Electronic voting system and method based on homogeneous cryptography

1. An electronic voting method in a voter terminal, the electronic voting method comprising:

(a) generating a serial number sn by using election identification information eid and a his/her secret key, wherein the election identification information eid is shared through a block chain;

(b) encrypting a voting message M through verifiable homogeneous cryptography to generate a ciphertext CT, and generating a zero-knowledge proof key π for the voting message; and

(c) transmitting an electronic ballot including the serial number sn, the ciphertext CT, and the zero-knowledge proof key π to a block chain network as a transaction.

2. The electronic voting method of claim 1 , wherein each of an administrator terminal and the voter terminal receiving the transaction through the block chain network discards the transaction when the serial number sn is duplicated on the block chain.

3. The electronic voting method of claim 2 , further comprising:

verifying the zero knowledge proof using at least some of the CRS, the ciphertext CT, the zero knowledge proof key π, the serial number sn, the election identification information, and a Merkle route rt when the serial number sn is not duplicated on the block chain;

rerandomizing the ciphertext CT and the zero-knowledge proof key π by using a public key; and

publishing the rerandomized ciphertext CT′, zero-knowledge proof key π′, and serial number sn on the block chain as a block.

4. The electronic voting method of claim 3 , further comprising:

confirming whether the voting is included by verifying the ciphertext CT′ and zero-knowledge proof key π′ published on the block chain by using the generated serial number sn, after step (c).

5. The electronic voting method of claim 1 , wherein before the step (a), the administrator terminal generates a list of voters, generates a Merkle route rt using the list of voters, generates election identification information eid, and

publishes a list of voters pklist, a Merkle root rt, an election public key, an election verification key and election identification information eid on the block chain.

6. The electronic voting method of claim 1 , further comprising:

receiving an electronic ballot including the serial number, the ciphertext CT, and the zero-knowledge proof key π from each voter terminal by means of the administrator terminal, after step (c), wherein the ciphertext CT is encrypted by homogeneous cryptography;

merging the ciphertext CTs received from each of the voter terminals to obtain a merged ciphertext CTsum; and

decrypting the merged ciphertext CTsum using a secret key, generating a voting result Msum, and transmitting the generated voting result to each voter terminal through a block chain network along with a decryption proof key.

7. A voter terminal comprising:

a voting encryption unit configured to generate a serial number sn using the election identification information eid and its own secret key, encrypt a voting message M through verifiable homogeneous cryptography to generate a ciphertext CT, and generate a zero-knowledge proof key π for the voting message M, wherein the election identification information eid is pre-shared through a block chain; and

a communication unit configured to transmit an electronic ballot including the serial number sn, the ciphertext CT, and the zero-knowledge proof key π to a block chain network as a transaction.

8. The voter terminal of claim 7 , wherein each of block chain nodes receiving the transaction through the block chain network discards the transaction when the serial number sn is duplicated on the block chain, and

the block chain nodes are a plurality of voters and an administrator participating in the election.

9. The voter terminal of claim 8 , wherein each of the administrator terminal and the voter terminals receiving the transaction through the block chain network verifies the zero knowledge proof using at least some of the CRS, the ciphertext CT, the zero knowledge proof key π, the serial number sn, the election identification information, and a Merkle route rt, when the serial number sn is not duplicated on the block chain, and

rerandomizes the ciphertext CT and the zero-knowledge proof key π using a public key, and adds the rerandomized ciphertext CT′, zero-knowledge proof key π′, and serial number sn on the block chain as a block.

10. The voter terminal of claim 9 , further comprising:

a voting verification unit configured to confirm whether the voting of the voter is included by verifying the ciphertext CT′ and zero-knowledge proof key π′ published on the block chain by using the generated serial number sn.

11. The voter terminal of claim 7 , wherein the administrator terminal generates a list of voters, generates a Merkle route rt using the list of voters, generates election identification information eid, and

publishes a list of voters pklist, a Merkle root rt, an election public key, an election verification key and election identification information eid on the block chain.

12. An electronic voting system comprising:

a voter terminal configured to generate a serial number sn, encrypt a voting message M through verifiable homogeneous cryptography to generate a ciphertext CT, generate a zero-knowledge proof key π for the voting message M, and transmit an electronic ballot including the serial number sn, the ciphertext CT, and the zero-knowledge proof key π to a block chain network; and

an administrator terminal configured to verify the zero knowledge proof using at least some of the CRS, the ciphertext CT, the zero knowledge proof key π, the serial number sn, the election identification information, and a Merkle route rt, when the serial number sn is not duplicated on the block chain, rerandomize the ciphertext CT and the zero-knowledge proof key π using a public key, and add the rerandomized ciphertext CT′, zero-knowledge proof key π′, and serial number sn on the block chain as a block.

13. The electronic voting system of claim 12 , wherein the administrator terminal decrypts the rerandomized ciphertext CT′ using a secret key, collects a voting result, and then transmits the collected voting result to the voter terminal through the block chain network.

14. The electronic voting system of claim 12 , wherein the voter terminal confirms whether the voting of the voter is included by verifying the ciphertext CT′ and zero-knowledge proof key π′ published on the block chain by using the generated serial number sn.