quantification step. A polynomial generating step for generating a polynomial based on information about the bidders, and a value determined for each server by substituting a predetermined value for each server into the polynomial generated by the polynomial generating step. A calculating step for calculating the value, wherein the transmitting step transmits the value of the polynomial calculated by the calculating step to the server.

In the auction bidding method according to the present invention as set forth in the invention described above , the digitizing step digitizes information on the bidder using a public key issued by a seller.

The auction winning bid amount determining method according to the present invention relates to the auction winning bid amount determining method performed based on bid information including information related to a bid amount transmitted from a terminal device connected to a network. Based on the information, a polynomial is generated, and a bid of a predetermined rank other than the highest bid is determined from information on each bid that is distributed and stored in a plurality of servers connected to the network using the generated polynomial. When calculating only the amount, the value of the other polynomial is calculated by reducing the degree of the other polynomial derived from the polynomial.

The auction winning bidder determination method according to the present invention relates to the auction winning bidder determination method performed based on bid information including information related to a bidder transmitted from a terminal device connected to a network. Information is digitized using the public key issued by the seller, a polynomial is generated based on the digitized information, and the generated polynomial is used to distribute and store the information on a plurality of servers connected to the network. From the information, only bidders with a predetermined rank are extracted.

A computer-readable recording medium according to the present invention records a program for causing a computer to execute the above method.

  With reference to the accompanying drawings, an auction system, an information processing apparatus, an auction bidding method, an auction winning bid amount determining method, an auction winning bidder determining method, a program for causing a computer to execute these methods, A preferred embodiment of a computer-readable recording medium on which a program is recorded will be described in detail.

(Outline of anonymous auction system)
First, an outline of the auction system according to the embodiment of the present invention will be described.

  The auction system according to this embodiment does not require registration of personal information, and the personal information is protected from the system administrator. This system is fundamentally different from the conventional so-called “anonymous auction system”.

  The conventional “anonymous auction system” is an auction in which information other than the winner, that is, who has participated in the bid, is not known to the seller or auction organizer, and it is not necessary to register personal information in advance. .

  In a general auction, when bidding is performed, personal information of the bidder is required first. This is because if a bid is made without registration, a bid price that is not so serious is easily canceled and the auction itself becomes invalid. By registering personal information, it is possible to prevent the auction from being disturbed, but for the bidder, personal information is known to others and there is a risk of suffering an unexpected disadvantage.

  In the auction system according to the present embodiment, a bidder can bid without registration of personal information, and only the seller can know who the winning bidder is. In order to prevent easy cancellation, for example, a countermeasure of using electronic payment can be considered. This is not a general bid-up method, and there is only one bid. Once you bid, you cannot cancel or change the amount. Therefore, it is necessary for the bidder to bid at a price that he considers truly appropriate. Thus, the auction system according to the present embodiment is fundamentally different from the conventional so-called “anonymous auction system” and has at least the following four features.

(1) Protection of bidder's anonymity Registration of personal information is unnecessary, and the bidder's anonymity is maintained for all participants including the system administrator. A bidder's bid value and personal information are unknown to all other bidders, system administrators, and sellers from the beginning to the end. Therefore, it is a mechanism in which neither a bidder nor an administrator can cheat.

(2) Protection of bid price confidentiality Bidding prices other than the bid price are hidden from all participants including the system administrator. It is possible to specify the winning bidder and the winning bid price while maintaining anonymity even in the aggregation process for determining the winning bidder.

(3) Protection of successful bidder information Only the seller can know the personal information of the successful bidder. Eventually, the seller is informed of the personal information and the winning bid price only for the winning bidder, and the winning bid price is informed to all bidders. All other information is not available to system administrators, as well as bidders and sellers.

(4) Compatible with multiple auction methods Both “first price auction” and “second price auction” are supported.

  Here, an auction in which the highest price among the bid values is the winning bid price is referred to as a “first price auction”. On the other hand, the successful bidder is the person who bids the highest price, but the auction in which the successful bid price is the bid price of the bidder with the second highest price is called a “second price auction”.

  Many of the auctions currently held on the Internet are "auction type" first price auctions. In the case of “auction type”, the highest bid price during the bidding is disclosed, and the bidder can repeatedly bid. Even in the first price auction, there is an auction in which the bidder bids only once and the bid price is kept secret. This method is called a sealed method or a shielded bid method. Even in the second price auction, there is a shield bit type auction in which the bidder bids only once.

  The first price auction has an advantage that it does not require much time until a successful bid because the highest bidder within the deadline is the winning bidder. On the other hand, however, there is a drawback that the winning price is far from the market price. In addition, the organizer needs to know all the bid information when opening the bid. As a tenderer's psychology, tenders tend to bid cheaper than their limits, trying to reduce their payments as little as possible when making a successful bid. On the other hand, in the second-price auction method, a bidder bids close to the limit he can make, because the bidder will not win at that price even if he bids to his limit.

  There is an automatic bidding method with an upper limit price setting for the first price auction. This is because if the bidder sets the highest bid price that he can make a successful bid in advance, the proxy will see the current highest bid price and automatically set the bid price at that + α (step size). It will be updated. In this case, the winning bidder can buy the product at the second highest bid price + α (step size), and the smaller α is, the closer the winning bid price is to the second price auction. That is, as a result, the first price auction and the second price auction of the automatic bidding method with the upper limit price setting are the same.

  The auction system according to the present embodiment can be compatible with both a shielded bid first price auction and a second price auction. In this anonymous auction system, each auction method is implemented using a separate secret calculation protocol. In particular, the anonymous second price auction system is configured using a plurality of secret calculation protocols. The feature of this anonymous auction system is that when one bidder bids, the bid information can be sent to multiple servers, and one bid can be made for each product once. By bidding for the highest price you think, you can make a successful bid for a product at a reasonable price.

  In particular, the anonymous second price auction system is configured using a plurality of secret calculation protocols. A secret computation protocol is an algorithm of how to achieve a certain goal while maintaining anonymity. For example, assume that servers A, B, and C have values of a, b, and c, respectively. However, it is not possible to know what value other servers have. At this time, the target that all servers want to know the average values of a, b, and c while keeping their own values secret is realized.

  An anonymous auction protocol is an algorithm that calculates the price of a successful bid while keeping the bid price sent to each server secret, and can be positioned as one of the secret calculation protocols. In particular, in the case of the second price auction, there is a difficulty in calculating the second highest bid price without revealing the highest bid price and the third bid price or lower. In the auction system according to the present embodiment, this is the case. Is possible. The auction according to the present embodiment is characterized in that a plurality of auction servers are used and information is encrypted and transmitted / received.

(Auction method realized by this system)
As described above, the auction system according to the present embodiment enables two auctions of the first price method and the second price method. The first price method is a type of auction in which a bidder with the highest bid price makes a successful bid at that price. The second price method is an auction in which a bidder with the highest bid price makes a successful bid at the second bid price.

(About various auction methods)
(1) Auction classification (1) Whether the bidder and the current bid price will be public or private (anonymous)
▲ 2 ▼ Whether the highest bid (first price) or the second price (second price)
▲ 3 ▼ Whether to determine the winning bid value in a single bid,
There are several methods depending on the situation.

(2) Representative auctions currently in operation Many of the auctions currently held on the Internet are open-type and are called “price-up”, and people who bid the highest price within the deadline. The winning bidder is the winning bid amount. (Also called English auction). As a modification, there is an automatic bidding method for setting an upper limit price as a first price auction auction method. When the bidder specifies his / her budget in advance, the system automatically bids a price slightly higher than the current maximum amount. This has almost the same effect as the second price auction on the bidder's winning bid amount. In either case, even if a nickname is used, anonymity is not sufficiently maintained, and there is a possibility of personal information leakage and fraud.

(3) Auction system according to this embodiment {circle over (1)} Each is a private one-time bidding method. Since it can be carried out while keeping the bidder's information secret, it is possible to prevent personal information leakage and fraud.
(2) For price determination, the first price method and the second price method are available. It can be applied not only to determination of the maximum amount but also to determination of the minimum amount (such as a tender of a government office).
(3) The second price auction is an auction method in which the person who bids the highest price within the deadline is the winning bidder, and the bid price of the bidder who bids the second highest is the winning bid amount. The tenderer feels that even if he bids up to his limit, he will not win at that price, so he bids close to his limit. It can also meet the needs of bidders who want to get a product.

(Principle of auction system)
Next, the principle of the auction system will be described. 1 to 3 are explanatory diagrams showing the basic principle of the auction system according to the embodiment of the present invention.

(1) Bid information is encrypted and transmitted to a plurality of servers. In order to protect the personal information of participants, transmission is performed only once instead of the normal auction method. Compared to ordinary auction-type auctions, the gameability is low, but after making a successful bid, the state of so-called `` winner's melancholy '' that regrets that `` it was not supposed to be like this '' at the price that I bid too much It is more likely to be avoided. In addition, the price at which the bidder can bid is limited to a predetermined variance value (a value between the lowest value and the highest value). As shown in FIG. 1, a plurality of (102-1, 102-2, 102-n) auction servers 102 for receiving bid information 111 including bid prices and personal information input from the bidder terminal device 101 are installed. . The bid information 111 is transmitted from the bidder terminal to the plurality of auction servers 102-1, 102-2, 102-n.

This information to the distributed values to transmitted to the auction server 102 for multiple (112-1,112-2,112-n). A detailed calculation method will be described later . Auctions server 102, as long as the bid information is not performed summary calculations can not restore the original values.

  Further, unless the plurality of auction servers 102 collide, unnecessary information is not leaked. Therefore, if a plurality of auction servers 102 are managed by independent and reliable institutions, it is extremely difficult to cause extra information leakage.

(2) Determining the Successful Winner While Encrypted As shown in FIG. 2, when the deadline is reached, communication is performed between the auction servers 102, and the secret-distributed values are collected and the total calculation is performed. At this time, only the information on the winning bidder and the winning bid price are reproduced, and the bid information of bidders other than the winning bidder is not reproduced.

(3) Decrypting the successful bidder information encrypted only by the seller As shown in FIG. 3, when the seller terminal device 103 makes an inquiry to the auction server 102, the encrypted successful bid price and the successful bidder information 121, which are the aggregated results, are obtained. Send. In the seller terminal device 103, the successful bid price and the successful bidder information 131 can be confirmed by decrypting the encrypted information 121.

  In order to make sure that the winning bid price and the winning bidder information are not known to anyone other than the seller, a method of encrypting the bidder's personal information using a public key cryptosystem is adopted. This method uses separate keys for encryption and decryption (returning the encrypted one), and only the seller has to decrypt the information encrypted with the seller's public key. You need a private key. On the other hand, the bidder can confirm whether or not he / she was able to make a successful bid by comparing the tabulated results with the personal information transmitted (encrypted). In this way, after the seller confirms the winning bid price and the winning bidder information, the selling and buying is established between the seller and the winning bidder.

(Configuration of auction system)
FIG. 4 is an explanatory diagram showing the system configuration of the auction system according to this embodiment of the present invention. 4, the auction system includes a meta server 100, a plurality of auction servers 102-1, 102-2, 102-3,..., A terminal device 401 functioning as a bidder terminal device 101 or a seller terminal device 103, 402 and 403 are connected to a network 400 such as the Internet.

