Block chain transaction method based on elliptic curve symmetric homomorphic encryption

Abstract

The invention discloses a block chain transaction method based on elliptic curve symmetric homomorphic encryption. The method comprises the steps of 1, generating a transaction key; 2, encrypting the transaction amount through the transaction key by using an elliptic curve encryption algorithm to obtain a current transaction amount ciphertext; 3, executing a ciphertext updating algorithm on the ciphertext of the historical transaction amount to obtain an updated historical ciphertext; 4, executing a ciphertext updating algorithm on the current transaction amount ciphertext, and updating the current transaction amount ciphertext into a ciphertext under the same target key to obtain an updated current ciphertext; step 5, packaging the updated historical ciphertext, the auxiliary ciphertext, the updated current ciphertext and other transaction information between the historical transaction participants into a transaction; and step 6, the miner verifies the validity of the transaction. According to the method, the traditional addition and multiplication homomorphic operation is supported, the ciphertext updating operation can also be supported, the comparison homomorphic operation after ciphertext updating is supported, and the transaction content can be subjected to diversified operation and verification in the ciphertext state.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and specifically to a blockchain transaction method based on elliptic curve symmetric homomorphic encryption. Background Technology

[0002] For blockchain transactions, protecting the privacy of transaction content is one of the core technical requirements. Current blockchain transaction privacy protection technologies mainly revolve around homomorphic encryption, zero-knowledge proofs, and trusted execution environments. Among them, homomorphic encryption technology has become a research hotspot in this field because it can achieve "computable but not visible" data, that is, it can directly perform operations on ciphertext without decryption, thus naturally protecting data privacy without the need for additional hardware assistance.

[0003] Existing homomorphic encryption schemes, such as Paillier encryption, ElGamal encryption, and their variants, are mostly based on public-key cryptography. In these schemes, data is encrypted using the recipient's public key, and their homomorphism (such as addition or multiplication) is built upon the mathematical structure of public-key cryptography. However, these public-key-based homomorphic encryption schemes have several inherent drawbacks:

[0004] First, these solutions generally rely on Public Key Infrastructure (PKI) for key management and distribution, which introduces additional complexity, management overhead, and communication costs. Second, the encryption and decryption process of public-key cryptography typically involves multiple time-consuming modulo-exponential operations, resulting in low computational efficiency. In scenarios like blockchain, which require batch and rapid verification of transactions, this can easily become a performance bottleneck. Furthermore, existing solutions have relatively limited homomorphic operation types, mostly supporting only addition or multiplication homomorphism, making it difficult to directly support the more complex operations required in blockchain (such as comparisons between ciphertexts). In addition, a key security risk lies in the fact that on-chain data is usually encrypted with the same public key. Once the private key corresponding to this public key is leaked, all related on-chain transaction data will be exposed, lacking fine-grained security isolation.

[0005] Compared to public-key cryptography, symmetric cryptography typically involves only operations such as substitution, permutation, and XOR, offering significant advantages in terms of low computational complexity and fast encryption / decryption speeds, making it highly suitable for handling batch data in blockchains. Furthermore, symmetric cryptography is more flexible, potentially enabling the construction of homomorphic encryption schemes that support a wider range of operations. More importantly, through key negotiation mechanisms, a "one session, one key" approach can be achieved. Even if the key is leaked in a single session, only that single transaction's data will be exposed, without compromising other historical or future transactions, thus providing greater security flexibility and forward security.

[0006] However, research on homomorphic encryption based on symmetric cryptography is still in its early stages both domestically and internationally. Directly transforming traditional symmetric cryptographic algorithms (such as AES) into homomorphic schemes faces significant challenges. Utilizing efficient asymmetric cryptographic foundations to negotiate session keys and then constructing a symmetric homomorphic encryption system is a feasible technical path. Elliptic curve cryptography (ECC), with its advantages over RSA and classical ElGamal cryptography (such as lower computational cost, smaller storage space, and higher security strength), has become an ideal foundation for achieving this goal.

