KR100338330B1 - Voting method for a receipt-free electronic voting system - Google Patents

Abstract

The present invention relates to an electronic voting system. In the ordinary voting system in which voters attend the polling place and vote on the ballots, an enormous election management cost is required. With the development of information and communication networks such as the Internet, a lot of researches have been conducted to implement the election system by electronic method using cryptographic techniques. The conventional electronic voting system using secret dispersion and threshold password has a disadvantage in that it does not provide a ticketing prevention function, but the present invention provides a ticketing prevention function using a co-creation technique of secret information.

Description

VOTING METHOD FOR A RECEIPT-FREE ELECTRONIC VOTING SYSTEM}

The present invention relates to an electronic voting method using a cryptographic technique that allows a voter to attend a polling place and vote directly on the ballot by replacing the conventional voting method with an electronic method using an information communication network such as the Internet.

Typically, physical voting requires a great deal of time, space, and money for both voters and poll managers. In other words, the voter is inconvenient to spend time because he has to attend and vote in the polling place, and the voting manager needs to set up and operate the polling place and requires a lot of manpower for counting. . In order to improve the inconvenience of the conventional physical voting method, an electronic voting method has been proposed.

Electronic voting is a method of replacing the conventional physical voting method with an electronic method using a cryptographic method, and should satisfy the following characteristics when compared with the conventional physical voting method.

That is, the confidentiality that a voter's vote must not be known by a third party, the integrity that all valid votes must be counted correctly, the soundness that dishonest voters must not disturb the election, and the voter can vote only once. The impossibility of double voting, the eligibility that only those with the voting power to vote, the fairness that nothing should affect the election, the verification that it must be able to verify the validity of the vote, and some voting management In the event of problems with the system, voting must be robust and voting must be impossible to buy and sell.

Electronic voting began to be studied in the 1980s with the development of cryptographic protocols and can be classified into two categories. The first group uses blind signature techniques and a mix-net method, which is typical of the work of Fujioka-Okamoto-Ohta in 1993. Another class is the study of Cramer-Gennaro-Schoenmaker in 1997 using secret sharing and threshold cryptography.

Fujioka-Okamoto-Ohta method using hidden signature and anonymous communication channel is difficult to implement anonymous communication to prevent the connection between voter and vote value, and the number of message communication between voter and election manager There are many disadvantages, and it is difficult to find out who cheated among the voters and administrators when a voting error occurred.

The Cramer-Gennaro-Schoenmaker method, which uses secrets and thresholds, provides the robustness of the system due to secrets and allows the counting to be done at once using the threshold encryption technique. have. However, the Cramer-Gennaro-Schoenmaker method has a disadvantage in that the user can later prove his / her vote value, so that the ticket can be sold. In other words, if the voter stores the random number used in the vote and presents it to the buyer, the voter can prove his / her vote and can be used for the ticket.

Therefore, an object of the present invention is to provide a voting method of a new electronic voting system that provides an anti-voting function based on a technique using secret dispersion and threshold password.

Another object of the present invention is to provide a voting method of an electronic voting system in which two participants jointly generate secret information while maintaining mutual confidentiality of information in order to implement the electronic voting system.

Voting method of the electronic voting system according to the present invention for achieving the above object comprises the steps of: transmitting to the verifier a vote value (x, y) for the candidate selected by the voter; Generating, by the verifier, a verifier random number (u, v) for disabling proof of the vote value (x, y) and providing it to the voter; The voter certifying the validity of the vote value (x, y), and generating a response (d _i , r _i ) to the proof and providing it to the verifier; In response to the response d _i , r _i , the verifier verifies the validity of the first voting value (x, y) and verifies the validity of the verifier random number (u, v) Transmitting to the voter; In response to the response r, the voter validates the validator random number (u, v) and, if valid, multiplies the vote value (x, y) by the validator random number (u, v). Calculating a final vote value (x _f , y _f ) and posting it on the bulletin board; The verifier includes the step of verifying the validity of the final vote values (x _f, y _f) posted on the public bulletin board posting a sure sign for the final vote values (x _f, y _f) on the public bulletin board Characterized in that.

1 is a block diagram illustrating a voting process of an electronic voting system composed of several steps according to the present invention;

Figure 2 is a flow chart illustrating the detailed message calculation and operation of the voting process performed in the electronic voting system according to the present invention.

<Description of the symbols for the main parts of the drawings>

100: election manager 200: voter

300: validator 400: public bulletin board

Hereinafter, the present invention will be described in detail with reference to the accompanying drawings.

1 is a schematic block diagram of an electronic voting system according to the present invention. The main participants of the electronic voting system are the election manager 100, the voter 200, the verifier 300, and the public bulletin board 400. Each of these participants may be implemented as a computer system interconnected through communication means well known in the art. Each participant in the electronic voting system performs the following functions.

The election manager 100 performs a function of registering and counting the ballot value after registering the public bulletin board 400 after authenticating the identity according to the voter registration request of the voter 200.

