Blockchain Transaction Verification Using Homomorphic Encryption
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Solution Overview
Problem
Existing blockchain systems face inefficiencies in verifying multiple transactions sequentially, which can be time-consuming and resource-intensive, particularly in time-sensitive tasks, due to the need for sequential verification of range proofs associated with account balances.
Innovation Solution
Implementing non-interactive privacy-preserving verification methods using commitment schemes and homomorphic encryption, allowing blockchain nodes to validate multiple transactions in parallel without revealing transaction amounts or random numbers, enabling zero-knowledge proofs for transaction validation without interaction between nodes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If sequential verification of range proofs is used to ensure transaction validity, then measurement precision of transaction validity is improved, but productivity of transaction verification deteriorates
Solution Approach 1:
The verification process is segmented into independent parallel tasks. Instead of verifying range proofs sequentially for each transaction, the system divides the verification into separate computational threads that can execute simultaneously, each handling different aspects of transaction validation independently while maintaining cryptographic security guarantees
Solution Approach 2:
Range proofs and commitment schemes are prepared in advance during transaction creation. The proofs are pre-computed and structured so that verification can be performed efficiently in parallel without requiring sequential processing, allowing multiple transactions to be validated simultaneously while maintaining cryptographic correctness
2Reliability
If commitment schemes with random numbers are used to hide transaction amounts, then security of transaction data is improved, but device complexity of managing random numbers worsens
Solution Approach 1:
A trusted execution environment or secure enclave acts as an intermediary for generating and managing random numbers. This specialized hardware component handles the complex random number generation and commitment scheme operations, shielding the main system from the complexity while ensuring cryptographic security and preventing random number leakage
Solution Approach 2:
Instead of managing complex random number states across multiple transactions, the system uses replicated commitment structures where each transaction has its own independent commitment instance. This copying approach simplifies management by making each commitment self-contained while maintaining the privacy guarantees through cryptographic equivalence
3Measurement precision
If interaction between blockchain nodes is required for verification, then measurement precision of verification accuracy is improved, but loss of time for verification worsens
Solution Approach 1:
All verification data including range proofs, commitment schemes, and cryptographic evidence are prepared and included in the transaction package before submission. This preliminary preparation eliminates the need for interactive verification exchanges between nodes, as all necessary information is already present for independent parallel verification
Solution Approach 2:
The transaction structure is designed to be self-verifying, with all necessary cryptographic proofs and commitment data embedded within the transaction itself. Blockchain nodes can independently verify transactions without requiring interaction with other nodes, enabling parallel verification while maintaining verification accuracy through cryptographic self-containment
Data Source
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AI summary
Implementations of the specification include receiving transaction data associated with the transaction, the transaction data comprising: data representative of a plurality of assets, a first commitment that hides a first random number and a transaction amount of the transaction, a second commitment that hides a second random number and a change, the transaction amount and a third random number both encrypted by a public key of the second node based on a probabilistic homomorphic encryption (HE) scheme, the change and a fourth random number both encrypted by a public key of the first node based on the probabilistic HE scheme, and a zero-knowledge proof (ZKP); determining, based on the ZKP, whether the transaction is valid based on determining if the first random number is equal to the third random number, the second random number is equal to the fourth random number, and the transaction amount hidden in the first commitment is equal to the transaction amount encrypted by the public key of the second node.