[0007] Therefore, this invention aims to explore a homomorphic encryption scheme based on elliptic curve cryptography. The core of this scheme lies in dynamically generating a shared symmetric key between the transacting parties using an elliptic curve key negotiation protocol; subsequent encryption, homomorphic operations, and ciphertext updates all utilize this symmetric key or its derivatives. This method cleverly combines the security and efficiency of elliptic curve cryptography with the advantages of symmetric cryptography in terms of computational speed and key flexibility, ultimately forming a novel blockchain transaction privacy protection scheme that combines high efficiency, high security, and rich homomorphic computation capabilities. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention provides a blockchain transaction method based on elliptic curve symmetric homomorphic encryption, comprising:

[0009] Step 1: The transaction participants generate a transaction key through a key negotiation protocol;

[0010] Step 2: Using the transaction key, encrypt the transaction amount using an elliptic curve cryptography algorithm to obtain the ciphertext of the current transaction amount;

[0011] Step 3: Execute the ciphertext update algorithm on the ciphertext of the historical transaction amount to obtain the updated historical ciphertext;

[0012] Step 4: Execute the ciphertext update algorithm on the current transaction amount ciphertext to update it with ciphertext under the same target key, and obtain the updated current ciphertext;

[0013] Step 5: Package the updated historical ciphertext, auxiliary ciphertext, updated current ciphertext, and other transaction information between historical transaction participants into a transaction;

[0014] Step 6: Miners verify the validity of the transaction, including digital signature verification, homomorphic addition, and comparison operations to verify the non-negativity, balance, and reasonableness of the amount; if valid, it is recorded on the blockchain; otherwise, the transaction is discarded.

[0015] Preferably, in step 1, the transaction participants generate a transaction key through a key negotiation protocol, including:

[0016] Step 1.1: The transaction sender and receiver jointly negotiate and set a large prime number to form an elliptic curve equation; based on the elliptic curve equation, determine the base point and order of the elliptic curve; Step 1.2: The current transaction receiver generates a first random number and a second random number; based on the first random number, determine a first parameter; based on the second random number, determine a second parameter; Step 1.3: The current transaction sender generates a third random number; based on the third random number, determine a third parameter; Step 1.4: The current transaction receiver sends the first parameter and the second parameter to the current transaction sender; the current transaction sender sends the third parameter to the current transaction receiver;

[0017] Step 1.5: The current transaction recipient calculates the shared transaction key using the first random number, the second random number, and the received third parameter, and the current transaction sender calculates the third random number, the received first parameter, and the second parameter.

[0018] Preferably, the transaction key satisfies the following formula:

[0019]

[0020] in, For transaction keys, The first random number, The second random number, The third random number, is the base point of the elliptic curve. It is a large prime number with more than 160 digits.

[0021] Preferably, in step 3, the encrypted historical transaction amount is processed using a ciphertext update algorithm to obtain the updated historical ciphertext, including:

[0022] Step 3.1: Obtain the historical transaction key corresponding to the ciphertext of the historical transaction amount; based on the transaction key, set a ciphertext with a plaintext value of 0. The corresponding plaintext transaction key and target key;

[0023] Step 3.2: Based on the historical transaction key and the target key, generate a historical amount ciphertext update factor; based on the plaintext transaction key and the target key, generate a ciphertext update factor with plaintext value of 0;

[0024] Step 3.3: Based on the historical amount ciphertext update factor and the plaintext update factor of 0, perform a ciphertext update algorithm on the ciphertext of the historical transaction amount to obtain the updated historical ciphertext.

[0025] Preferably, the encrypted amount update factor satisfies the following formula:

[0026]

[0027] in, The ciphertext update factor for the amount. The second random number corresponding to the historical transaction key. The third random number corresponding to the historical transaction key; A random number corresponding to the target key. This is another random number corresponding to the target key. A random number for the plaintext transaction key. This is another random number for the plaintext transaction key; This indicates the order of the elliptic curve.

