JP2001076061A - Electronic bidding method, recording medium with electronic bidding method recorded therein, and electronic bidding apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain an electronic bidding method, which enables all bidders to verify that there is no illegal act such as alteration, and that a bidder and a bidding price are proper without using commitment by an undeniable signature and makes secret bidding prices other than that of the bidder. SOLUTION: A bidding device calculates a bid value for the bid price of a bidder, calculates commitment by the chain of a unidirectional function for the bid value, sends a set of the commitment and its signature to a bid opening apparatus, which receives bids, verifies that signatures are valid after all bidders placed bids, opens the bids of all the bidders to the public, receives bid values from bidding apparatuses, verifies the propriety of the commitment after the bid values of all the bidders are received and discloses all bid values to the public, and determines a bidder and its bid price and discloses them to the public.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an application technology of information security technology, in which a plurality of bidders distributed on a communication network such as the Internet bid using electronic communication. The present invention relates to an electronic bidding device, an electronic bidding method, and a recording medium that records the electronic bidding method.

[0002]

2. Description of the Related Art As a typical example of the conventional system, an electronic bidding system by Miyazaki and Sakurai (S. Miyazaki, K. Sakurai, an electronic bidding system that can use a secret bulletin board using a public bulletin board, SCIS '99 41-
46 (1999)).

[0003]

In the conventional method, a commitment based on a non-repudiation signature (a signature scheme capable of proving that a bidder has not bid at a certain price) has been used. There is a problem that the efficiency is inefficient because a lot of calculation and communication are required for the / confirmation / denial procedure.

[0004]

Since the electronic bidding apparatus and method proposed by the present invention are configured using a commitment by a chain of one-way functions, a practical one such as SHA-1 can be used as the one-way function. By using a typical one-way function, a more efficient bidding method than the conventional method is realized.

[0005]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below. FIG. 1 is a diagram showing the overall configuration of the present invention. Bidder _{B 1, B 2, ···,} B n (100) are coupled via a communication channel (300) and the tender opening's A (200). Example 1 First, as shown in FIG. 2, bidder A first performs [preprocessing],
Next, each bidder B _{i (i = 1, ..., N)} performs a [bid procedure] (110-150).
Bidder A, and finally, bidder A enters [Bid opening procedure] (2
10-250) to open a bill.

FIG. 3 is a block diagram showing a bidding procedure of the bidder B _i (100). FIG. 4 shows a block diagram of a bid opening procedure of bidder A (200). [Preprocessing] Bidder A has a bid price table ｛ω ₁ , ..., ω _v-1 ,
ω _v , ..., ω _x ｝ (for example, ¥ 1 million in sales of used cars,
..., 600,000 yen, 500,000 yen, ..., 100,000 yen, that is, the bidder presents a price range of 1 million yen to 100,000 yen and a specific bid price. ) And one-way function H: {0,1} ^s × {0,1} ^t → {0,1} ^t (where {0,1} ^s is an s-bit of a set of {0,1}) The entire set of bit strings, {0,1} ^t indicates the entire set of t-bit bit strings consisting of the set of {0,1}.) In practice, a practical one-way function such as SHA-1 is used as the one-way function. In addition, no (message not successful bid) and yes (message successful bid) {0,1} ^s are released. Bid Procedure] Bidder B _i is bidding procedure shown in FIG. 4 (110-15
Bid by 0). (Step 110) The bidder B _i enters the bid price table {ω ₁ ,.
· Select a bid price ω _vi from ω _-1 , ω _v ,..., Ω _x 50 (for example, 500,000 yen). (Step 120) Bid price for bid price ω _vi Is calculated.

(For example, bidder _Bi is 600,000 yen,..., 1
If you do not wish to make a bid for ¥ 100,000 but wish for ¥ 500,000, ｛ω ₁ (¥ 1 million), ..., ω _v-1 (¥ 600,000), ω _vi
(500,000 yen) {b _i1 , ... b _{i, vi-1,} b _{i, vi} } for｝ is {no, ..., no, yes}. (Step 130) Calculate the commitment L _{i, j} = H (b _{i, j,} L _{i, j + 1} ) (1 ≦ j ≦ vi) for the bid value b _{i, j} .