  Here, the meta server 100 is a server for centrally managing a plurality of auction servers 102. The terminal device includes, for example, a laptop personal computer 401, a laptop or mobile personal computer 402, and a portable device having a function of connecting to the network 400 (for example, an NTT Docomo i-mode function). A portable information terminal device 403 such as a PDA (Personal Digital Assistant) equipped with a telephone or a communication function may be connected to the Internet 400.

  FIG. 5 is an explanatory diagram showing the connection relationship between each server and terminal device according to this embodiment of the present invention. In FIG. 5, the meta server 100 is connected to the bidder terminal device 101, and transmits, for example, information on the currently held auction and the bidder client 110 that is an application for the bidder to the bidder terminal device 101. In addition, the meta server 100 is connected to the seller terminal device 103 and receives, for example, information from the seller terminal device 103 regarding a product desired to be auctioned. In addition, information related to the auction and information related to the auction server and the seller client 113 which is a seller application are transmitted to the seller terminal device 103.

  In addition, the meta server 100 is connected to each auction server 102 and transmits, for example, information related to the auction (auction ID, highest bid price, lowest bid price, deadline time, etc.) to each auction server 102. Each auction server 102 is mutually connected with other auction servers 102, and transmits information stored in the own server to other auction servers and receives information stored in other auction servers.

  Further, the bidder terminal device 101 is connected to a plurality of auction servers 102 by executing the bidder client 110, and performs a bid operation by transmitting information on auctions distributed for each auction server to each auction server 102. .

  Further, the seller terminal device 103 is connected to one of the auction servers 102 by executing the seller client 113 and acquires (receives) information regarding the winning bid price and the winning bidder from the auction server 102.

  Alternatively, a plurality of auction servers 102, a meta server 100 that manages the auction server 102, a bidder client 110 of a Java applet created using Java manufactured by Sun Microsystems, for example, and a seller client 113 may be used.

(Metal server, bidder terminal device, auction server, seller terminal device hardware configuration)
FIG. 6 is a block diagram showing the hardware configuration of the meta server 100, bidder terminal apparatus 101, auction server 102, and seller terminal apparatus 103 according to this embodiment of the present invention. In the block diagram of FIG. 6, the meta server 100, the auction server 102 (102-1, 102-2, 102-3,...) Are a CPU 601, a ROM 602, a RAM 603, an HDD (hard disk drive) 604, and an HD. (Hard disk) 605, FDD (floppy disk drive) 606, FD (floppy disk) 607 as an example of a removable recording medium, display 608, KB (keyboard) 609, mouse 610, scanner 611 A network I / F (interface) 612 and a printer 613. Each component is connected by a bus 614.

  Here, the CPU 601 governs overall control of the meta server 100 and the auction server 102. The ROM 602 stores programs such as a boot program. The RAM 603 is used as a work area for the CPU 601. The HDD 604 controls reading / writing of data with respect to the HD 605 according to the control of the CPU 601. The HD 605 stores data written under the control of the HDD 604.

  The FDD 606 controls reading / writing of data with respect to the FD 607 according to the control of the CPU 601. The FD 607 stores data written under the control of the FDD 606. In addition to the FD 607, the removable recording medium may be a CD-ROM (CD-RW), MO, DVD (Digital Versatile Disk), or the like. The display 608 displays a window (browser) related to data such as a document, an image, and function information as well as a cursor, an icon, or a tool box. For example, CRT, TFT liquid crystal display, plasma display and the like.

  The KB 609 includes keys for inputting characters, numerical values, various instructions, etc., and performs data input. The mouse 610 performs cursor movement, range selection, window movement, size change, and the like. A trackball, a joystick, or the like may be used as long as it has a similar function as a pointing device.

  The scanner 611 optically reads an image. A network I / F (interface) 612 is connected to a network 300 (not shown) through a communication line, and is connected to the bidder terminal device 101 and the seller terminal device 103 via the network 400. The network I / F 612 controls an interface between the network and the inside, and controls data input / output from other servers and terminal devices. The printer 613 prints image data and document data. For example, a laser printer or an ink jet printer.

  Further, the bidder terminal device 101 and the seller terminal device 103 are detachably attached to the CPU 651, ROM 652, RAM 653, HDD (hard disk drive) 654, HD (hard disk) 655, and FDD (floppy disk drive) 656. An FD (floppy disk) 657 as an example of a recording medium, a display 658, a KB (keyboard) 659, a mouse 660, a scanner 661, a network I / F (interface) 662, and a printer 663 are provided. Yes. In addition, each of the above components is connected by a bus 664. Since the content of each component is the same as the content of each component in the meta server 100 and the auction server 102, description thereof is omitted.

(Functional configuration of meta server)
FIG. 7 is a block diagram functionally showing the configuration of the metaserver 100 according to this embodiment of the present invention. In the block diagram of FIG. 7, the metaserver 100 is configured to include at least a storage unit 700, a reception unit 701, a transmission unit 702, and an ID issue processing unit 703.

  The storage unit 700 receives various types of information received from the receiving unit 701, for example, information about the product transmitted from the seller terminal device 103 (product name, product overview, minimum bid price, maximum bid price, bid price range, deadline time, Information related to the auction server 102 including the public key), the auction ID, and the address of the auction server 102 (such as an auction server ID) is stored. The storage unit 700 realizes its function by, for example, the HD 605 shown in FIG. 6, the RAM 603, or the FD 607.

  The receiving unit 701 receives various information transmitted from the bidder terminal device 101, the auction server 102, and the seller terminal device 103 via the network 400. For example, a response is received from the auction server 102. The receiving unit 701 realizes its function by the network I / F 612, for example.

  The transmission unit 702 transmits the seller client 113 to the seller terminal device 103, transmits the bidder client 110 to the bidder terminal device 101 via the network 400, and other auctions issued by the ID issuance processing unit 703. ID, auction server ID, etc. are transmitted. In addition, the name of the auction currently being held, the auction ID, and the like are transmitted to the bidder terminal device 101. The transmission unit 702 realizes its function by the network I / F 612, for example.

  The ID issue processing unit 703 issues (provides) an auction ID and an auction server ID. The ID issuance processing unit 703 realizes its function by the CPU 601 executing a program stored in the ROM 602, RAM 603, HD 605, FD 607, or the like.

(Functional configuration of bidder terminal device)
FIG. 8 is a block diagram functionally showing the configuration of the bidder terminal apparatus 101 according to this embodiment of the present invention. In the block diagram of FIG. 8, the bidder terminal device 101 includes at least a storage unit 800, a reception unit 801, a transmission unit 802, a display unit 803, an input unit 804, and a distributed processing unit 805. ing.

  The storage unit 800 is installed with the bidder client 110 received from the reception unit 801 and transmitted from the meta server 100. In addition, personal information of the bidder himself / herself and information regarding the determined bid amount are stored. Further, various information received from the receiving unit 801 such as a bid ID transmitted from the auction server 102 is stored. The storage unit 800 realizes its function by, for example, the HD 655, the RAM 653, and the FD 657 shown in FIG.

  The receiving unit 801 receives various information transmitted from the meta server 100 and the auction server 102 via the network 400. The reception unit 801 realizes its function by the network I / F 662, for example.

  In addition, the transmission unit 802 transmits a request for information necessary for bidding to the meta server 100 via the network 400 and transmits distributed bid information to the auction server 102. The transmission unit 802 realizes its function by, for example, the network I / F 662.

  The display unit 803 displays a list of auction information transmitted from the meta server 100 and received by the receiving unit 801. The display unit 803 realizes its function by, for example, the display 658. The input unit 804 inputs information necessary for bidding. The input unit 804 implements its function with the KB 659 or the mouse 660.

  The distribution processing unit 805 distributes the bid information to a predetermined number using a predetermined algorithm. More specifically, a polynomial is generated based on the information regarding the bid price included in the bid information, and the information regarding the bid price is distributed using the generated polynomial. That is, by substituting a predetermined value for each server into the polynomial, the value of the polynomial is calculated for each server, and the value is used as distributed information.

In addition, the distributed processing unit 805 encrypts the information regarding the bidder included in the bid information using the public key issued by the seller , quantifies the information regarding the encrypted bidder, and relates to the digitized bidder. A polynomial is generated based on the information, and information regarding the bidder is distributed using the generated polynomial . Distributed processing unit 805, ROM652, RAM653, HD655, FD657 stored in such realizes its function by CPU651 a program including an application program such as bidders client 110 executes.

(Functional configuration of auction server)
FIG. 9 is a block diagram functionally showing the configuration of the auction server 102 according to this embodiment of the present invention. In the block diagram of FIG. 9, the auction server 102 includes at least a storage unit 900, a reception unit 901, a transmission unit 902, and an arithmetic processing unit 903.

  The storage unit 900 receives various types of information received from the receiving unit 901, for example, information on the auction ID, the minimum bid price, the maximum bid price, and the bid price range transmitted from the meta server 100, and distributed bids from the bid terminal device 101. Forehead and personal information are stored. The storage unit 900 realizes its function by, for example, the HD 605 shown in FIG. 6, the RAM 603, or the FD 607.

  The receiving unit 901 receives various information transmitted from the bidder terminal device 101, the auction server 102, and the seller terminal device 103 via the network 400. For example, information necessary for totaling the winning bid amount from another auction server 102 is received. The reception unit 901 realizes its function by, for example, the network I / F 612.

  The transmission unit 902 transmits various types of information to the meta server 100, the bidder terminal device 101, and the seller terminal device 103 via the network 400. For example, a response or the like is transmitted to the meta server 100. In addition, a bid ID is transmitted to the bidder terminal device 101. In addition, the encrypted personal information of the winning bidder and the winning bid amount are transmitted to the seller terminal device 103. The transmission unit 902 realizes its function by the network I / F 612, for example.

  The arithmetic processing unit 903 executes a successful bid amount totaling algorithm and a successful bidder totaling algorithm. Details of the winning bid amount totaling algorithm and the successful bidder totaling algorithm will be described later. The arithmetic processing unit 903 realizes its function when the CPU 601 executes a program stored in the ROM 602, RAM 603, HD 605, FD 607, or the like.

(Functional configuration of seller terminal)
FIG. 10 is a block diagram functionally showing the configuration of the seller terminal device 103 according to this embodiment of the present invention. In the block diagram of FIG. 10, the seller terminal device 103 includes at least a storage unit 1000, a reception unit 1001, a transmission unit 1002, a display unit 1003, an input unit 1004, and a public / private key issue processing unit 1005. It is a configuration that includes.

  The storage unit 1000 is installed with the seller client 113 received from the receiving unit 1001 and transmitted from the meta server 100. Further, various information received from the receiving unit 1001 such as an auction ID and an auction server ID is stored. The storage unit 1000 realizes its function by, for example, the HD 655, the RAM 653, and the FD 657 shown in FIG.

  The receiving unit 1001 receives various information transmitted from the meta server 100 and the auction server 102 via the network 400. The receiving unit 1001 realizes its function by, for example, the network I / F 662.

  Further, the transmission unit 1002 transmits product information to the meta server 100 via the network 400, or requests the auction server 102 for the encrypted personal information of the winning bidder. The transmission unit 1002 realizes its function by, for example, the network I / F 662.

  The display unit 1003 displays the winning bidder information transmitted from the auction server 102. The display unit 1003 realizes its function by, for example, the display 658. The input unit 1004 inputs product information related to bidding. The input unit 1004 realizes its function with the KB 659 or the mouse 660.