[0028] Preferably, the updated historical ciphertext satisfies the following formula:

[0029]

[0030] in, For the updated historical ciphertext, This is the encrypted data of historical transaction amounts. The ciphertext is the plaintext value of 0. is the base point of the elliptic curve. The ciphertext update factor for historical amounts. The ciphertext update factor for historical amounts. It is a large prime number with more than 160 digits.

[0031] Preferably, the auxiliary ciphertext is auxiliary verification information used for verifying the validity of the transaction;

[0032] The verification information includes: range proof and balance proof;

[0033] The range proof is used to allow miners to verify that the plaintext amount corresponding to the updated current transaction amount ciphertext is non-negative and within a preset reasonable range; the balance proof is used to allow miners to verify, through homomorphic addition and comparison operations, that the sum of all updated historical input amount ciphertexts is equal to the sum of all updated current output amount ciphertexts.

[0034] Compared with the prior art, the beneficial effects of the present invention are:

[0035] (1) This invention realizes an efficient blockchain transaction method based on elliptic curve symmetric homomorphic encryption by using elliptic curve key negotiation and symmetric encryption. Compared with the previous blockchain transaction methods based on public key homomorphic encryption, this invention does not require public key infrastructure, thus avoiding a series of overheads caused by public key generation, management, and storage; in addition, this invention is based on the elliptic curve cryptography construction scheme, which has the advantages of being lightweight, efficient, and easy to implement, and can significantly improve the processing speed of transaction data in the blockchain.

[0036] (2) In terms of security, the present invention can be reduced to the discrete logarithm problem on elliptic curves, which can fully guarantee the semantic security of the ciphertext. In addition, the present invention implements one key per session. Losing a session key will only expose one transaction data on the chain and will not leak other related transaction data, which has higher flexibility.

[0037] (3) The transaction method proposed in this invention, in addition to supporting traditional homomorphic operations of addition and multiplication, can also support ciphertext update operations and comparison homomorphic operations after ciphertext update. It realizes diversified operations and verification of blockchain transaction content in ciphertext state.

[0038] Compared with public-key homomorphic encryption, symmetric-based homomorphic encryption has the following advantages: (1) It does not use public-key infrastructure, avoiding the overhead of public key generation, management, and storage; (2) Symmetric encryption operations generally only involve low-complexity and more efficient operations such as substitution, permutation, and XOR, which are suitable for batch data processing; (3) Symmetric cryptography is more flexible and can construct homomorphic encryption schemes that support more types of operations; (4) It can be combined with mechanisms such as key negotiation to achieve one key per session. Losing a session key will only expose one transaction data on the chain and will not leak other related transaction data, thus having greater flexibility. Obviously, compared with public-key homomorphic encryption, symmetric-based homomorphic encryption is more suitable for blockchain. However, there is still little research on symmetric-based homomorphic encryption at home and abroad, and symmetric-based homomorphic encryption has great research potential and value. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of a blockchain transaction method based on elliptic curve symmetric homomorphic encryption according to the present invention.

[0040] Figure 2 This is a flowchart of a blockchain transaction method based on elliptic curve symmetric homomorphic encryption according to the present invention; Detailed Implementation

[0041] like Figure 1As shown, an embodiment of a blockchain transaction method based on elliptic curve symmetric homomorphic encryption according to the present invention includes the following steps:

[0042] Step 1: Generate transaction key:

[0043] Step 1.1: The two parties in the transaction are the senders of the current transaction. and the current transaction recipient Firstly, by and Choose an elliptic curve together ,in Equals 13, take the base point as . The level Infinity The order of the elliptic curve is .

[0044] Step 1.2 Select random number and Calculate the parameters , .

[0045] Step 1.3 Select random number And calculate parameters .

[0046] Step 1.4 Its parameters and Send to ; Its parameters Send to .