(The above calculation is {0,1}^tRandomly from
L chosen_{i, vi + 1}With L as the initial value _{i, vi}= H (b_{i, vi,}
L_{i, vi + 1}), ..., L_{i, 2}= H (b_{i, 2,}L_{i, 3}), L_{i, 1}=
H (b_{i, 1,}L_{i, 2}). (Step 140) b_{i, 1}Commitment to L_{i, 1}Against
And the signature σ_i= Sig_Bi(L_{i, 1}) Is calculated. (This signature
Bid is indeed bidder B_iThat was done
I understand. ) (Step 150) b_{i, 1}Commitment to L_{i, 1}Toso
Signature σ_iSet (L_{i, 1}, Σ_i) As bid and open bidder A
Send to [Bid Opening Procedure] The bidder A performs the bid opening procedure shown in FIG.
0), open bids, and all bidders B_{i (i = 1,2, ..., n)}Bid on
Value ｛b_1,1, b_1,2,..._,b_{1, vi}｝ (Bidder B₁), ・ ・ ・
｛B_{i, 1}, b_{i, 2,}..._,b_{i, vi}｝ (Bidder B_i), ・ ・ ・, ｛B
_{n, 1}, b_{n, 2,}..._,b_{n, vi}｝ (Bidder B_n)] Sent in order
Then, open the bid according to the bid opening procedure (210-250). (Step 210) Bidder B_iBid from (L_{i, 1}, σ_i)
Received, all bidders B_{i (i = 1,2, ..., n)}Bid from ｛L_{i, 1},
σ_i｝_{(i = 1,2, ..., n)}Is complete, the signature σ_iCheck the legitimacy of
Proof, all bids ｛(L_{i, 1,}σ_i)｝_{(i = 1,2, ..., n)}Publish
You. (For example, ｛(L_1,1,σ₁), ..., (L
_{n, 1,}σ_n) ① is displayed on the display device and made public. (This table
No specific bid price can be known from the data. However
Then, if the bid price or the like is falsified, ｛(L
_1,1,σ₁), ..., (L_{n, 1,}σ_n｝ Changes and is falsified
You can see that (Step 220) j = 1 (that is, the bid price ω₁Against
All bidders B_{i (i = 1,2, ..., n)}Bid price of ｛b_{1 , 1}, b_2,1, ...
・, B_{n, 1}｝, J = 2 (ie, bid price ω_TwoFull entry for
Bidder (B₁, ..., B_i, ..., B_n) Bid price ｛b_1,2, b
_2,2, ・ ・ ・, B_{n, 2}｝, ... are released in order, and j =
Perform the following steps (230-250) for each of 1,2, ... (Step 230) Bidder B_iFrom the bid price (b_{i, j}, L_{i, j + 1})
Received, the total bid value ｛(b_{i, j}, L_{i, j + 1})｝_{( i = 1,2, ... n)}Assortment
If so, the validity of the commitment L_{i, j}= H (b_{i, j}, L_{i, j + 1}), And the total bid price ｛(b_{i, j}, L_{i, j + 1})｝
_{(i = 1,2, ..., n)}Publish. (Step 240) Bid price b for all i_{i, j}= No
Then, the process returns to step 230 with j = j + 1. (Step 250) Bid value b for a certain i_{i, j}= If yes,
Assuming v = j, B_iIs released as the winning bidder and ωv as the winning bid
You.

Embodiment 2 FIG. 5 shows a block diagram of an electronic bidding apparatus of the present invention. The electronic bidding device 1 includes a bidding device 2 and a bid opening device 3. The bidding apparatus 1 includes bid price selecting means 4, bid value calculating means 5, commitment calculating means 6, signature calculating means 7, and one-way function storing means 8.

[0010] bidder _{B i (i = 1,2, ···} , n) , the bid has been published price list _{ω j (j = 1,2, ···} , v, ···, x) 9, the bid price ω _vi is selected by the bid price selecting means 4. Bid value calculation means 5, bid value b _i for the bidding price ω _vi against the bid price _{ω vi, 1 = b i,} 2 = ··· = b i, vi-1 = no ( not bid), b _{i , vi} = yes (to win) Commitment calculation means 6, a one-way function bid using chain H b _i, commitment to _{j L i, j = H (} b i, j, L
_{i, j + 1} ). The signature calculation means 7 calculates a signature σ _i for the commitment L _{i, 1} . Then, the bidding device 2 transmits the bid (L _{i, 1} , σ _i ) to the bid opening device, and the bid opening device verifies that the signature σ _i is valid, and publishes all the bids. Is the bid price (b _{i, j} , L
_{i, j + 1} ) to the bidding apparatus, the bidding apparatus verifies the validity of the commitment L _{i, j} , and confirms the release of this bid value. Then, the bidding value (b _{i, j + 1} , L _{i, j + 2} ), (b _{i, j + 2} , L
_{i, j + 3} ), ... are transmitted.