The voter 200 requests the election manager 100 to register to vote, registers as a valid voter on the public bulletin board 400, and then interacts with the verifier 300 to determine his or her initial vote value and verifier 300. It calculates the final vote value by multiplying the verifier random number provided and serves to register it in the public bulletin board (400).

The verifier 300 verifies the validity of the vote of the voter 200, generates a verifier random number, provides the voter 200, and verifies that the final vote value is valid to register a confirmation signature on the public bulletin board 400. Do this.

The public bulletin board 400 serves as a public bulletin board that registers the voter 200, publishes the voter 200 's vote value, and publishes the verification signature of the verifier 300, as shown in FIG. 1D. . The public bulletin board 400 checks the final ballot value by the name column 410 where the name of the voter 200 is posted, the ballot column 430 where the final vote value of the voter 200 is posted, and the verifier 300. A signature column 450 is posted where the signature is posted. All content posted on the bulletin board 400 can be retrieved by each voter 200 and verifier 300, but each voter 200 and verifier 300 is assigned to itself in the bulletin board 400. Messages can only be posted to the designated area.

The electronic voting system of the present invention composed of the above-described participants operates in sequence through the voter registration process of FIG. 1A, the voting process of FIG. 1B, and the counting process of FIG. 1C, and the present invention provides a voter 200 and a verifier. 300 relates to a protocol of the voting process that jointly generates a final voting value.

In the voter registration process of FIG. 1A, the voter 200 transmits a registration request message to the election manager 100 including personal information for verifying his / her identity for registration as a voter. The election manager 100 confirms the identity of the voter 200 in response to the registration request message of the voter 200 and registers as a valid voter 200 in the public bulletin board 400. Voter 200 can check whether their registration from the public bulletin board (400).

In the voting process of FIG. 1B, the voter 200 and the verifier 300 generate the first vote value generated by the voter 200 and the verifier random number generated by the verifier 300 using the voting protocol described below. Multiply and jointly generate the final vote. The voter 200 registers the generated final vote value in the public bulletin board 400, and the verifier 300 registers the verification signature in the public bulletin board 400 after validating the final vote value.

In the counting process of FIG. 1C, the election manager 100 collects all the ballot values registered in the public bulletin board 400 after the voting ends, counts the counts using their private keys, calculates the voting result, and then public bulletin board again. Register at 400. The voter 200 may check the voting result from the public bulletin board 400.

The electronic voting system of the present invention uses an Elgamal type public key cryptosystem based on discrete algebra to calculate the voting value. The election manager 100 generates an Elgamal-type private key and public key pair to keep the private key secret and the public key is issued in the form of a public key certificate from a certificate authority, and posts it on the public bulletin board 400 so that all voters ( 200) to make it available. In the case of using multiple election managers 100, public keys can be jointly generated by using well-known secret distribution techniques and the secret keys can be distributed to more completely protect the confidentiality of voting and provide the robustness of an electronic voting system. have. Each voter 200 and verifier 300 likewise receives a public key certificate from the certification authority to use for mutual authentication.

The message flow of the voting stage illustrated in FIG. 1B, which is a major feature of the present invention, is described in more detail with reference to the flowchart of FIG. 2.

In step 510, voter 200 selects one of k candidates G, for example, ith candidate G _i , where 1 ≦ _i ≦ k, and then selects any random number α ( here, To select a random number that satisfies p) and calculates a first voting value (x, y) as shown in Equation 1 below as a vote for the i th candidate.

(x, y) = (g ^α , h ^α Gi)

In Equation 1, g is a generator of galoa field 'GF (p)', h is a public key of the election manager 100 ((h = g ^s mod p)), and p is gal It is a prime number to generate the loa field GF (p), and G _i means generators independent of each other representing k candidates.

In a next step 520, the voter 200 generates a random random number w ₁ , where To calculate the random number (a _i , b _i ) for the encryption of the first voting value (x, y) as shown in Equation 2 below, and to k-1 j other than i (J = 1,..., I-1, i + 1,..., K) any random value (d _j , r _j ), where Satisfies), and encrypts the primary voting value (x, y) by Equation 3 below to encrypt the primary voting value (a _j , b _j ) (= (a ₁ , b ₁ ), ... Calculate. (a _k , b _k )) The encrypted primary voting values (a _j , b _j ) thus calculated are used to verify the validity of the primary voting values (x, y). The encrypted primary voting values (a _j , b _j ) are then simply defined as random numbers (A, B).

(a _i , b _i ) = (g ^w1 , h ^w1 )

(a _j , b _j ) = (g ^rj x ^dj , h ^rj (y / Gj) ^dj )

In a next step 530, the voter 200 sends the primary vote values (x, y) and the encrypted primary vote values (A, B) to the verifier 300.

In step 540, the verifier 300 generates a random random number β and w ₂ , where The random number satisfying) is selected and the verifier random numbers (u, v) and (a, b) are calculated using Equations 4 and 5. The verifier random numbers (u, v) are random numbers generated by the verifier 300 and provided to the voter 200 and used to disable the proof of the vote.