[0047] Step 1.5 and Both can calculate the key using their own parameters and the other party's parameters. .

[0048] Step 2 Using transaction keys The current transaction amount Encryption is performed to obtain ciphertext. .

[0049] Step 3 Use the new key ciphertext of past transaction amounts Execute the key update algorithm, where Update the original ciphertext to the new ciphertext. This step can be further divided into:

[0050] Step 3.1: Input ciphertext The original key is Input a ciphertext with a plaintext value of 0. Its key is Enter new key .

[0051] Step 3.2, Generate , .

[0052] Step 3.3: Output the new ciphertext .

[0053] Step 4: Using the same process as in Step 3, finally output the new encrypted value of the current transaction amount. .

[0054] Step 4.1: The miner uses homomorphic addition to add the ciphertexts of the two past transaction amounts. The two ciphertexts are as follows: and The keys are all Output the sum of the two ciphertexts. The corresponding key is Repeat the above process to calculate the past. The total amount of the transactions Calculate the current Total transaction amount Methods and calculations same.

[0055] Step 4.3: The miner verifies the two ciphertexts. and The size relationship. and The corresponding plaintexts are respectively (The corresponding numerical plaintext is) ), (The corresponding numerical plaintext is) The corresponding keys are all Subtracting the ciphertext from the original text yields the result. ,make The corresponding value is ,available Therefore, it can be determined that... .

[0056] Through the above specific examples and implementation methods, it can be seen that the blockchain transaction method based on elliptic curve symmetric homomorphic encryption proposed in this invention is feasible and effective. It can perform data operations quickly while satisfying the correctness of encryption and decryption, and has homomorphic operation properties, making it suitable for practical scenarios of data encryption and operation in blockchain.

[0057] The embodiments and accompanying drawings described herein are intended for illustrative purposes to help the reader understand the principles of the method and the ideas contributed by the inventors to promote the application of the invention, and should be understood as not being limited to such specific examples and conditions. Furthermore, all equivalents or extensions made according to the spirit and essence of the invention should be covered within the scope of protection of this invention.

[0058] This invention also has the following advantages and positive results:

[0059] (1) This invention realizes an efficient blockchain transaction method based on elliptic curve symmetric homomorphic encryption by using elliptic curve key negotiation and symmetric encryption. Compared with the previous blockchain transaction methods based on public key homomorphic encryption, this invention does not require public key infrastructure, thus avoiding a series of overheads caused by public key generation, management, and storage; in addition, this invention is based on the elliptic curve cryptography construction scheme, which has the advantages of being lightweight, efficient, and easy to implement, and can significantly improve the processing speed of transaction data in the blockchain.

[0060] (2) In terms of security, the present invention can be reduced to the discrete logarithm problem on elliptic curves, which can fully guarantee the semantic security of the ciphertext. In addition, the present invention implements one key per session. Losing a session key will only expose one transaction data on the chain and will not leak other related transaction data, which has higher flexibility.

[0061] (3) The blockchain transaction method proposed in this invention, in addition to supporting traditional homomorphic operations of addition and multiplication, can also support ciphertext update operations and comparison homomorphic operations after ciphertext update. It realizes diversified operations and verification of blockchain transaction content in ciphertext state.

[0062] The method of this invention utilizes elliptic curve cryptography, which offers advantages over RSA and ElGamal cryptography in terms of lower computational complexity, faster processing speed, and higher efficiency. Therefore, this invention is implemented within an elliptic curve cryptosystem. The method designed in this invention avoids the inefficiency of existing public-key homomorphic encryption methods, possessing high-efficiency encryption and data processing capabilities, and can meet the low-latency requirements of batch data processing in blockchain.

[0063] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention (including the claims) is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in the details for the sake of brevity.