[0011] The bid opening device 3 includes a signature verification means 10-1 and all bids.
Open means 10-2, Commitment verification means 11-1, Total bid price
Disclosure means 11-2, successful bid calculation means 12, disclosure of successful bidders and contract prices
Means 13 and a one-way function storage means 8.
The signature verification unit 10-1 and the all bid disclosure unit 10-2
(L_{i, 1}, σ_i) And the signature σ_iWhen verifying the validity of
Together, all bids ｛(L_{i, 1}, σ_i)｝_{(i = 1,2, ..., n)}Publish
You. Commitment verification means 11-1 and all bid value disclosure means 11
-2 is the bid price (b_{i, j}, L _{i, j + 1}) Receives and one-way function
Commitment L using H_{i, j}Verifying the validity of
, The total bid price ｛(b_{i, j}, L_{i, j + 1})｝_{(i = 1,2, ..., n)} Public
Open. Further, the successful bid calculation means 12 calculates the bid value b_{i, j}Receive
And the bid price b for all i_{i, j}= No, j = j + 1
Commitment verification means 11-1, all bid value disclosure means 11-2
To the bid price b for some i_{i, j}If = yes, successful bid
And sends it to the highest bidder / contract price disclosure means 13 to make a successful bid.
Publish the bidder and contract price. [Exception handling] bid value (b_{i, j}, L_{i, j + 1})
B_iIf there is, the bidder B_iAnd bid again, except
Restart. (Actually, bidder B who does not disclose_iAgainst
Should take additional measures such as penalties for forfeiture of deposits.
And )

[0012]

The electronic bidding method and apparatus proposed in the present invention are configured by using a commitment by a chain of one-way functions, so that a practical one-way function such as SHA-1 is used. An electronic bidding method and apparatus that is more efficient than the conventional method using a commitment based on a nonrepudiable signature is realized.

Further, it is necessary as an electronic bidding method and apparatus.
It has the following properties. Since the bids are disclosed in the order of [accuracy], the minimum v
Responding ω_vThe bidder who has bid in is awarded. [Verifiability] Bid $ b_{i, 1}, b_{i, 2,}..._,b_{i, v}｝ And Komi
Statement ｛L_{i, 1}, L_{i, 2}, ・ ・ ・, L_{i, v + 1}｝ Is public
Anyone can verify tampering. [Fairness] Commitment members were released before the bid
L_{i, 1}Only until the bid is opened
do not know. [Price confidentiality] When the winning bidder comes out, the bidding is finished and
Bid after the bidder came out ｛b_{i, v + 1}, b _{i, v + 2}, ・ ・ ・, B
_{i, vi}｝ Is not disclosed, so bid prices other than the winning bid
It is concealed. [Non-repudiation] Commitment L_{i, 1}Is the bidder's signature σ
_i= Sig_Bi(L_{i, 1}) Can not be denied. [Possibility of Identifying Unauthorized Person] Commitment L_{i, j} Is published
Because it has a bid b_{i, j}Can be identified. Also one
Due to the unidirectionality of the direction function H, the commitment L_{i, j} 
Cannot be altered later.

[Brief description of the drawings]

FIG. 1 is a diagram showing an overall configuration of the present invention.

FIG. 2 is a diagram showing an overall procedure of the present invention.

FIG. 3 is a block diagram of the tender procedure bidders B _i.

FIG. 4 is a block diagram showing a bid opening procedure of bidder A.

