Implementation of Ring Signatures in Blockchain Transactions

Short Answer Questions

Briefly describe the meaning of Confidential Transaction and its role in blockchain.

Why does the traditional ring signature scheme have the "double-spending" problem when applied to blockchain transactions?

Explain the concept of "key mirror" and how it solves the "double-spending" problem of ring signatures in blockchain transactions?

How to use elliptic curve cryptography to generate and verify key mirrors?

In the proposed technical solution, how to hide the identity of the participants in the remittance transaction?

What role does the "fake remitter" play in the technical solution proposed in this patent?

In the proposed technical solution, how to ensure the validity of the transfer amount (for example, the amount is not less than 0)?

In the proposed account model, the relationship between "income balance", "main balance" and "assets".

In the process of verifying the linkable ring signature, what are the main verification operations that the verifier needs to perform?

What are the differences in account updates between the proposed technical solution and the traditional UTXO model?

Answers to short-answer questions

Confidential transactions are a privacy-protecting transaction scheme that hides sensitive information such as transaction amounts and account balances through commitment schemes, and only records the commitment value on the blockchain to prevent transaction information leakage and enhance privacy.

The traditional ring signature scheme can only hide the identity of the transaction initiator, and cannot determine whether the same funds are used multiple times, so it is easy to cause double-spending problems in blockchain transactions.

The key image is a unique value corresponding to each transaction, which is generated by the private key, public key and transaction information of the transaction initiator. By recording the key image in a historical key image set, it is possible to detect and prevent the same funds from being used for multiple transactions.

The hash function and scalar multiplication operation in elliptic curve cryptography are used to combine the private key, public key and asset identifier of the transaction initiator to generate a unique key image.

By introducing "false remitters" and "false recipients" and converting the transaction amounts of all participants into homomorphic ciphertexts, external observers cannot determine the real remitter and recipient.

"Fake remitters" refer to participants other than the real remitter, whose identities and asset information are used to confuse the identity of the real remitter and increase the anonymity of the transaction.

Using zero-knowledge proof technology, especially interval proof technology, such as Bulletproofs, a range proof is generated to prove that the transfer amount is not less than 0, and the proof is included in the transaction content.

"Income balance" is used to receive remitted funds, "main balance" is the main fund storage part of the account, and "assets" are generated by dividing the "main balance" for transaction transfers. The income balance can be regularly merged into the main balance.

The verifier needs to verify the ownership of the asset, the validity of the linkable ring signature, the validity of the range proof, and whether the key image already exists in the historical key image set.

Unlike the UTXO model, the real remitter's account will not be updated immediately after the transaction is completed in this patent, but the record of the assets that have been spent will be retained, and double spending is only prevented through the key image, which further enhances privacy.

Paper title

Compare and contrast the confidential transaction scheme proposed by the patent with other mainstream privacy-preserving transaction schemes (e.g., zero-knowledge proof, ring signature, Mimblewimble), and analyze their respective advantages and disadvantages.

Discuss the advantages and limitations of the account model proposed by the patent in practical applications, and compare and analyze it with the account model of Ethereum.

Analyze the potential risks and challenges of the technical scheme proposed by the patent in terms of security, privacy and efficiency, and propose corresponding improvement measures.

Study the application scenarios and applicability of the technical scheme proposed by the patent in different types of blockchain networks (e.g., public chain, alliance chain, private chain).

Combined with specific application cases, explore how the technical scheme proposed by the patent can be combined with other blockchain technologies (e.g., smart contracts, cross-chain technology) to achieve richer functions and applications.

Glossary

Term DefinitionsConfidential TransactionA privacy-preserving transaction scheme that hides information such as transaction amount through a commitment scheme. Ring SignatureA digital signature scheme that allows the signer to hide in a group of users without revealing his true identity. Key Image is a unique value generated by the private key, public key and transaction information of the transaction initiator, used to prevent double spending. Linkable Ring Signature is an improved ring signature scheme that allows the detection and prevention of multiple signatures generated by the same private key. Commitment Scheme is a cryptographic technique that allows users to commit to a value and prove that they know the value without revealing it. Pedersen Commitment is a homomorphic encryption commitment scheme with additive homomorphism, which can perform addition operations on committed values. Range Proof is a zero-knowledge proof technique used to prove that a value is within a specific range without revealing the specific information of the value. Bulletproofs is a short, non-interactive zero-knowledge proof system that can be used for range proof. UTXO (Unspent Transaction Output) is an unspent transaction output, a transaction model adopted by Bitcoin and its derivative cryptocurrencies. Homomorphic Encryption is an encryption technique that allows operations to be performed on encrypted data, and the result generated after decryption is the same as the result of the same operation on the plaintext. Elliptic Curve Cryptography is a public key cryptography system based on the mathematical theory of elliptic curves, which has the characteristics of short keys and high security.