  The public key / private key issue processing unit 1005 issues a public key used for encrypting the bidder's personal information and a secret key for decrypting the personal information encrypted by the public key. Since the public key / private key technique may be a well-known technique, a detailed description thereof is omitted here. The public key / private key issuance processing unit 1005 realizes its function when the CPU 651 executes a program including application programs such as the seller client 113 stored in the ROM 652, RAM 653, HD 655, FD 657, and the like.

(Processing content of the auction system)
First, as a premise, each auction server has a uniquely assigned auction server identifier, and information on a plurality of auction servers 102 including an operation confirmation flag indicating an operating state and an address of the auction server 102 is stored in the meta server 100. (Referred to as an auction server list). However, the operation status flag is a flag indicating any one of “in operation”, “operable but currently unused”, and “discontinued using the authority of the meta server administrator”.

  The seller terminal device 103 downloads the seller client 113 from the network 400 and activates the seller client 113 on the seller terminal device 103. The seller's personal information (name, e-mail address, password) is input using the activated seller client 113, and a public key and a secret key are created. The created personal information, public key, and secret key are stored in the seller terminal device 103. When there is a product to be auctioned, a public key and product information (seller contact information, deadline time, minimum bid price, maximum bid price, bid price range, public key) are transmitted to the meta server 100. (Auction for this product will be held from this point.)

  Upon receiving the seller's contact information and merchandise information from the seller client 113, the meta server 100 generates an auction identifier and, based on the auction server list, stores all the auction servers 102 that are “active” or “operable but currently unused”. In contrast, an auction identifier, a minimum bid price, a maximum bid price, and a bid price range are transmitted.

  When responses are received from all transmitted auction servers 102, there are more than a certain number of auction servers 102 that returned normally completed responses (the required number determined in advance for anonymity is 3 or more, called the number of restorations). In this case, the auction server identifier is stored in the meta server 100 together with the auction server identifier (collectively referred to as detailed auction information), and the auction server identifier and the address of the auction server 102 are transmitted to the seller client 113 together with a normal end flag. If it is less than a certain number, an error flag indicating that the auction registration did not end normally is transmitted to the seller client 113.

  The auction server 102 that has received the auction identifier, the lowest bid price, the highest bid price, and the bid price range from the meta server 100 stores them in the auction server 102 (referred to as auction holding information), and the processing to the meta server 100 ends normally. Send a response indicating whether or not

  The bidder terminal apparatus 101 downloads the bidder client 110 from the network 400 and activates the bidder client 110 on the bidder terminal apparatus 101. Bidders' personal information (name, e-mail address, password) is input using the activated bidder client 110 and stored in the bidder terminal device 101.

  The bidder uses a browser displayed on the display to obtain a list of products currently being auctioned from the meta server 100, and if there is a product to be bid, from the meta server 100, the auction identifier, minimum bid price, maximum bid price, Auction detailed information including a bid price range, a deadline time, an auction server identifier of the auction server 102 being used, an address of the auction server 102, and a bid reservation identifier uniquely allocated in the auction is acquired.

The bidder determines which of the prices divided by the bid price range that is greater than or equal to the lowest bid price and less than or equal to the highest bid price. To decentralize the bid price at auctions server identifier. Also, the bidder's personal information is encrypted and distributed using another means. A bid reservation identifier, an auction identifier, bid information, and distributed personal information are transmitted to each auction server 102.

  However, at this time, all the bid information and distributed personal information transmitted to the auction server 102 are distributed using the auction server identifier of the auction server 102. If a bid acceptance identifier and a processing result are received from the auction server 102 and a processing result indicating normal completion equal to or greater than the number of restorations is received, it is determined that the bidding processing has been completed normally in the log file of the bidder client 110 in the bidder terminal device 101. The bid acceptance identifier, the auction identifier, and the successfully completed auction server identifier are stored.

The auction server 102 that has received the bid reservation identifier, the auction identifier, the bid information, and the distributed personal information from the bidder client 110 searches the auction holding information stored in the auction server 102, and
(1) Is there an auction that matches the auction identifier received from the bidder client 110?
(2) Whether the bid information is valid.
If it is valid, a bid acceptance identifier is generated from the bid reservation identifier and stored in the auction server 102. A response is sent to the bidder client 110 as to whether or not the job has ended normally.

  The meta server 100 acquires the auction detailed information stored in the meta server 100 for the auction whose deadline is reached, and transmits the auction identifier and all auctions to be transmitted to the auction server 102 stored in the auction detailed information. A deadline / aggregation instruction including the address of the server 102 and the auction server identifier is transmitted. However, the auction server 102 to be transmitted is limited to the auction server 102 stored in the auction detailed information whose operation status flag is “active” or “operable but currently unused”.

  If the number of auction servers 102 to be transmitted is not greater than the number of restorations, the aggregation is impossible, and the error is written to the meta server log file and terminated. When the deadline / aggregation instructions are transmitted to all the auction servers 102, the process ends.

  Upon receiving the deadline / end instruction, the auction server 102 finishes accepting bids for the auction identifier included in the deadline / end instruction, and transmits a response to the meta server 100. Tally the bid information that has been bid so far. As a result, when there is only one bidder who bids the maximum amount, the contact information of the successful bidder is counted.

  However, the result totaled at this time is obtained by encrypting the personal information of the successful bidder with the public key of the seller. In addition, when there are a plurality of bidders who bid for the maximum amount, it is also possible to identify the bidders and perform a tie-up with only them.

  When the seller transmits the auction identifier to the auction server 102 after the counting process is completed, the seller can obtain the successful bid amount and the personal information of the successful bidder encrypted with the seller's public key. This can be decrypted with the secret key in the seller terminal device 103 and contacted with the successful bidder.

  When the bidder transmits the auction identifier stored in the bidder terminal device 101 to the auction server 102, the bidder can acquire the winning bid amount. Compared with the bid amount stored in the bidder terminal device 101, if it is equal to or higher than the winning bid amount, he / she bids the highest amount (it is not necessarily the winning bidder because there is a possibility that a tie break may occur). I can know. Otherwise, you know that you are not the highest bidder or the highest bidder.

  More specific processing contents of the auction system according to the embodiment of the present invention will be described in the following five phases. Note that this system only offers bidding once per person. In addition, this is an auction format (second price auction) in which the highest bidder is the winning bidder and the second highest bid is the winning bid amount.

(1) Product registration phase (2) Bid face (3) Aggregation phase (4) Auction price aggregation algorithm (5) Successful bidder aggregation algorithm

(Processing content of product registration phase)
FIGS. 11 to 13 are flowcharts showing the contents of the process of the auction system according to the embodiment of the present invention, and show the contents of the process in the product registration phase. In FIG. 11, first, the meta server 100 stores the address of each auction server 102 in the storage unit 700 (for example, hard disk (HD) 605) of the meta server 100 (step S1101). Next, an ID (auction server ID) is uniquely assigned to each auction server 102, and the auction server ID is stored in the storage unit 700 in association with the address stored in step S1101 (step S1102).

  Further, the seller terminal device 103 connects to the meta server 100 through a communication line (network 400), and acquires a seller client as a seller application (step S1103). Next, using the seller client, the seller's personal information, for example, the seller's name and email address, is stored (registered) in the storage unit 1000 (eg, hard disk (HD) 655) of the seller terminal device 103 (step). S1104). Then, the seller client generates a public key and a secret key based on the registered personal information of the seller (step S1105).

  In FIG. 12, the seller determines a product to be put on the auction (step S1201). Then, the seller terminal device 103 uses the seller client to communicate the product name, product overview, minimum bid price, maximum bid price, bid price range, and deadline time, and the public key generated in step S1105 as a communication line (network 400). To the meta server 100 (step S1202).

  The meta server 100 receives the product name, product overview, minimum bid price, maximum bid price, bid price range, and deadline time from the seller terminal device 103 (step S1203). Next, a unique ID (auction ID) is assigned to the auction based on the information received in step S1203 (step S1204). Then, to the auction server 102 corresponding to the auction server ID stored in the storage unit 700 in step S1102 shown in FIG. 11, the auction ID, the lowest bid price, the highest bid price, the bid price range, the deadline time, Are transmitted (step S1205).

  Next, the auction server 102 receives the auction ID, the lowest bid price, the highest bid price, the bid price range, and the deadline time from the meta server 100 (step S1206). Then, the auction ID, the lowest bid price, the highest bid price, and the bid price range received in step S1206 are stored in the storage unit 900 (step S1207). Furthermore, a process of closing the bid for the auction with the auction ID at the deadline time received in step S1206 is registered (step S1208).

  Thereafter, a response indicating that the processing related to the auction related to the auction ID has been normally completed is transmitted to the meta server 100 (step S1209). The meta server 100 receives the response transmitted from the auction server 102 in step S1209 (step S1210), and proceeds to step S1301. The meta server 100 performs the process of step S1205 for a predetermined number of auction servers 102, and receives a response from each auction server 102 in step S1210.

  In FIG. 13, the meta server 100 determines whether or not a response indicating that the processing has been normally completed has been received from a predetermined number or more of the auction servers 102 within a certain time after performing the processing in step S 1205 (step S 1301). ). Here, when a response indicating that the processing has been normally completed is received from a predetermined number or more of the auction servers 102 within the predetermined time (step S1301: Yes), the auction ID, the product name, and the product The storage unit 700 includes an outline, a minimum bid price, a maximum bid price, a bid price range, a deadline time, a public key, and an auction server ID of the auction server 102 that has received a response indicating that the normal reception has been successfully performed. (Step S1302).

  Thereafter, the auction ID and the auction server ID of the auction server 102 that has received the normally received response are transmitted to the seller terminal device 103 (step S1303). Next, the seller terminal device 103 receives the auction ID and the plurality of auction server IDs (step S1304), and stores the received auction ID and the plurality of auction server IDs in the storage unit 1000 (step S1305). Thereby, product registration is completed.

  On the other hand, in step S1301, if a response indicating that the processing has been normally completed is not received from a predetermined number or more of the auction servers 102 within the predetermined time (step S1301: No), registration of the auction has failed, and The error message is transmitted to the seller terminal device 103 (step S1306). The seller terminal device 103 receives an error message from the meta server 100 (step S1307), and displays the error message on a display screen (display) (step S1308). Thereafter, the process proceeds to step S1202 shown in FIG.

(Bid phase processing details)
FIG. 14 and FIG. 15 are flowcharts showing the processing procedure of the auction system according to the embodiment of the present invention, and show the processing procedure of the bidding phase. In FIG. 14, first, in the meta server 100, the bidder terminal apparatus 101 is connected to the meta server 100 through a communication line (network 400), and acquires a list of commodities in the auction (step S1401).

  Next, if there is a product to be bid, it connects to the meta server 100 through a communication line, and obtains a bidder application ("bidder client 110"). This bidder client 110 only needs to acquire the first time (step S1402). Therefore, it is not acquired after the second time. From the second time on, the meta server 100 transmits the name of the auction currently being held and the auction ID to the bidder client 110 of the bidder terminal device 101 (step S1403).

  Thereafter, the bidder client 110 is used to input personal information such as the bidder's name and e-mail address, and store them in the storage unit 800 (step S1404). This process may be performed only for the first time. Then, the auction ID of the auction whose details are to be acquired from the meta server 100 is transmitted to the meta server 100 (step S1405).