FIG. 5 is a block diagram of the electronic bidding device of the present invention.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Electronic bidding device 2 Bidding device 3 Bidding device 4 Bid price selection means 5 Bid price calculation means 6 Commitment calculation means 7 Signature calculation means 8 One-way function storage means 9 Bid price table 10-1 Signature verification means 10-2 All bids Disclosure means 11-1 Commitment verification means 11-2 All bid value disclosure means 12 Successful bid calculation means 13 Successful bidder / contract price disclosure means

Claims (9)

[Claims] [Claim 1] A plurality of bidders on a bidder side for a bidder A on the bidder side.
Bidder B_{i (i = 1,2, ..., n )}When bidding by
Network with a bid opening device provided on the tender side
E-bidding method of connecting and bidding through a network
Bidder A is a bid price table ω_{j (j = 1,2, ..., v, ..., x)}And one
Procedure 1 for determining and publishing the directional function H, and the bidding device is bidder B_iBid price ω_viBid price b
_{i, 1}= b_{i, 2}= ・ ・ ・ = B_{i, vi- 1}= no (do not win), b_{i, vi}= ye
Procedure 2 for calculating s (successful bid), and commit method by chaining one-way function H
L_{i, j}= H (b_{i, j}, L _{i, j + 1}) Calculate and commit men
L_{i, 1}And its signature σ_iSet of (L_{i, 1}, σ_i) Open as a bid
Procedure 3 for sending to the bidding device, and the bidding device uses the transmitted bidding (L_{i, 1}, σ_i) To receive
Step 4 and signing σ when bids from all bidders' bid devices are completed_iIs positive
Verify that it is correct and bid from all bidders' bid devices
, And Step 6 where j = 1, and the bid value (b_{i, j}, L_{i, j + 1}) And receive all
Commitment L once bidders have bid_{i, j}The legitimacy of L
_{i, j}= H (b_{i, j}, L_{i, j + 1}) And the total bid ｛(b_{i, j}, L
_{i, j + 1}) Step 7 to publish｝_{i, j}If no, j = j + 1 and step 7
Step 8 to return to, and bid price b for a certain i_{i, j}= yes if B_iThe successful bidder, ω_jTo
Procedure 9 to determine and release as the winning bid
There is no fraud such as tampering
All bidders can verify that there is
Securing the bill price and committing it by chaining one-way functions
That bids can be efficiently implemented by using
Electronic bidding method characterized by the above-mentioned. 2. A plurality of bidders on the bidding side for bidder A on the bidding side.
Bidder B_{i (i = 1,2, ..., n)} When bidding by
Network with a bid opening device provided on the tender side
E-bidding method of connecting and bidding through a network
Bidder A is a bid price table ω_{j (j = 1,2, ..., v, ..., x)}And one
Procedure 1 for determining and publishing the directional function H, and the bidding device is bidder B_iBid price ω_viBid price b
_{i, 1}= b_{i, 2}= ・ ・ ・ = B_{i, vi- 1}= no (do not win), b_{i, vi}= ye
Procedure 2 for calculating s (successful bid), and commit method by chaining one-way function H
L_{i, j}= H (b_{i, j}, L _{i, j + 1}) Calculate and commit men
L_{i, 1}And its signature σ_iSet of (L_{i, 1}, σ_i) Open as a bid
Procedure 3 for sending to the bidding device, and the bidding device uses the transmitted bidding (L_{i, 1}, σ_i) To receive
Step 4 and signing σ when bids from all bidders' bid devices are completed_iIs positive
Verify that it is correct and bid from all bidders' bid devices
, And Step 6 where j = 1, and the bid value (b_{i, j}, L_{i, j + 1}) And receive all
Commitment L once bidders have bid_{i, j}The legitimacy of L
_{i, j}= H (b_{i, j}, L_{i, j + 1}) And the total bid ｛(b_{i, j}, L
_{i, j + 1}) Step 7 to publish｝_{i, j}If no, j = j + 1 and step 7
Step 8 to return to, and bid price b for a certain i_{i, j}= yes if B_iThe successful bidder, ω_jTo
Procedure 9 to determine and release as the winning bid
There is no fraud such as tampering
All bidders can verify that there is
Securing the bill price and committing it by chaining one-way functions
That bids can be efficiently implemented by using
The recording medium which recorded the electronic bidding method characterized by the above-mentioned. 3. A bid device bidder _{B i (i = 1,2, ···} , n) the bid price list _{ω j (j = 1,2, ···} , v, ···, x) Bid price ω selected from