[0064] This invention is intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A blockchain transaction method based on elliptic curve symmetric homomorphic encryption, characterized in that, include: Step 1: The transaction participants generate a transaction key through a key negotiation protocol; Step 2: Using the transaction key, encrypt the transaction amount using an elliptic curve cryptography algorithm to obtain the ciphertext of the current transaction amount; Step 3: Execute the ciphertext update algorithm on the ciphertext of the historical transaction amount to obtain the updated historical ciphertext; Step 4: Execute the ciphertext update algorithm on the current transaction amount ciphertext to update it with ciphertext under the same target key, and obtain the updated current ciphertext; Step 5: Package the updated historical ciphertext, auxiliary ciphertext, updated current ciphertext, and other transaction information between historical transaction participants into a transaction; Step 6: Miners verify the validity of the transaction, including digital signature verification, homomorphic addition, and comparison operations to verify the non-negativity, balance, and reasonableness of the amount; If valid, record it on the blockchain; otherwise, discard the transaction.

2. The method according to claim 1, characterized in that, In step 1, the transaction participants generate a transaction key through a key negotiation protocol, including: Step 1.1: The transaction sender and receiver jointly negotiate and set a large prime number to form an elliptic curve equation; based on the elliptic curve equation, determine the base point and order of the elliptic curve; Step 1.2: The current transaction receiver generates a first random number and a second random number; based on the first random number, determine a first parameter; based on the second random number, determine a second parameter; Step 1.3: The current transaction sender generates a third random number; based on the third random number, determine a third parameter; Step 1.4: The current transaction receiver sends the first parameter and the second parameter to the current transaction sender; the current transaction sender sends the third parameter to the current transaction receiver; Step 1.5: The current transaction recipient calculates the shared transaction key using the first random number, the second random number, and the received third parameter, and the current transaction sender calculates the third random number, the received first parameter, and the second parameter.

3. The method according to claim 2, characterized in that, The transaction key satisfies the following formula: in, For transaction keys, The first random number, The second random number, The third random number, , is the base point of the elliptic curve. It is a large prime number with more than 160 digits.

4. The method according to claim 1, characterized in that, In step 3, the encrypted historical transaction amount is processed using a ciphertext update algorithm to obtain the updated historical ciphertext, including: Step 3.1: Obtain the historical transaction key corresponding to the ciphertext of the historical transaction amount; based on the transaction key, set a ciphertext with a plaintext value of 0. The corresponding plaintext transaction key and target key; Step 3.2: Based on the historical transaction key, the plaintext transaction key, and the target key, generate a historical amount ciphertext update factor; based on the plaintext transaction key and the target key, generate a ciphertext update factor with a plaintext value of 0; Step 3.3: Based on the historical amount ciphertext update factor and the plaintext update factor of 0, perform a ciphertext update algorithm on the ciphertext of the historical transaction amount to obtain the updated historical ciphertext.

5. The method according to claim 4, characterized in that, The monetary ciphertext update factor satisfies the following formula: in, The ciphertext update factor for the amount. The second random number corresponding to the historical transaction key. The third random number corresponding to the historical transaction key; A random number corresponding to the target key. This is another random number corresponding to the target key. A random number for the plaintext transaction key. This is another random number for the plaintext transaction key; This indicates the order of the elliptic curve.

6. The method according to claim 4, characterized in that, The updated historical ciphertext satisfies the following formula: in, For the updated historical ciphertext, This is the encrypted data of historical transaction amounts. The ciphertext is the plaintext value of 0. , is the base point of the elliptic curve. The ciphertext update factor for historical amounts. The ciphertext update factor for historical amounts. It is a large prime number with more than 160 digits.

7. The method according to claim 1, characterized in that, The auxiliary ciphertext is auxiliary verification information used to verify the validity of the transaction; The verification information includes: range proof and balance proof; The range proof is used to allow miners to verify that the plaintext amount corresponding to the updated current transaction amount ciphertext is non-negative and within a preset reasonable range; the balance proof is used to allow miners to verify, through homomorphic addition and comparison operations, that the sum of all updated historical input amount ciphertexts is equal to the sum of all updated current output amount ciphertexts.

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