  Then, the meta server 100 receives the auction ID transmitted from the bidder terminal apparatus 101 (step S1406). Next, detailed information on the auction is searched by the auction ID (step S1407). The detailed information includes a product name, an outline of the product, a minimum bid price, a maximum bid price, a bid price range, a deadline time, a plurality of auction server IDs and auction server addresses, a public key, and the like. Next, the detailed information of the searched auction is transmitted to the bidder terminal apparatus 101 (step S1408).

  The bidder terminal apparatus 101 receives the detailed information of the auction from the meta server 100 (step S1409). Then, referring to the detailed information, the bidder determines the bid amount, stores the bid amount in the bidder terminal device 101 through the bidder client 110 (step S1410), and proceeds to step S1501 shown in FIG.

15, the bidders terminal device 101, to disperse the bidding amount to the number of auction server ID in the detailed information (step S1502). At this time, each auction server ID is distributed as a key.

  Further, only the personal information is encrypted using the public key (step S1503). Hereinafter, this is referred to as “encrypted personal information”. Next, the encrypted personal information is distributed to the number of auction server IDs in the detailed information (step S1504). At this time, each auction server ID is distributed as a key. Then, the auction ID, the distributed bid amount, and the distributed personal information are transmitted to the auction server 102 using each as a key (step S1505).

Each auction server 102 receives the auction ID, the distributed bid amount, and the distributed personal information from the bidder client 110 of the bidder terminal device 101 (step S1506). Then, the received auction ID is searched from the storage unit 900, and the lowest bid price, the highest bid price, and the bid price range are acquired (step S1507). Further, in order to confirm whether or not the received bid amount is normal, the number of bidable prices for the received auction ID is calculated (step S1508). To calculate the number of bids available,
(Maximum bid price-Minimum bid price) / Bid price range + 1
It becomes.

  Then, as a result of the calculation in step S1508, it is determined whether or not the received bid amount is normal (step S1509). Here, when the received bid amount is normal (step S1509: Yes), a unique ID (bidder ID) is created for the bidder (step S1510). Next, the auction ID, the distributed bid amount, the distributed personal information, and the bidder ID are stored in the storage unit 900 (step S1511). Then, the bidder ID is transmitted to the bidder terminal apparatus 101 (step S1512).

  The bidder terminal apparatus 101 receives the bidder ID from the auction server 102 (step S1513). Then, the bidder ID, the auction ID, and the bid amount are stored in the storage unit 800 (step S1514). Thereby, a bid is completed.

  On the other hand, if the received bid amount is not normal in step S1509 (step S1509: No), “0” is assigned as the bidder ID, and that fact is transmitted to the bidder terminal apparatus 101 (step S1515). The bidder terminal apparatus 101 receives “0” as the bidder ID from the auction server 102 (step S1516), and displays an error message upon reception of “0” (step S1517).

(Processing details in the aggregation phase)
FIG. 16 is a flowchart showing a processing procedure of the auction system according to the embodiment of the present invention, and shows a processing procedure of the counting phase. In FIG. 16, the meta server 100 first determines whether or not the auction deadline time registered in advance matches the system time (step S1601). Here, when it matches after waiting for a match (step S1601: Yes), the auction ID of the auction is acquired (step S1602).

  Next, the auction with the acquired auction ID is removed from the auction list requested by the bidder client 110 (step S1603). Then, a plurality of auction server IDs described in the auction detailed information of the acquired auction ID are acquired (step S1604). Next, the address of the auction server 102 represented by the acquired auction server ID is acquired, and the auction ID is transmitted to the acquired auction server 102 (step S1605).

  The auction server 102 receives the auction ID transmitted from the meta server 100 (step S1606). Then, the bid for the received auction ID is closed (step S1607). Thereafter, the winning bid amount in the auction is tabulated (determined) by a winning bid amount calculating algorithm described later (step S1608). Similarly, the winning bidders of the auction are counted (determined) by the winning bidder counting algorithm described later (step S1609).

  Next, the encrypted personal information of the winning bidder and the winning bid amount are transmitted to the seller client of the seller terminal device 103 (step S1610). The seller terminal device 103 receives the encrypted personal information and the winning bid amount of the winning bidder from the auction server (step S1611).

  Then, the seller terminal device 103 decrypts the encrypted personal information of the winning bidder with the secret key stored in the storage unit 1000, and acquires the winning bidder's personal information (step S1612). Thereafter, based on the personal information of the winning bidder, it is possible to contact the winning bidder and consult about a settlement method and a delivery method (step S1613).

(Successful bid amount calculation algorithm)
Next, the contents of the winning bid amount totaling algorithm in step S1608 will be described. Here, as an example, the minimum bid price is “100 (yen)”, the highest bid price is “700 (yen)”, and the bid price range is “100 (yen)”. Then, the possible bid amounts are “100 (yen)”, “200 (yen)”, “300 (yen)”, “400 (yen)”, “500 (yen)”, “600 (yen)”, Seven types of “700 (yen)” Therefore, when these orders are converted into binary representation, they can be numbered as “000”, “001”, “010”, “011”, “100”, “101”, “111”.

  Here, if the bidder A is “300 (yen)” and the bidder B is “400 (yen)”, the bid amount of the bidder A is “010” and the bid amount of the bidder B is “ 011 ".

Next, a random quadratic polynomial is created for each digit of the binary representation according to the following rules.
(Rule 1) If the value is 0, the constant term is 0.
(Rule 2) If the value is not 0, the constant term is a non-zero value with the modulus p.
However, p = 10007 is a sufficiently large prime number.

According to the rules 1 and 2, each bidder generates three random polynomials corresponding to the number of digits in binary representation. That is,
Bidder A ’s random polynomial is
F11 (x) = x
F12 (x) = 1 + 2x
F13 (x) = 3x
Bidder B ’s random polynomial
F21 (x) = 3x
F22 (x) = 2 + 4x
F23 (x) = 4 + x
And

  Also, the auction server IDs of the three auction servers 1, 2, and 3 are “2”, “3”, and “4”, respectively. At this time, the bidder A substitutes each auction server ID for “x” of the random polynomial. By doing so, the auction server 1 has F11 (2) = 2, F12 (2) = 5, F13 (2) = 6, the auction server 2 has F11 (3) = 3, F12 (3) = 7, F13 (3) = 9, and F11 (4) = 4, F12 (4) = 9, and F13 (4) = 12, are transmitted to the auction server 3, respectively.

  Similarly, the bidder B sends the auction server 1 to F21 (2) = 6, F22 (2) = 10, F23 (2) = 6, and the auction server 2 to F21 (3) = 9, F22 (3). = 14, F23 (3) = 7, and F21 (4) = 12, F22 (4) = 18, and F23 (4) = 8 are transmitted to the auction server 3, respectively.

  Further, all bidders transmit personal information encrypted with the seller's public key together with the bid amount and distributed using the auction server ID as a key to each auction server. Details will be described in the successful bidder totalization algorithm described later.

  In addition, a flag of “0 (default)” or “1” is defined for aggregation. This flag takes the value “1” when two or more values other than “0” appear in the digits to be processed among all the bid amounts converted into the binary representation. When this flag is “0”, the calculation of v = u + F * w can be simplified to v = u + F.

All calculations are closed in a ring modulo a prime number p (p = 10007). That is, for any integer a
a = a ′ + p * n (n is an arbitrary integer)
, “A” and “a ′” are regarded as the same number, and are described as “a ′”.

  17 to 33 are flowcharts showing the contents of the processing of the auction system according to this embodiment of the present invention, and show the contents of the processing of the winning bid amount totaling algorithm.

(1) Initial Value Setting Face In FIG. 17, the auction server 1 receives 2, 5, and 6 from bidder A and 6, 10, and 6 from bidder B as bid amounts (step S1701a). . Similarly, the auction server 2 receives 3, 7, and 9 from bidder A and 9, 14, and 7 from bidder B as bid amounts (step S1701b). Similarly, the auction server 3 receives 4, 9, and 12 from the bidder A and 12, 18, and 8 from the bidder B as bid amounts (step S1701c).

  Next, the auction servers 1, 2, and 3 receive the auction ID and the deadline / aggregation instruction from the meta server 100 (steps S1702a, 1702b, and 1702c). Then, the bid for the received auction ID is closed (steps S1703a, 1703b, 1703c). Thereafter, the auction server 1 generates a random polynomial by the number of bidders × 2 with the modulus p (step S1704a). In this case, since there are two bidders A and B, the random polynomials are u111 (x) = 3 + x, u121 (x) = 5 + 2x, and w111 (x) = 1 + 3x, w121 (x) = 4 + x. Two each are generated.

Similarly, the auction server 2 generates a random polynomial by the number of bidders × 2 with the modulus p (step S1704b). In this case, since there are two bidders A and B, the random polynomials are u211 (x) = 1 + 2x, u221 (x) = 6 + 3x, w211 (x) = 7 + x, w221 (x) = 2 + 4x Two each are generated. Thereafter, the process proceeds to step S1705b shown in FIG. Similarly, the auction server 3 generates random polynomials by the number of bidders × 2 with the modulus p (step S1704c). Also in this case, two random polynomials are generated: u311 (x) = 2 + 2x, u321 (x) = 4 + x, w311 (x) = 2 + 5x, and w321 (x) = 6 + x. Thereafter, the process proceeds to step S1705c shown in FIG.

  Next, using the polynomial generated in step S1704a, the auction server ID (“2”, “3”, “4”) is substituted for x of the polynomial, the values of the polynomials are respectively calculated, and u111 (3), The calculation results of u121 (3), w111 (3), and w121 (3) are sent to the auction server 2, and the calculation results of u111 (4), u121 (4), w111 (4), and w121 (4) are sent to the auction server 3. Each is transmitted (step S1705a). Then, the auction server 2 and the auction server 3 respectively receive the auction ID and the polynomial calculation result transmitted from the auction server 1.

  The auction server 1 determines whether or not the auction ID and the result of the polynomial have been received from the auction server 2 and the auction server 3 (step S1706a), waits for reception of each, and receives both (step S1706a). : Yes) proceeds to step S1901a. The auction server 2 and the auction server 3 perform the same processing as the auction server 1 (steps S1706b and S1706c).

  At this time, the auction server 1 includes u111 (2) = 5, u121 (2) = 9, u211 (2) = 5, u221 (2) = 12, u311 (2) = 6, u321 (2) = 6. , W111 (2) = 7, w121 (2) = 6, w211 (2) = 9, w221 (2) = 10, w311 (2) = 12, w321 (2) = 8 , The auction server 2 includes u111 (3) = 6, u121 (3) = 11, u211 (3) = 7, u221 (3) = 15, u311 (3) = 8, u321 (3) = 7, w111 The values of (3) = 10, w121 (3) = 7, w211 (3) = 10, w221 (3) = 14, w311 (3) = 17, w321 (3) = 9 are stored, and the auction For server 3, u111 (4) = 7, u121 (4) = 1 , U211 (4) = 9, u221 (4) = 18, u311 (4) = 10, u321 (4) = 8, w111 (4) = 13, w121 (4) = 8, w211 (4) = 11, The values w221 (4) = 18, w311 (4) = 22, and w321 (4) = 10 are stored.

  In FIG. 19, the auction server 1 calculates u11 (2) = u111 (2) + u211 (2) + u311 (2) = 5 + 5 + 6 = 16 using the stored value. Similarly, u21 (2) = u121 (2) + u221 (2) + u321 (2) = 27, w11 (2) = w111 (2) + w211 (2) + w311 (2) = 28, w21 (2) = w121 ( 2) Calculate + w221 (2) + w321 (2) = 24, respectively (step S1901a).