bid value for _{vi b i, 1 = b i} , 2 = ··· = b i, vi-1 = no ( not _bid), b _i, Step 1 to calculate the _vi = yes (to bid)
Calculates the commitment L _{i, j} = H (b _{i , j} , L _{i, j + 1} ) by chaining the one-way function H to the bid value b _{i, j} , and calculates the bid value (b
_{i, j} , L _{i, j + 1} ) to the bid opening device, and a set (L _{i, 1} , σ _i ) of the commitment Li _{i, 1} and its signature σ _i as a bid to the bid opening device. A bidding method characterized by comprising step 3. 4. A bid device bidder _{B i (i = 1,2, ···} , n) the bid price list _{ω j (j = 1,2, ···} , v, ···, x) Bid price ω selected from
bid value for _{vi b i, 1 = b i} , 2 = ··· = b i, vi-1 = no ( not _bid), b _i, Step 1 to calculate the _vi = yes (to bid)
Calculates the commitment L _{i, j} = H (b _{i , j} , L _{i, j + 1} ) by chaining the one-way function H to the bid value b _{i, j} , and calculates the bid value (b
_{i, j} , L _{i, j + 1} ) to the bid opening device, and a set (L _{i, 1} , σ _i ) of the commitment Li _{i, 1} and its signature σ _i as a bid to the bid opening device. A recording medium that records a bidding method, characterized by comprising step 3. 5. The bid opening device is a bidder B._{i (i = 1,2, ..., n)}Sent from
Trusted bid (L_{i, 1}, σ_i) [Bid price b_{i, 1}Is a bid
Price list ω_{j (j = 1,2, ..., v, ..., x)}Ω ₁To
Bid price (yes: win, no: do not win), L_{i, 1}
= H (b_{i, 1}, L_{i, 2}) Is the bid price b_{i, 1} Commitment, σ
_i Is commitment L_{i, 1}Signature 1), and when the bids from the bidding devices of all bidders are completed, the signature σ_iIs positive
Verify that it is correct and bid from all bidders' bid devices
, And Step 3 where j = 1, and the bid value (b_{i, j}, L_{i, j + 1}) And receive all
Commitment L once bidders have bid_{i, j} The legitimacy of L
_{i, j} = H (b_{i, j}, L_{i, j + 1}) And the total bid ｛(b_{i, j},
L_{i, j + 1}) Step 4 to publish｝, and bid price b for all i_{i, j}If no, j = j + 1 and step 4
Step 5 to return to, and bid price b for a certain i_{i, j}= yes if B_iThe successful bidder, ω_jTo
Procedure 6 to determine and release as the winning bid
A bill opening method characterized by that. 6. The bid opening device is a bidder B._{i (i = 1,2, ..., n)}Sent from
Trusted bid (L_{i, 1}, σ_i) [Bid price b_{i, 1}Is a bid
Price list ω_{j (j = 1,2, ..., v, ..., x)}Ω ₁To
Bid price (yes: win, no: do not win), L_{i, 1}
= H (b_{i, 1}, L_{i, 2}) Is the bid price b_{i, 1} Commitment, σ
_i Is commitment L_{i, 1}Signature 1), and when the bids from the bidding devices of all bidders are completed, the signature σ_iIs positive
Verify that it is correct and bid from all bidders' bid devices
, And Step 3 where j = 1, and the bid value (b_{i, j}, L_{i, j + 1}) And receive all
Commitment L once bidders have bid_{i, j} The legitimacy of L
_{i, j} = H (b_{i, j}, L_{i, j + 1}) And the total bid ｛(b_{i, j},
L_{i, j + 1}) Step 4 to publish｝, and bid price b for all i_{i, j}If no, j = j + 1 and step 4
Step 5 to return to, and bid price b for a certain i_{i, j}= yes if B_iThe successful bidder, ω_jTo
Procedure 6 to determine and release as the winning bid
A recording medium on which a bill opening method is recorded. 7. The electronic bidding device connects via a network.
It consists of a continuous bidding device and a bid opening device.
Statement calculation means, signature calculation means and one-way function description
And Bidder B_{i (i = 1,2, ..., n)}Is bid by bid price selection means
Price list ω_{j (j = 1,2, ..., v , ..., x)}From the bid price ω_vichoose
And the bidding price calculating means calculates the bidding price ω_viBid price b
_{i, 1}= b_{i, 2}= ・ ・ ・ = B_{i, vi-1}= no (do not win), b_{i, vi}= ye
s (successful bid), and the commitment calculation means
Bid value b using a chain of one-way functions H_{i, j}Komi against
Statement L_{i, j}= H (b_{i, j}, L_{i, j + 1}) Calculate the signature total
The calculation means is commitment L_{i, 1}The signature σ_iTotal
And the bidding device calculates the bid (L _{i, 1}, σ_i)
And the signature is signed by the bid opening device._iIs legitimate
Testimony, publish all bids, and the bidding device
