RSA Accumulator Lookup Argument for Composite Numbers and Duplicates
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Solution Overview
Problem
Existing RSA accumulator-based proof of membership methods are limited to prime numbers and cannot handle duplicate elements, restricting their application in systems requiring privacy verification.
Innovation Solution
A method that converts composite numbers into prime numbers using concatenation operations and generates a prime number table vector, allowing for RSA accumulator-based lookup arguments to handle duplicates by replacing and processing them within a zero-knowledge proof framework.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If RSA accumulator-based proof of membership method is used, then privacy verification is enabled, but it is limited to prime numbers only and cannot handle duplicate elements
Solution Approach 1:
The patent applies preliminary action by performing concatenation operations during the setup phase to pre-convert composite numbers into prime numbers. This preparation is done before the actual proof generation, so that when proofs are generated later, the system can directly use prime number properties without additional conversion overhead. The prime number table is pre-computed and stored, enabling efficient lookup and proof generation for composite number systems.
Solution Approach 2:
The patent introduces an intermediary mechanism by using a prime number table as a mapping layer between composite number systems and prime number-based RSA accumulators. The concatenation operation acts as an intermediary transformation that maps composite numbers to corresponding prime numbers, allowing the system to leverage prime number properties while maintaining compatibility with composite number inputs. This intermediary layer resolves the contradiction by bridging the gap between composite number requirements and prime number constraints.
2Adaptability or versatility
If prime number conversion is performed using concatenation operations, then composite numbers can be processed, but additional processing steps are required
Solution Approach 1:
The conversion of composite numbers to prime numbers through concatenation operations is performed in advance during the setup phase, before any proof generation occurs. The prime number table is pre-computed and cached, so that during actual proof generation, the system only needs to perform lookups rather than conversions. This eliminates conversion time from the critical proof generation path, resolving the time loss issue while maintaining adaptability to composite numbers.
Solution Approach 2:
The system dynamically adapts its processing based on whether numbers are already prime or composite. During setup, composite numbers are converted to prime numbers and stored in a prime number table. During proof generation, the system dynamically looks up pre-converted prime numbers rather than performing conversions. This dynamic behavior optimizes performance by performing heavy conversion work only when necessary (during setup) and using efficient lookups during operational phases.
3Adaptability or versatility
If duplicated elements are processed by replacing with prime number table values, then duplicates can be handled, but modification of index values is required
Solution Approach 1:
The patent applies copying by replacing duplicate index values with corresponding values from the pre-computed prime number table. Instead of attempting to process duplicates directly, the system creates copies of prime number table entries and uses these copies in place of duplicate indices. This copying mechanism allows the RSA accumulator to handle duplicate elements by treating them as separate prime number instances, thereby enabling duplicate handling without modifying the fundamental proof structure.
4Reliability
If zero-knowledge proof is performed on concatenation results, then privacy is maintained, but additional proof generation steps are needed
Solution Approach 1:
Zero-knowledge proofs are performed in advance during the setup phase to verify the correctness of prime number conversions and table generation. By performing these verification proofs beforehand, the system ensures reliability and accuracy of the prime number table without requiring additional verification proofs during operational proof generation. The pre-generated proofs serve as cryptographic certificates that the table is correct, eliminating the need for repeated verification and reducing time loss during actual use.
Data Source
AI summary
The technical concept of the present invention relates to an RSA accumulator-based lookup argument method for performing lookup argument on a composite number and duplicated element. According to an embodiment of the present disclosure, RSA accumulator-based lookup argument method performed by at least one processor may include obtaining a table vector including a plurality of table values, generating a plurality of prime number random values, generating a plurality of prime number table values respectively corresponding to the plurality of table values by using the plurality of prime number random values, generating a prime number table vector by using the plurality of prime number table values and the plurality of prime number random values, publishing the prime number table vector, and performing RSA accumulator-based lookup argument by using the prime number table vector to check whether an index value is included in the table vector.