  Similarly, the auction server 2 uses the stored values to make u11 (3) = u111 (3) + u211 (3) + u311 (3) = 21, u21 (3) = u121 (3) + u221 (3) + U321 (3) = 33, w11 (3) = w111 (3) + w211 (3) + w311 (3) = 37, w21 (3) = w121 (3) + w221 (3) + w321 (3) = 30, respectively The calculated values (u11 (3), u21 (3)) are transmitted to the auction server 1 (step S1901b).

  Similarly, the auction server 3 uses the stored values to obtain u11 (4) = u111 (4) + u211 (4) + u311 (4) = 26, u21 (4) = u121 (4) + u221 ( 4) + u321 (4) = 39, w11 (4) = w111 (4) + w211 (4) + w311 (4) = 46, w21 (4) = w121 (4) + w221 (4) + w321 (4) = 36, respectively The calculated values (u11 (4), u21 (4)) are transmitted to the auction server 1 (step S1901c).

  The auction server 1 determines whether values have been received from the auction server 2 and the auction server 3 (step S1902). If it is received after waiting for reception (step S1902: Yes), then using the interpolation method, u11 (4) = 26, u11 (3) = 21, and u11 (2) = 1. , U11 (0) = 6. Similarly, u21 (0) = 15 is calculated (step S1903).

  Further, u111 (x) = 10004 + x and u121 (x) = 9997 + 2x are substituted so that u11 (0) = 0 and u21 (0) = 0 (mod p (p = 10007)) (step S1904). And it transfers to step S2001 shown in FIG.

  In FIG. 20, the auction server 1 determines that u111 (2) = 10006, u111 (3) = 0, u111 (4) = 1, u121 (2) = 10001, u121 (based on the replacement performed in step S1904. 3) = 10003 and u121 (4) = 10005 are calculated. Then, u111 (3) = 0 and u121 (3) = 10003 are transmitted to the auction server 2, and u111 (4) = 1 and u121 (4) = 10005 are transmitted to the auction server 3 (step S2001).

  Thereafter, in the auction server 1, u11 (2) = u111 (2) + u211 (2) + u311 (2) = 10006 + 5 + 6 = 10, u21 (2) = u121 (2) + u221 (2) + u321 (2) = 10001 + 12 + 6 = 12. Is calculated again (step S2002a).

  On the other hand, the auction servers 2 and 3 determine whether or not there is reception from the auction server 1 (steps S1905b and S1905c), and if there is reception (steps S1905b: Yes, 1905c: Yes), steps S2002b and S2002c. Respectively.

    In the auction server 2, u11 (3) = u111 (3) + u211 (3) + u311 (3) = 15 and u21 (3) = u121 (3) + u221 (3) + u321 (3) = 18 are calculated again. (Step S2002b). Similarly, in the auction server 3, u11 (4) = u111 (4) + u211 (4) + u311 (4) = 20 and u21 (4) = u121 (4) + u221 (4) + u321 (4) = 24 are again set. Calculate (step S2002c).

(2) First Price Range Aggregation Phase In the auction server 1, the first value “of the bid amounts received from the bidders A, 2, 5, 6 and the bidders B, 6, 10, 6” received in step S1701a “ “2” and “6” are taken out (step S2003a). Similarly, the auction server 2 also takes out the first values “3” and “9” of each bid amount (step S2003b). Similarly, the auction server 3 takes out the initial values “4” and “12” of each bid amount (step S2003c).

  Next, v11 (2) = u11 (2) + F11 (2) = 10 + 2 = 12, v21 (2) = u21 (2) + F21 (2) = 12 + 6 = 18 is calculated (step S2004a). Here, originally, it should be calculated as v11 (x) = u11 (x) + F11 (x) * w11 (x), v21 (x) = u21 (x) + F21 (x) * w21 (x). At this point in time, as described above, the flag defined in totaling the winning bid amount is “0 (default)”, so that the equation can be simplified as described above. Thereafter, the process proceeds to step S2101a shown in FIG.

  Similarly, the auction server 2 calculates v11 (3) = u11 (3) + F11 (3) = 15 + 3 = 18, v21 (3) = u21 (3) + F21 (3) = 18 + 9 = 27 (step S2004b). Thereafter, the process proceeds to step S2101b shown in FIG. Similarly, the auction server 3 calculates v11 (4) = u11 (4) + F11 (4) = 20 + 4 = 24 and v21 (4) = u21 (4) + F21 (4) = 24 + 12 = 36 (step S2004c). Then, the process proceeds to step S2101c shown in FIG.

  In FIG. 21, the auction server 1 calculates S1 (2) = v11 (2) * v21 (2) = 12 * 18 = 216 (step S2101a). Similarly, the auction server 2 calculates S1 (3) = v11 (3) * v21 (3) = 486 (step S2101b). Similarly, the auction server 3 calculates S1 (4) = v11 (4) * v21 (4) = 864 (step S2101c).

  Thereafter, each auction server 1, 2, 3 transmits the value calculated in step S2101 to another auction server (steps S2102a, S2102b, S2102c).

  Each auction server 1, 2, 3 determines whether or not the data transmitted in step S2102 has been received (received) from the other two auction servers (steps S2103a, S2103b, S2103c) and received. Is received (step S2103a: Yes, S2103b: Yes, S2103c: Yes), S1 (0) is then calculated using an interpolation method (steps S2104a, S2104b, S2104c). When calculated using the interpolation method from S1 (4) = 864, S1 (3) = 486, and S1 (2) = 216, S1 (0) = 0.

  Next, it is determined whether or not S1 (0) = 0 (steps S2105a, S2105b, and S2105c). Here, as calculated in step S2104, since S1 (0) = 0 (steps S2105: Yes, S2105b: Yes, S2105c: Yes), in the auction server 1, u12 (2) = v11. (2) = 12, u22 (2) = v21 (2) = 18, w12 (2) = w11 (2) = 28, w22 (2) = w21 (2) = 24 are calculated (step S2106a).

  Similarly, in the auction server 2, u12 (3) = v11 (3) = 18, u22 (3) = v21 (3) = 27, w12 (3) = w11 (3) = 37, w22 (3) = w21 (3) = 30 is calculated (step S2106b). Similarly, in the auction server 3, u12 (4) = v11 (4) = 24, u22 (4) = v21 (4) = 36, w12 (4) = w11 (4) = 46, w22 (4) = w21 (4) = 36 is calculated (step S2106c).

(3) Second Price Range Aggregation Phase FIG. 22 shows the contents of processing in the second price range aggregation phase. In FIG. 22, the auction server 1 takes out the second value of each bid amount (step S2201a). In this case, 5 and 10. Similarly, the auction server 2 takes out 7 and 14 (step S2201b). Similarly, the auction server 3 takes out 9 and 18 (step S2201c).

  Next, v12 (2) and v22 (2) are calculated (step S2202a). Here, v12 = u12 (2) + F12 (2) = 12 + 5 = 17, and v22 (2) = u22 (2) + F22 (2) = 18 + 10 = 28. Similarly, the auction server 2 calculates v12 (3) = 25 and v22 (3) = 41 (step S2202b). Similarly, the auction server 3 calculates v12 (4) = 33 and v22 (4) = 54 (step S2202c).

  Thereafter, the auction server 1 calculates S2 (2) = v12 (2) * v22 (2) = 476 (step S2203a). Similarly, the auction server 2 calculates S2 (3) = v12 (3) * v22 (3) = 1025 (step S2203b). Similarly, the auction server 3 calculates S2 (4) = v12 (4) * v22 (4) = 1784 (step S2203c).

  Furthermore, each auction server 1, 2, 3 transmits the calculated S2 (2), S2 (3), S2 (4) to the other auction servers (steps S2204a, S2204b, S2204c).

  Then, the auction server 1 determines whether or not S2 (3) and S2 (4) are received from the auction servers 2 and 3, respectively (step S2205a), and if received (step S2205a: Yes), S2 (0) is calculated using an interpolation method (step S2206a). The same processing is performed in the auction server 2 and the auction server 3 (steps S2205b and S2206b, steps S2205c and S2206c).

  Next, in step S2207a, b, c, S2 (0) = “2” and does not become “0”, so the flag is set to “1” in steps S2208a, b, c (steps S2208a, S2208b). , S2208c).

  Thereafter, in the auction server 1, u13 (2) = u12 (2) = 12, u23 (2) = u22 (2) = 18, w13 (2) = v12 (2) = 17, w23 (2) = v22 ( 2) = 28 is calculated (step S2209a). Similarly, in the auction server 2, u13 (3) = u12 (3) = 18, u23 (3) = u22 (3) = 27, w13 (3) = v12 (3) = 25, w23 (3) = v22 (3) = 41 is calculated (step S2209b). Similarly, in the auction server 3, u13 (4) = u12 (4) = 24, u23 (4) = u22 (4) = 36, w13 (4) = v12 (4) = 33, w23 (4) = v22 (4) = 54 is calculated (step S2209c).

(4) Third Price Range Aggregation Phase In FIG. 23, the auction server 1 includes the bid amounts received from step S1701a (from bidders A, 2, 5, 6 and from bidders B, 6, 10, 6). The third values “6” and “6” are extracted (step S2301a). Similarly, the auction server 2 also takes out the initial values “9” and “7” of each bid amount (step S2301b). Similarly, the auction server 3 takes out the initial values “12” and “8” of each bid amount (step S2301c).

  Next, v13 (2) = u13 (2) + F13 (2) * w13 (2) = 12 + 6 * 7 = 114, v23 (2) = u23 (2) + F23 (2) * W23 (2) = 18 + 6 * 28 = 186 is calculated (step S2302a). Here, since the flag is “1”, the equation is not simplified as in step S2004a of the first price range aggregation phase. The process proceeds to step S2303a.

  Similarly, in the auction server 2, v13 (3) = u13 (3) + F13 (3) * w13 (3) = 18 + 9 * 25 = 243, v23 (3) = u23 (3) + F23 (3) * w23 (3 ) = 27 + 7 * 41 = 314 (step S2302b), and then the process proceeds to step S2303b. Similarly, in the auction server 3, v13 (4) = u13 (4) + F13 (4) * w13 (4) = 24 + 12 * 33 = 420, v23 (4) = u23 (4) + F23 (4) * w23 ( 4) = 36 + 8 * 54 = 468 is calculated (step S2302c), and then the process proceeds to step S2303c.

を作成する（ステップＳ２３０３ａ、Ｓ２３０３ｂ、Ｓ２３０３ｃ）。Next, in each auction server 1, 2, 3, 3 * 3 matrix

Is created (steps S2303a, S2303b, and S2303c).

  This indicates the number of auction servers * the number of auction servers. The elements of this matrix are the auction server IDs of the respective auction servers arranged in order from the left to the 0th power, the 1st power, and the 2nd power from the top. The auction server IDs that are elements of this matrix must be in the same order in the auction server 2 and the auction server 3.

を作成する（ステップＳ２３０４ａ、Ｓ２３０４ｂ、Ｓ２３０４ｃ）。Then, the inverse matrix of the matrix created in step S2303

Is created (steps S2304a, S2304b, and S2304c).