Along with this, the verifier 300 attempts to validate the primary voting value (x, y) as any random number (c ₁ ) (where, Random number that satisfies a), and then the verifier random numbers (u, v) and (a, b) and any random number (c ₁ ) are sent to the voter 200 (step 550).

In a next step 560, the voter 200 verifies the validity of the primary voting value using any random number c ₁ for validating the validator 300 (d _i , r _k ). Calculated as Equation 6 below.

If k (d _i , r _i ), i.e. (d ₁ , r ₁ ), ... (d _k , r _k ) are (D, R), then the response to the validity of the primary voting value is do.

In addition, the voter 200 attempts to prove the validity of the verifier random numbers (u, v) provided from the verifier 300, where any random number c ₂ (where, Random number satisfies a) and transmits the response values (D, R) and any random number (c ₂ ) for the validity of the primary vote to the verifier 300 (step 570).

In the next step 580, the verifier 300 uses (D, R), (A, B), any random number (c ₁ ) to validate the primary voting value (x, y). Then, it is checked whether the conditions shown in Equations 7 and 8 are satisfied.

c ₁ = d ₁ + ..., + d _k

(a _j , d _j ) = (g ^rj x ^dj , h ^rj (y / G _j ) ^dj )

In addition, the verifier 300 calculates a response (r) to any random number (c ₂ ) provided from the voter to prove the validity of the verifier random number (u, v) as shown in Equation (9), and then the voter The calculated response r is transmitted to the 200.

r = w ₂ + β _c2

In a next step 590, the voter 200 validates the validator random number g ^r using Equation 10 below to validate the validator random number u, v provided from the validator 300. , h ^r ).

(g ^r , h ^r ) = (au ^c1 , bv ^c1 )

When the validity of the validator random number (u, v) is verified from Equation 10, the first voting value (x, y) and the validator random number (u, v) are multiplied to determine the final voting value (x _f , y). _f ) (= (xu, yv)) is calculated and the calculated final vote value (x _f , y _f ) is posted in the ballot box 430 of the bulletin board 400. As such, the final vote values (x _f , y _f ) are jointly generated by the voter 200 and the verifier 300, so that the voter 200 cannot prove his / her vote to the third buyer, so that the voter 200 You can prevent it.

Then, in step 600, the verifier 300 validates the final vote value (x _f , y _f ) of the voter 200 posted in the ballot column 430 of the public bulletin board 400 If it is verified as shown in Figure 11 and the vote is valid, a verification signature as shown in Equation 12 is posted in the signature column 450.

(x _f , y _f ) = (xu, yv)

Sig (H (ID, x _f , y _f , Time, OK))

Then, after the voting process described with reference to FIG. 2 is finished, in the counting process illustrated in FIG. 1C, the election manager 100 collects all valid final voting values posted on the bulletin board 400 and calculates their final product. After that, the final result can be obtained by decrypting using the private key of the election manager 100.

The method of jointly generating the voting value by the interaction between the voter and the verifier of the present invention described above is not only an electronic voting method, but also other methods that require two participants to jointly generate secret information while maintaining mutual confidentiality. It can also be applied to other applications. For example, when the secret information of the first participant cannot be proved to other participants, the second participant cannot verify the secret information of the first participant, but can verify the validity of the secret information. 1 Participant does not know the secret of the random number information provided by the second participant, but can verify its validity, and the final password is generated by multiplying the secret information of the first participant by the random number of the second participant For example, it is possible to keep confidential information co-generated by two participants.

Therefore, in calculating the final voting value in the electronic voting system according to the present invention, the final voting value is jointly generated by the voting party and the validator by multiplying the primary voting value generated by the voter and the validator random number provided by the validator. Done. Therefore, the voter can not prove his or her vote contents to the third buyer, so the anti-voting function can be provided. In addition, although the verifier can verify the validity of the voting contents through the method performed in the electronic voting system of the present invention, since the specific voting contents are unknown, the validity and confidentiality can be guaranteed. The present invention can additionally provide a ticketing prevention function in the electronic voting system using the secret dispersion, the threshold password of the prior art.

Claims (2)

Claim 1 has been deleted. In the voting method of the electronic voting system consisting of a voter, an election manager, a verifier and a public bulletin board implemented as a computer system connected through each communication means, Transmitting the voter value (x, y) made to the candidate selected by the voter to the verifier; Generating, by the verifier, a verifier random number (u, v) for disabling proof of the vote value (x, y) made by the voter and providing it to the voter; The voter certifying the validity of the vote value (x, y), and generating a response (d _i , r _i ) to the verifier and providing it to the verifier; In response to the responses d _i and r _i , a verifier verifies the validity of the vote value (x, y) and returns a response r that verifies the validity of the verifier random number (u, v). Transmitting to; In response to the response r, the voter validates the validator random number (u, v) and multiplies the first voting value (x, y) by the validator random number (u, v). Calculating a final vote value (x _f , y _f ) and posting it on the bulletin board; The verifier includes the step of verifying the validity of the final vote values (x _f, y _f) posted on the public bulletin board posting a sure sign for the final vote values (x _f, y _f) on the public bulletin board Voting method of an electronic voting system, characterized in that.