Confidential blockchain transactions

1. A computer-implemented method, comprising:

obtaining, by a blockchain node of a blockchain, a linkable ring signature corresponding to a remittance transaction between a remitter and one or more payees, wherein the linkable ring signature comprises a plurality of key images, wherein a value of each key image is related to a remitter public key of the remitter, a remitter private key of the remitter, and an asset commitment value of a respective asset to be spent in the remittance transaction, and

wherein the linkable ring signature is generated based on the remitter public key, the remitter private key, a remitter pseudo private key, and a remitter pseudo public key,

wherein the remitter pseudo public key is based on the asset commitment values of the assets to be spent, transfer amount commitment values of transfer amounts corresponding to respective payees of the one or more payees, and a first set of one or more random numbers, and wherein the remitter pseudo private key is based on a second set of one or more random numbers;

determining, based on the linkable ring signature, that the remitter pseudo private key and the remitter pseudo public key satisfy a key pair relationship;

determining, based on the linkable ring signature, that a sum of asset amounts of the assets to be spent equals a sum of the transfer amounts;

determining, based on the linkable ring signature, that the plurality of key images are different from historical key images corresponding to previous remittance transactions; and

based on determining that the plurality of key images are different from historical key images corresponding to previous remittance transactions, executing the remittance transaction.

2. The computer-implemented method of claim 1 , wherein the linkable ring signature further comprises an additional key image generated based on a public key of a cover party and a pseudo public key of the cover party, the pseudo public key of the cover party being generated based on asset commitment values of assets held by the cover party, and

wherein determining that the plurality of key images are different from the historical key images comprises determining that the additional key image is different from the historical key images.

3. The computer-implemented method of claim 2 , comprising:

obtaining one or more pairs of intermediate parameters, wherein a first intermediate parameter of each pair corresponds to the remitter, and wherein a second intermediate parameter of each pair corresponds to the cover party; and

verifying the one or more pairs of intermediate parameters, comprising

recalculating the one or more pairs of intermediate parameters based on a third set of one or more random numbers or derived values of the third set of one or more random numbers included in the linkable ring signature, and

verifying, based on the recalculated one or more pairs of intermediate parameters, that a respective ring value determining rule is satisfied between first and second intermediate parameters of each pair.

4. The computer-implemented method of claim 1 , wherein the key images are I 1 to I m , the remitter public key is P j , the remitter private key is x j , asset identifiers of the assets to be spent are ID 1 to ID m , and wherein the key images are generated using the following equation:

I d =x j ×Hash G (P j , ID j,d ), d∈[1, m], wherein Hash G ( ) is a hash function from an elliptic curve to the elliptic curve.

5. The computer-implemented method of claim 1 , comprising storing the plurality of key images to the blockchain to be compared to key images of future transactions.

6. The computer-implemented method of claim 1 , comprising verifying that a stored mapping relationship exists between each asset to be spent and the remitter public key.

7. The computer-implemented method of claim 1 , comprising:

obtaining data representing the remittance transaction, and

verifying, using range proofs in the data representing the remittance transaction, that the transfer amounts are not less than zero.

8. A non-transitory, computer-readable medium storing one or more instructions that, when executed by a computer system, cause the computer system to perform operations comprising:

obtaining, by a blockchain node of a blockchain, a linkable ring signature corresponding to a remittance transaction between a remitter and one or more payees, wherein the linkable ring signature comprises a plurality of key images, wherein a value of each key image is related to a remitter public key of the remitter, a remitter private key of the remitter, and an asset commitment value of a respective asset to be spent in the remittance transaction, and

wherein the linkable ring signature is generated based on the remitter public key, the remitter private key, a remitter pseudo private key, and a remitter pseudo public key,

wherein the remitter pseudo public key is based on the asset commitment values of the assets to be spent, transfer amount commitment values of transfer amounts corresponding to respective payees of the one or more payees, and a first set of one or more random numbers, and wherein the remitter pseudo private key is based on a second set of one or more random numbers;

determining, based on the linkable ring signature, that the remitter pseudo private key and the remitter pseudo public key satisfy a key pair relationship;

determining, based on the linkable ring signature, that a sum of asset amounts of the assets to be spent equals a sum of the transfer amounts;

determining, based on the linkable ring signature, that the plurality of key images are different from historical key images corresponding to previous remittance transactions; and

based on determining that the plurality of key images are different from historical key images corresponding to previous remittance transactions, executing the remittance transaction.

9. The non-transitory, computer-readable medium of claim 8 , wherein the linkable ring signature further comprises an additional key image generated based on a public key of a cover party and a pseudo public key of the cover party, the pseudo public key of the cover party being generated based on asset commitment values of assets held by the cover party, and

wherein determining that the plurality of key images are different from the historical key images comprises determining that the additional key image is different from the historical key images.