を作成する（ステップＳ２３０５ａ、Ｓ２３０５ｂ、Ｓ２３０５ｃ）。この行列Ｐは、（多項式ｖ１３の次数）＊（多項式ｖ１３の次数）型の射影行列である。その後、図２４に示すステップＳ２４０１ａ、Ｓ２４０１ｂ、Ｓ２４０１ｃへそれぞれ移行する。Next, 3 * 3 matrix (number of auction servers * number of auction servers)

Is created (steps S2305a, S2305b, S2305c). This matrix P is a projection matrix of the type (degree of polynomial v13) * (degree of polynomial v13). Thereafter, the process proceeds to steps S2401a, S2401b, and S2401c shown in FIG.

In FIG. 24, the auction server 1 uses v13 (2) = 114 and v23 (2) = 186 calculated in step S2302a,
v13 (2) * a11 = 114 * 10006 = 9873
v13 (2) * a12 = 114 * 4999 = 9494
v13 (2) * a13 = 114 * 9999 = 9095
v23 (2) * a11 = 186 * 10006 = 9821
v23 (2) * a12 = 186 * 4999 = 9170
v23 (2) * a13 = 186 * 9999 = 8519
Is calculated (step S2401a).

Similarly, the auction server 2 uses v13 (3) = 243 and v23 (3) = 314 calculated in step S2302b,
v13 (3) * a21 = 243 * 4 = 972
v13 (3) * a22 = 243 * 10 = 2430
v13 (3) * a23 = 243 * 16 = 3888
v23 (3) * a21 = 314 * 4 = 1256
v23 (3) * a22 = 314 * 10 = 3140
v23 (3) * a23 = 314 * 16 = 5024
Is calculated (step S2401b).

Similarly, the auction server 3 uses v13 (4) = 420 and v23 (4) = 468 calculated in step S2302c,
v13 (4) * a31 = 420 * 10005 = 9167
v13 (4) * a32 = 420 * 4999 = 8117
v13 (4) * a33 = 420 * 10000 = 7067
v23 (4) * a31 = 468 * 10005 = 9071
v23 (4) * a32 = 468 * 4999 = 7901
v23 (4) * a33 = 468 * 10000 = 6731
Is calculated (step S2401c).

Next, the auction server 1 calculates in step S2401a,
v13 (2) * a11 = 9873
v13 (2) * a12 = 9449
v13 (2) * a13 = 9095
v23 (2) * a11 = 9821
v23 (2) * a12 = 9170
v23 (2) * a13 = 8519
Is generated as a constant term (step S2402a). However, the degree of the polynomial to be generated is a number obtained by subtracting 1 from the order of v13 and dividing by 2, and rounding down the decimal part.

As a result, the generated polynomial is as follows.
G1311 (x) = 9873 + x
G1312 (x) = 9494 + 2x
G1313 (x) = 9095 + 5x
G2311 (x) = 9821 + 2x
G2312 (x) = 9170 + 3x
G2313 (x) = 8519 + x

Similarly, the auction server 2 calculates in step S2401b.
v13 (3) * a21 = 972
v13 (3) * a22 = 2430
v13 (3) * a23 = 3888
v23 (3) * a21 = 1256
v23 (3) * a22 = 3140
v23 (3) * a23 = 5024
Is generated as a constant term (step S2402b).

As a result, the generated polynomial is as follows.
G1321 (x) = 972 + 3x
G1322 (x) = 2430 + 4x
G1323 (x) = 3888 + 6x
G2321 (x) = 1256 + 2x
G2322 (x) = 3140 + 3x
G2323 (x) = 5024 + 3x

Similarly, the auction server 3 calculates in step S2401c,
v13 (4) * a31 = 9167
v13 (4) * a32 = 8117
v13 (4) * a33 = 7067
v23 (4) * a31 = 9071
v23 (4) * a32 = 7901
v23 (4) * a33 = 6731
Is generated as a constant term (step S2402c).

As a result, the generated polynomial is as follows.
G1331 (x) = 9167 + 2x
G1332 (x) = 8117 + x
G1333 (x) = 7067 + 3x
G2331 (x) = 9071 + 3x
G2332 (x) = 7901 + 5x
G2333 (x) = 6731 + 7x

Next, the auction server 1 calculates from the above polynomial as follows (step S2403a).
G1311 (2) = 9895
G1311 (3) = 9896
G1311 (4) = 9897
G1312 (2) = 9498
G1312 (3) = 9500
G1312 (4) = 9502
G1313 (2) = 9105
G1313 (3) = 9110
G1313 (4) = 9115
G2311 (2) = 9825
G2311 (3) = 9827
G2311 (4) = 9829
G2312 (2) = 9176
G2312 (3) = 9179
G2312 (4) = 9182
G2313 (2) = 8521
G2313 (3) = 8522
G2313 (4) = 8523

Similarly, the auction server 2 calculates from the above polynomial as follows (step S2403b).
G1321 (2) = 978
G1321 (3) = 981
G1321 (4) = 984
G1322 (2) = 2438
G1322 (3) = 2442
G1322 (4) = 2446
G1323 (2) = 3900
G1323 (3) = 3906
G1323 (4) = 3912
G2321 (2) = 1260
G2321 (3) = 1262
G2321 (4) = 1264
G2322 (2) = 3146
G2322 (3) = 3149
G2322 (4) = 3152
G2323 (2) = 5030
G2323 (3) = 5033
G2323 (4) = 5036

Similarly, the auction server 3 calculates from the polynomial as follows (step S2403c).
G1331 (2) = 9171
G1331 (3) = 9173
G1331 (4) = 9175
G1332 (2) = 8119
G1332 (3) = 8120
G1332 (4) = 8121
G1333 (2) = 7073
G1333 (3) = 7076
G1333 (4) = 7079
G2331 (2) = 9077
G2331 (3) = 9080
G2331 (4) = 9083
G2332 (2) = 7911
G2332 (3) = 7916
G2332 (4) = 7921
G2333 (2) = 6745
G2333 (3) = 6752
G2333 (4) = 6759

25 to 29, the auction server 1 then selects G1311 (3) = 9896
G1312 (3) = 9500
G1313 (3) = 9110
G2311 (3) = 9827
G2312 (3) = 9179
G2313 (3) = 8522
Is transmitted to the auction server 2 (step S2501a),
G1311 (4) = 9897
G1312 (4) = 9502
G1313 (4) = 9115
G2311 (4) = 9829
G2312 (4) = 9182
G2313 (4) = 8523
Is transmitted to the auction server 3 (step S2502a).

Similarly, the auction server 2
G1321 (2) = 978
G1322 (2) = 2438
G1323 (2) = 3906
G2321 (2) = 1260
G2322 (2) = 3146
G2323 (2) = 5030
Is transmitted to the auction server 1 (step S2501b),
G1321 (4) = 984
G1322 (4) = 2446
G1323 (4) = 3912
G2321 (4) = 1264
G2322 (4) = 3152
G2323 (4) = 5036
Is transmitted to the auction server 3 (step S2502b).

Similarly, the auction server 3
G1331 (2) = 9171
G1332 (2) = 8119
G1333 (2) = 7073
G2331 (2) = 9077
G2332 (2) = 7911
G2333 (2) = 6745
Is transmitted to the auction server 1 (step S2501c),
G1331 (3) = 9173
G1332 (3) = 8120
G1333 (3) = 7076
G2331 (3) = 9080
G2332 (3) = 7916
G2333 (3) = 6752
Is transmitted to the auction server 2 (step S2502c).

  Next, the auction server 1 determines whether the six values transmitted from the auction server 2 (step S2501b) and the six values transmitted from the auction server 3 (step S2501c) have been received (received). (Step S2503a). The six values mean the number of auction servers * the number of bidders.

Then, after waiting for reception (step S2503a: Yes), next,
H131 (2) = G1311 (2) + G1321 (2) + G1331 (2) = 9895 + 978 + 9171 = 30
H132 (2) = G1312 (2) + G1322 (2) + G1332 (2) = 9498 + 2438 + 8119 = 41
H133 (2) = G1313 (2) + G1323 (2) + G1333 (2) = 9105 + 3900 + 7073 = 64
H231 (2) = G2311 (2) + G2321 (2) + G2331 (2) = 9825 + 1260 + 9077 = 148
H232 (2) = G2312 (2) + G2322 (2) + G2332 (2) = 9176 + 3146 + 7911 = 219
H233 (2) = G2313 (2) + G2323 (2) + G2333 (2) = 8521 + 5030 + 6745 = 282
Is calculated (step S2504a).

  Then, H132 (2) = 41 and H232 (2) = 219 are transmitted to the auction server 2 (step S2505a), and H133 (2) = 64 and H233 (2) = 282 are transmitted to the auction server 3 (step S2505a). S2506a).

  Similarly, the auction server 2 determines whether the six values transmitted from the auction server 1 (step S2501a) and the six values transmitted from the auction server 3 (step S2502c) have been received (received). (Step S2503b).

Then, when waiting for reception (step S2503b: Yes), next,
H131 (3) = G1311 (3) + G1321 (3) + G1331 (3) = 9896 + 981 + 9173 = 36
H132 (3) = G1312 (3) + G1322 (3) + G1332 (3) = 9500 + 2442 + 8120 = 48
H133 (3) = G1313 (3) + G1323 (3) + G1333 (3) = 9110 + 3906 + 7076 = 78
H231 (3) = G2311 (3) + G2321 (3) + G2331 (3) = 9827 + 11262 + 9080 = 155
H232 (3) = G2312 (3) + G2322 (3) + G2332 (3) = 9179 + 3149 + 7916 = 230
H233 (3) = G2313 (3) + G2323 (3) + G2333 (3) = 8522 + 5033 + 6752 = 293
Is calculated (step S2504b).

  Then, H131 (3) = 36 and H231 (3) = 155 are transmitted to the auction server 1 (step S2505b), and H133 (3) = 78 and H233 (3) = 293 are transmitted to the auction server 3 (step S2505b). S2506b).

  Similarly, the auction server 3 determines whether six values transmitted from the auction server 1 (step S2502a) and six values transmitted from the auction server 2 (step S2502b) have been received (received). Judgment is made (step S2503c).

Then, after waiting for reception (step S2503c: Yes), next,
H131 (4) = G1311 (4) + G1321 (4) + G1331 (4) = 9897 + 984 + 9175 = 42
H132 (4) = G1312 (4) + G1322 (4) + G1332 (4) = 9502 + 2446 + 811 = 55
H133 (4) = G1313 (4) + G1323 (4) + G1333 (4) = 9115 + 3912 + 7079 = 92
H231 (4) = G2311 (4) + G2321 (4) + G2331 (4) = 9829 + 1264 + 9083 = 162
H232 (4) = G2312 (4) + G2322 (4) + G2332 (4) = 9182 + 3152 + 7921 = 241
H233 (4) = G2313 (4) + G2323 (4) + G2333 (4) = 8523 + 5036 + 6759 = 304
Is calculated (step S2504c).

  Then, H131 (4) = 42 and H231 (4) = 162 are transmitted to the auction server 1 (step S2505c), and H132 (4) = 55 and H232 (4) = 241 are transmitted to the auction server 2 (step S2505c). S2506c).

  Next, the auction server 1 determines whether or not two values transmitted from the auction server 2 (step S2505b) and two values transmitted from the auction server 3 (step S2505c) have been received (received). (Step S2507a).