(B_{i, j}, L_{i, j + 1}) To the bidding device, and the bidding device
Statement L_{i, j}The legitimacy of L_{i, j}= H (b_{i, j}, L_{i, j + 1})
After confirming the release of this bid value,
(B_{i, j + 1}, L_{i, j + 2}), (B_{i, j + Two}, L_{i, j + 3}), ...
At the same time, the bid opening device is used to verify signatures, open all bids, commit
Verification means, all bid value disclosure means, successful bid calculation means,
For example, means for disclosing bidder / bid price and means for storing one-way function
The signature verification means and all bid disclosure means are used for bidding (L_{i, 1}, σ_i)
Received and signed σ_iVerify the validity of all bids
Is released, commitment verification means and all bid value disclosure means
Is the bid price (b_{i, j}, L_{i, j + 1}A) Receive and Commit L
_{i, j}The legitimacy of L_{i, j}= H (b_{i, j}, L_{i, j + 1}) And verify
, The total bid price ｛(b_{i, j}, L_{i, j + 1})｝ Is released,
The bill calculation means calculates the bid value b for all i_{i, j}If = no
If j = j + 1, commitment verification means, all bid prices
Sent to the opening means, bid price b for a certain i_{i, j}= If yes
Judgment is successful and sent to the highest bidder / contract price disclosure means
The winning bidder / contract price disclosure means discloses the winning bidder and the contract price.
Open, no tampering, etc.
That all bidders can verify that
Commitment by concealing prices and chaining one-way functions
That bidding can be efficiently implemented by using
Characteristic electronic bidding device. 8. A bidding apparatus, comprising: a bidding price selecting means;
Calculating means, commitment calculating means, signature calculating means, and
And one-way function storage means, and bidder B_{i (i = 1,2, ..., n)}Is bid by bid price selection means
Price list ω_{j (j = 1,2, ..., v , ..., x)}From the bid price ω_vichoose
And the bidding price calculating means calculates the bidding price ω_viBid price b
_{i, 1}= b_{i, 2}= ・ ・ ・ = B_{i, vi-1}= no (do not win), b_{i, vi}= ye
s (successful bid), and the commitment calculation means
Bid value b using a chain of one-way functions H_{i, j}Komi against
Statement L_{i, j}= H (b_{i, j}, L_{i, j + 1}) Calculate the signature total
The calculation means is commitment L_{i, 1}The signature σ_iTotal
And the bidding device calculates the bid (L _{i, 1}, σ_i)
And the signature is signed by the bid opening device._iIs legitimate
Testimony, publish this bid, and the bidding device
(B_{i, j}, L_{i, j + 1}) To the bidding device, and the bidding device
Statement L_{i, j} The legitimacy of L_{i, j}= H (b_{i, j}, L_{i, j + 1})
After confirming the release of this bid value,
(B_{i, j + 1}, L_{i, j + 2}), (B_{i, j + 2}, L_{i, j + 3}), ...
A bidding device characterized by doing. 9. A bid opening apparatus comprising: signature verification means, all bid disclosure means, commitment verification means, all bid value disclosure means, successful bid calculation means, successful bidder / successful bid price disclosure means, one-way function storage means, and a bid price table. ω _{j (j = 1, 2,..., v,..., x).
i (i = 1,2, ..., n)} bid (L _{i, 1} , σ _i ) [However, bid price b
_{i, 1} the bid value for the ω ₁ (yes: the successful bid, no: not a successful _bid), L _{i, 1} the bid value b _{i, 1} of the commitment, σ _i receives the commitment L _{i, 1} of signature] , with verifying the validity of the signature sigma _i, the total bid _{{(L i, 1, σ} i)} exposes commitment verification means and the total bid public means, bid value (b _{i, j,} L _{i , j + 1} ), verify the validity L _{i, j} = H (b _{i, j} , L _{i, j + 1} ) of the commitment L _{i, j} , and verify the total bid value ｛(b _{i, j} , L _{i, j + 1} )｝ and the successful bid calculation means j = j + 1 if the bid price b _{i, j} = no for all i
Is transmitted to the commitment verification means and all bid value disclosure means, and if the bid value b _{i, j} = yes for a certain i, it is determined to be a successful bid and transmitted to the highest bidder and the successful bid price disclosure means, and The price opening means is a bid opening device which discloses the successful bidder and the winning bid price.