10. The non-transitory, computer-readable medium of claim 9 , wherein the operations comprise:

obtaining one or more pairs of intermediate parameters, wherein a first intermediate parameter of each pair corresponds to the remitter, and wherein a second intermediate parameter of each pair corresponds to the cover party; and

verifying the one or more pairs of intermediate parameters, comprising

recalculating the one or more pairs of intermediate parameters based on a third set of one or more random numbers or derived values of the third set of one or more random numbers included in the linkable ring signature, and

verifying, based on the recalculated one or more pairs of intermediate parameters, that a respective ring value determining rule is satisfied between first and second intermediate parameters of each pair.

11. The non-transitory, computer-readable medium of claim 8 , wherein the key images are I 1 to I m , the remitter public key is P j , the remitter private key is x j , asset identifiers of the assets to be spent are ID 1 to ID m , and wherein the key images are generated using the following equation:

I d =x j ×Hash G (P j , ID j,d ), d∈[1, m], wherein Hash G ( ) is a hash function from an elliptic curve to the elliptic curve.

12. The non-transitory, computer-readable medium of claim 8 , wherein the operations comprise storing the plurality of key images to the blockchain to be compared to key images of future transactions.

13. The non-transitory, computer-readable medium of claim 8 , wherein the operations comprise verifying that a stored mapping relationship exists between each asset to be spent and the remitter public key.

14. The non-transitory, computer-readable medium of claim 8 , comprising:

obtaining data representing the remittance transaction, and

verifying, using range proofs in the data representing the remittance transaction, that the transfer amounts are not less than zero.

15. A computer-implemented system, comprising:

one or more computers; and

one or more computer memory devices interoperably coupled with the one or more computers and having tangible, non-transitory, machine-readable media storing one or more instructions that, when executed by the one or more computers, cause the one or more computers to perform one or more operations comprising:

obtaining, by a blockchain node of a blockchain, a linkable ring signature corresponding to a remittance transaction between a remitter and one or more payees, wherein the linkable ring signature comprises a plurality of key images, wherein a value of each key image is related to a remitter public key of the remitter, a remitter private key of the remitter, and an asset commitment value of a respective asset to be spent in the remittance transaction, and

wherein the linkable ring signature is generated based on the remitter public key, the remitter private key, a remitter pseudo private key, and a remitter pseudo public key,

wherein the remitter pseudo public key is based on the asset commitment values of the assets to be spent, transfer amount commitment values of transfer amounts corresponding to respective payees of the one or more payees, and a first set of one or more random numbers, and wherein the remitter pseudo private key is based on a second set of one or more random numbers;

determining, based on the linkable ring signature, that the remitter pseudo private key and the remitter pseudo public key satisfy a key pair relationship;

determining, based on the linkable ring signature, that a sum of asset amounts of the assets to be spent equals a sum of the transfer amounts;

determining, based on the linkable ring signature, that the plurality of key images are different from historical key images corresponding to previous remittance transactions; and

based on determining that the plurality of key images are different from historical key images corresponding to previous remittance transactions, executing the remittance transaction.

16. The computer-implemented system of claim 15 , wherein the linkable ring signature further comprises an additional key image generated based on a public key of a cover party and a pseudo public key of the cover party, the pseudo public key of the cover party being generated based on asset commitment values of assets held by the cover party, and

wherein determining that the plurality of key images are different from the historical key images comprises determining that the additional key image is different from the historical key images.

17. The computer-implemented system of claim 16 , wherein the operations comprise:

obtaining one or more pairs of intermediate parameters, wherein a first intermediate parameter of each pair corresponds to the remitter, and wherein a second intermediate parameter of each pair corresponds to the cover party; and

verifying the one or more pairs of intermediate parameters, comprising

recalculating the one or more pairs of intermediate parameters based on a third set of one or more random numbers or derived values of the third set of one or more random numbers included in the linkable ring signature, and

verifying, based on the recalculated one or more pairs of intermediate parameters, that a respective ring value determining rule is satisfied between first and second intermediate parameters of each pair.

18. The computer-implemented system of claim 15 , wherein the key images are I 1 to I m , the remitter public key is P j , the remitter private key is x j , asset identifiers of the assets to be spent are ID 1 to ID m , and wherein the key images are generated using the following equation:

I d =x j ×Hash G (P j , ID j,d ), d∈[1, m], wherein Hash G ( ) is a hash function from an elliptic curve to the elliptic curve.

19. The computer-implemented system of claim 15 , wherein the operations comprise storing the plurality of key images to the blockchain to be compared to key images of future transactions.

20. The computer-implemented system of claim 15 , wherein the operations comprise verifying that a stored mapping relationship exists between each asset to be spent and the remitter public key.