And when waiting for reception and receiving (step S2507a: Yes), as shown in FIG.
H131 (2) = 30
H231 (2) = 148
H131 (3) = 36
H231 (3) = 155
H131 (4) = 42
H231 (4) = 162
In step S2508a, the zero point is obtained using the interpolation method.

The result is as follows.
H131 (0) = 18
H231 (0) = 134

  Similarly, the auction server 2 determines whether the two values transmitted from the auction server 1 (step S2505a) and the two values transmitted from the auction server 3 (step S2506c) are received (received). (Step S2507b).

And when waiting for reception, when receiving (step S2507b: Yes), next, as shown in FIG.
H132 (2) = 41
H232 (2) = 219
H132 (3) = 48
H232 (3) = 230
H132 (4) = 55
H232 (4) = 241
In step S2508b, the zero point is obtained using the interpolation method.

The result is as follows.
H132 (0) = 27
H232 (0) = 197

  Similarly, the auction server 3 determines whether or not two values transmitted from the auction server 1 (step S2506a) and two values transmitted from the auction server 2 (step S2506b) are received (received). Determination is made (step S2507c). The value “two” means a number obtained by subtracting 1 from the number of auction servers.

And when waiting for reception and receiving (step S2507c: Yes), as shown in FIG.
H133 (2) = 64
H233 (2) = 282
H133 (3) = 78
H233 (3) = 293
H133 (4) = 92
H233 (4) = 304
In step S2508c, the zero point is obtained using the interpolation method.

The result is as follows.
H133 (0) = 36
H233 (0) = 260

  Next, the auction server 1 assigns H131 (0) = 18 and H231 (0) = 134 to v13 (2) and v23 (2), respectively, and v13 (2) = 18 and v23 (2) = respectively. 134 (step S2509a). This is a value when v13 and v23 are originally quadratic expressions but are reduced to a linear expression, that is, when the quadratic terms are deleted while maintaining anonymity. Then, S3 (2) = v13 (2) * v23 (2) = 18 * 134 = 2412 is calculated (step S2510a).

  Similarly, the auction server 2 substitutes H132 (0) = 27 and H232 (0) = 197 for v13 (3) and v23 (3), respectively, and v13 (3) = 27 and v23 (3) = 197 (step S2509b). Then, S3 (3) = v13 (3) * v23 (3) = 27 * 197 = 5319 is calculated (step S2510b).

  Similarly, the auction server 3 assigns H133 (0) = 36 and H233 (0) = 260 to v13 (4) and v23 (4), respectively, and v13 (4) = 36 and v23 (4), respectively. = 260 (step S2509c). Then, S3 (4) = v13 (4) * v23 (4) = 36 * 260 = 9360 is calculated (step S2510c).

  Next, the auction server 1 sends S3 (2), the auction server 2 sends S3 (3), and the auction server 3 sends S3 (4) to different auction servers (steps S3001a, b, c). . Each of the auction servers 1, 2, and 3 determines whether or not a value transmitted from another auction server has been received (steps S3002a, b, and c). In steps S3002a, b, and c: Yes, S3 (0) is calculated using an interpolation method (steps S3003a, b, and c).

Then, it is determined whether or not S3 (0) = 0 (step S3004a). Since S3 (0) = 0 (step S3004a: Yes), the auction server 1
u14 (2) = v13 (2) = 18
u24 (2) = v23 (2) = 134
w14 (2) = w13 (2) = 17
w24 (2) = w23 (2) = 28
Is calculated (step S3005a).

Similarly, in the auction server 2,
u14 (3) = v13 (3) = 27
u24 (3) = v23 (3) = 197
w14 (3) = w13 (3) = 25
w24 (3) = w23 (3) = 41
Is calculated (step S3005b).

Similarly, in the auction server 3,
u14 (4) = v13 (4) = 36
u24 (4) = v23 (4) = 260
w14 (4) = w13 (4) = 33
w24 (4) = w23 (4) = 54
Is calculated (step S3005c).

(5) Counting Phase of Number of Successful Winners In FIG. 31, the auction server 1 transmits u14 (2) = 18 and u24 (2) = 134 to the auction server 2 and the auction server 3 (step S3101a).

  Similarly, the auction server 2 transmits u14 (3) = 27 and u24 (3) = 197 to the auction server 1 and the auction server 3 respectively (step S3101b). Similarly, the auction server 3 transmits u14 (4) = 36 and u24 (4) = 260 to the auction server 1 and the auction server 2 (step S3101c).

  Next, the auction server 1 has received (received) u14 (3), u24 (3) transmitted from the auction server 2, and u14 (4), u24 (4) transmitted from the auction server 3. (Step S3102a) and wait for reception. Similarly, the auction server 2 has received (received) u14 (2) and u24 (2) transmitted from the auction server 1 and u14 (4) and u24 (4) transmitted from the auction server 3. (Step S3102b) and wait for reception. Similarly, the auction server 3 has received (received) u14 (2) and u24 (2) transmitted from the auction server 1 and u14 (3) and u24 (3) transmitted from the auction server 2. It is determined whether or not (step S3102c), and the reception is awaited.

And when receiving by each auction server 1,2,3 (step S3102a, b, c: Yes),
u14 (2) = 18
u14 (3) = 27
u14 (4) = 36
u24 (2) = 134
u24 (3) = 197
u24 (4) = 260
Then, u14 (0) = 0 and u24 (0) = 8 are calculated using the interpolation method (steps S3103a, b, c).

  Next, it is determined whether or not the number of interpolated values is not “0” (step S3104a, b, c). Here, when the number whose value is not “0” is one (step S3104a, b, c: Yes), there is only one bidder who bids for the maximum amount, and that bidder is determined as the winning bidder (step S3105a, b, c). That is, the first bidder (bidder A) is u14 (0) = 0 and the second bidder (bidder B) is u24 (0) = 8 (≠ 0). This is the second bidder (bidder B).

  At this time, since S1 (0), S2 (0), S3 (0) = 0, 2, 0, this is regarded as a binary representation 010. That is, when considering S1 (0), S2 (0),... As a binary expression, attention is paid only to whether or not the value is 0, and if 0, 0 is converted, otherwise 1 is converted. . Since the binary representation 010 represents 300 yen, the winning bid price is 300 yen.

  On the other hand, in step S3104a, b, c, when there are a plurality of values whose complemented result values are not “0” (step S3104a, b, c: No), a state where a plurality of bidders are bidding on the maximum amount. A tie break occurs. In this case, the process proceeds to steps S3201a, b, and c shown in FIG.

  FIG. 32 shows the contents of processing when a tie break occurs. In FIG. 32, the above-described method of calculating u14 (2), u14 (3), u14 (4), u24 (2), u24 (3), u24 (4) (steps S3101a, b, c to step S3101a). W14 (2), w14 (3), w14 (4), w24 (2), w24 (3), w24 (4) are calculated by the same method as S3103a, b, c) (steps S3201a, b, c). ~ S3203a, b, c).

  If a tie break has occurred, the bidder whose value calculated by using the interpolation method is “0” is the highest bidder (step S3204). Since a tie break has occurred, there are naturally a plurality of bidders who take “0”. In this way, the tie breaker is identified. When a tie break occurs, a re-auction can be performed only with the identified tie break target person.

(Successful bidder counting algorithm)
Next, the contents of the successful bidder totaling algorithm in step S1609 will be described. All bidders transmit the personal information that is encrypted with the seller's public key along with the bid amount and distributed to the auction server using the auction server ID as a key. For example, when the input person A encrypts the mail address “a@xxx.co.jp” as personal information with the seller's public key, it is output as a character string. Let this character string be C (A). This character string is regarded as a 36-digit number using 0 to 9 and a to z. The number regarded as a 36-digit number is distributed to the number of auction servers by the following procedure.

A polynomial is created such that C (A) is a constant term. For example,
Fa (x) = C (A) + x + x ^ 2
And

At this time, the auction server IDs of the auction servers 1, 2, and 3 were 2, 3, and 4, respectively.
The auction server 1 includes Fa (2) = C (A) + 2 + 4 = C (A) +6,
The auction server 2 includes Fa (3) = C (A) + 3 + 9 = C (A) +12,
The auction server 3 includes Fa (4) = C (A) + 4 + 16 = C (A) +20
With the bid amount. In the procedure shown in FIG. 33, the bidder A corresponds to the “first bidder”, and C (A) = 25 and the successful bidder is counted.

  In FIG. 33, first, the auction server 1 finds that the winning bidder is the first bidder, and therefore acquires the first personal information Fa (2) = 31 from the storage unit 900 (step S3301a). Similarly, the auction server 2 finds that the winning bidder is the first bidder, and therefore acquires the first personal information Fa (3) = 37 from the storage unit 900 (step S3301b). Similarly, the auction server 3 finds that the winning bidder is the first bidder, and therefore acquires the first personal information Fa (4) = 45 from the storage unit 900 (step S3301c).

  Next, the auction server 1 transmits Fa (2) to the auction servers 2 and 3 (step S3302a). Similarly, the auction server 2 transmits Fa (3) to the auction servers 1 and 3 (step S3302b). Similarly, the auction server 3 transmits Fa (4) to the auction servers 1 and 2 (step S3302c).

  Thereafter, Fa (0) = 25 is calculated by using an interpolation method with Fa (2) = 31, Fa (3) = 37, and Fa (4) = 45 (steps S3303a, b, and c). As a result, “the personal information of the winning bidder encrypted with the seller's key” can be obtained (steps S3304a, b, and c).

  The algorithm for calculating only the next successful bid value while keeping the bid price secret is as shown in FIGS.

  As described above, according to this embodiment of the present invention, registration of personal information is unnecessary, personal information is protected from the system administrator, and only the seller can know the personal information of the successful bidder. .

  In addition to being sold as an auction engine, it is possible to build a system that includes customization and other e-commerce functions. Applicable fields include BtoC (company-to-person) CtoC (between-person) auctions and various BtoB (between-to-business) transactions that are highly required to prevent the leakage and misuse of bidders' personal information and fraudulent transactions. Yes. In particular, in BtoB purchasing / procurement systems, e-marketplaces, various bidding systems, etc., a system administrator and organizer can construct a mechanism that is not fraudulent in principle, and the fairness and reliability of the organizer is greatly appealing. it can.

  In addition, in a BtoB inventory disposal auction or a personnel dispatch auction, it is possible to respond to a request from a bidder company that it is not desired to know that it is bidding. By satisfying the bidder's request and seller's request, it is possible to develop a new market for auction using the Internet, and there is a great need for this system.

  As an anonymous auction, it is said that the system that "the bidder name is disclosed to the system administrator but is not open to the public" is called an anonymous auction system. It is a system that you do not know if you do not. In other words (assuming that there are m system managers in total), personal information cannot be leaked unless (m + 1) / 3 or more people collide.

  In addition, when a tie break occurs, it is possible to identify a plurality of people who had the highest price. As a result, only the bidder who gave the highest price after the tie break can make the final bid again. Also, seller and bidder registration is unnecessary due to encryption with the seller's key.

  In addition, the auction server 102 is automatically searched, the auction server 102 that has been dropped is excluded, and various obstacles are automatically covered. Various faults include detection of bid information whose communication is incomplete, transition to a processing wait state when the network is congested, and the like.

  In addition, registration of personal information is unnecessary, and the bid information is protected from the system administrator. A method for solving the problem of personal information leakage of an auction system on the Internet has been widely studied all over the world, and is collectively referred to as an anonymous auction protocol. The anonymous auction protocol according to this embodiment is greatly different from the conventional anonymous auction system in that the bid value and personal information of the bidder are protected from all auction participants including the system administrator. The bid price and personal information are structured so that only the seller of the winning bidder can understand it.

  In addition, auction sites on the Internet are now widespread, and a wide variety of sites have been launched, but a number of security issues are expanding at the same time. For example, when bidding for an auction, some personal information must be registered, which is predicated on the confidentiality of the system administrator. However, many leaks of personal information on the Internet have been reported so far, and the current situation is that they cannot be fully trusted (for example, replacing a WEB server in a company in January 2000) A case where some protections were lost due to inadequate work, and more than a dozen customer information leaked. In March of the same year, another company's WEB server opened a page containing the customer's name and phone number for several days. Etc.).

  In addition, at the end of June of the same year, it was announced that several major companies and other companies would operate an inventory disposal system using an anonymous auction system from September of the same year. Since the system administrator can know the personal information and bid price of all bidders, the anonymity according to the present embodiment is much weaker in anonymity.

  In the auction system according to the present embodiment, bid values are sent to a plurality of servers. However, if a plurality of server managers collaborate, it may be possible to know the bidder's personal information. However, in this anonymous auction system, it is not possible to know the bidder's personal information unless a certain number or more (three or more in the operating anonymous auction system) auction system administrators and the seller of the product are colluded. The structure is not possible. By managing each auction server 102 by an independent organization or company, it is possible to sufficiently reduce the possibility that a plurality of server managers and sellers collide. As a result, leakage of the bidder's personal information is eliminated.

  As an application field of the auction system according to the present embodiment, for example, it can be applied to fields such as government bidding, procurement of materials and the like in the public and private sectors (fraud prevention), and auction function of marketplace (fraud prevention).

  Further, as a future development of the auction system of the present embodiment, a BtoB development is envisioned. The company is also looking to sell and maintain an auction system, whether anonymous or non-anonymous. This anonymous auction system is considered to be effective for bids that require wide proof that the organizer cannot perform fraud, rather than just bidding values, such as government bidding.

  In addition, the auction system can also respond to requests from bidders who do not want to be generally informed of bidding, such as BtoB inventory disposal auctions and personnel dispatch auctions. By satisfying both the bidder's request and the seller's (seller) 's request, it is possible to expand the overall market demand by developing a new market for auction using the Internet.

  In addition, by making the bidder anonymous, there are dangers such as easy cancellation of the bidder and obstruction of the bid. For example, a credit card number (there is no secret leakage, so there will be no leakage on the way) will be settled. If you make it an operational rule, you can prevent easy cancellation. Other disturbances can be identified by recalculation under the agreement of each administrator.

  The method related to the anonymous auction system described in this embodiment of the present invention is realized by executing a program prepared in advance on a computer such as a personal computer or a workstation. This program is recorded on a computer-readable recording medium such as a hard disk, floppy disk, CD-ROM, MO, and DVD, and is read from the recording medium and executed by the computer. The program can be distributed through the recording medium or as a transmission medium via a network such as the Internet.

Effect of the invention

  As described above, according to the present invention, an auction system and an information processing apparatus that allow only the seller to know the personal information of the winning bidder while ensuring the confidentiality of the bid information of bidders other than the winning bidder. Thus, there is an effect that a computer-readable recording medium in which an auction bidding method, an auction successful bid amount determination method, an auction successful bidder determination method, and a program for causing a computer to execute these methods are recorded can be obtained.

  It is explanatory drawing which shows the principle of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows another principle of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows another principle of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows the system configuration | structure of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows the connection relation of each server and terminal device concerning this Embodiment of this invention.   It is a block diagram which shows the hardware constitutions of the metaserver, bidder terminal device, auction server, and seller terminal device concerning this Embodiment of this invention.   It is a block diagram which shows functionally the structure of the metaserver concerning this Embodiment of this invention.   It is a block diagram which shows functionally the structure of the bidder terminal device concerning this Embodiment of this invention.   It is a block diagram which shows functionally the structure of the auction server concerning this Embodiment of this invention.   It is a block diagram which shows functionally the structure of the seller terminal device concerning this Embodiment of this invention.   It is a flowchart which shows the content of the process (product registration phase) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (product registration phase) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (product registration phase) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows the content of the process (bid phase) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (bid phase) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows the content of the process (aggregation phase) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows the content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bid amount totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is a flowchart which shows another content of the process (successful bidder totaling algorithm) of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows the content of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows another content of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows another content of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows another content of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows another content of the auction system concerning this Embodiment of this invention.   It is explanatory drawing which shows another content of the auction system concerning this Embodiment of this invention.

DESCRIPTION OF SYMBOLS 100 Meta server 101 Bidder terminal device 102-1, 102-2, 102-3 Auction server 103 Seller terminal device 110 Bidder client (application)
113 Seller Client (Application)
400 network (Internet)
601,651 CPU
602, 652 ROM
603,653 RAM
604,654 HDD (hard disk drive)
605, 655 HD (hard disk)
606,656 FDD (floppy disk drive)
607,657 FD (floppy disk)
608,658 Display 609,659 KB (keyboard)
610,660 Mouse 611,661 Scanner 612,662 Network I / F (interface)
613, 663 Printer 614, 664 Bus 700, 800, 900, 1000 Storage unit 701, 801, 901, 1001 Reception unit 702, 802, 902, 1002 Transmission unit 703 ID issue processing unit 803, 1003 Display unit 804, 1004 Input unit 805 Distributed processing unit 903 Arithmetic processing unit 1005 Public key / private key issue processing unit

Claims (2)

A plurality of auction servers connected to a network, a meta server for centrally managing the plurality of auction servers, a bidder terminal device, and a seller terminal device, and an auction input to the seller terminal device The target product is an auction system for conducting a one-time auction based on the bid information input to the bidder terminal device,
The metaserver is
From the seller terminal device, the information on the target product, the minimum bid price of the target product, the maximum bid price of the target product, the information on the bid price range and the deadline time, and the information on the public key are transmitted via the network. Receiving means for receiving,
Storage means for storing information received by the receiving means (hereinafter referred to as “auction information”);
Transmitting means for transmitting the auction information stored in the storage means to the bidder terminal device;
With
The bidder terminal device
Receiving means for receiving the auction information from the meta server via the network;
Display means for displaying the auction information received by the receiving means;
Input means for accepting input of information regarding a bid amount and information regarding a bidder for the auction information displayed by the display means;
Based on the information on the bid amount input by the input means, the information on the bid amount is converted into binary representation, and for each digit of the binary representation, if the value is 0, the constant term is set to 0, If the value is not 0, a random first polynomial is generated so that the bidder's bidding order can be known according to the rule that the constant term is p (where p = 10007 is a sufficiently large prime number) and the value is not 0. Distributed processing means for calculating the value of the first polynomial for each auction server by substituting a predetermined value for each auction server into the first polynomial;
The value of the first polynomial for each auction server calculated by the distributed processing means is encrypted using the public key, digitized, and the number of the auction servers is calculated using the generated polynomial. A transmission means for transmitting to the respective auction servers via the network together with information on the distributed bidders;
With
Each of the auction servers includes a reception unit, a storage unit, an arithmetic processing unit, and a transmission unit,
The receiving unit receives the information about the values and the bidder of the first polynomial transmitted through the network from the bidders terminal device,
The storage means stores the information received by the receiving means;
The receiving means receives a deadline / aggregation instruction from the metaserver,
When the arithmetic processing means receives the instruction by the receiving means, it generates, for each auction server, a random second polynomial with the modulo p equal to the number of bidders × 2 , and for each auction server By substituting a predetermined value into the second polynomial to calculate the value of the second polynomial for each auction server,
It said transmission means transmits by said arithmetic processing means to the other of each of said auction server to the appropriate value of the second polynomial calculated for each of the auction server,
The receiving means receives the value of the second polynomial calculated by each of the other auction servers;
The arithmetic processing means is a value of the first polynomial stored by the storage means, a value calculated by the second polynomial, and a value received from each of the other auction servers by the receiving means. The bidder stored in the storage means is determined based on the bid amount and the bidder in the bidding order, and the information on the bidder is determined. And information on the successful bidder in an encrypted state based on the information on the bidder received from each of the other auction servers ,
The transmitting means transmits information on the successful bid amount determined by the arithmetic processing means and information on the successful bidder in the encrypted state calculated by the arithmetic processing means to the seller terminal device. An auction system characterized by
A plurality of auction servers connected to a network, a meta server for centrally managing the plurality of auction servers, a bidder terminal device, and a seller terminal device, and an auction input to the seller terminal device The target product is an auction method used in an auction system for performing an auction by a one-time bid based on bid information input to the bidder terminal device,
The metaserver is
From the seller terminal device, the information on the target product, the minimum bid price of the target product, the maximum bid price of the target product, the information on the bid price range and the deadline time, and the information on the public key are transmitted via the network. Receiving process to receive,
A storage step of storing information received by the reception step (hereinafter referred to as “auction information”) in a storage unit;
Transmitting the auction information stored in the storage means to the bidder terminal device;
Including
The bidder terminal device
Receiving the auction information from the metaserver via the network;
A display step of displaying the auction information received by the receiving step;
For the auction information displayed by the display step, an input step for accepting input of information regarding the bid amount and information regarding the bidder;
Based on the information regarding the bid amount input in the input step, the information regarding the bid amount is converted into binary representation, and for each digit of the binary representation, if the value is 0, the constant term is set to 0, If the value is not 0, a random first polynomial is generated so that the bidder's bidding order can be known according to the rule that the constant term is p (where p = 10007 is a sufficiently large prime number) and the value is not 0. A distributed processing step of calculating a value of the first polynomial for each auction server by substituting a predetermined value for each auction server into the first polynomial;
The value of the first polynomial for each auction server calculated by the distributed processing step is encrypted using the public key, digitized, and the number of the auction servers is calculated using the generated polynomial. A transmission step for transmitting to the respective auction server via the network together with information on the distributed bidders;
Including
Each said auction server
A first receiving step of receiving information on the bidder encrypted using the public key and the value of the first polynomial transmitted from the bidder terminal device via the network;
A storage step of storing the information received in the first reception step in a storage means;
A second receiving step of receiving a deadline / aggregation instruction from the metaserver;
When the instruction is received in the second receiving step, a random second polynomial is generated for each auction server by using p as the modulus and the number of bidders × 2 and predetermined for each auction server. An arithmetic processing step of calculating a value of the second polynomial for each of the auction servers by substituting the obtained value into the second polynomial;
A first transmission step of transmitting the value of the second polynomial calculated for each of the auction servers by the arithmetic processing step to each of the other corresponding auction servers;
A third receiving step of receiving the value of the second polynomial calculated by each of the other auction servers;
The value of the stored first polynomial in the storage means, the value calculated by the second polynomial by the arithmetic processing step, received from the third other of each of the auction server by the receiving process of And determining the successful bid amount and the number of bidders in the bidding order based on the value, and storing the information from the information on the number of bidders. A second calculation processing step of calculating information on the successful bidder in an encrypted state based on information on the bidder and information on the bidder received from each of the other auction servers ;
Information related to the successful bid amount determined in the second arithmetic processing step and information related to the successful bidder in the encrypted state calculated in the second arithmetic processing step are transmitted to the seller terminal device. A second transmission step;
An auction method comprising:

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