RSA Lookup Arguments for Composite Numbers and Duplicate Entries
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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 blockchain and cloud systems.
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 verification of index values is enabled, but the method is limited to prime numbers only and cannot handle composite numbers
Solution Approach 1:
The patent introduces an intermediary conversion process that transforms composite numbers into prime numbers through concatenation with random values followed by prime verification. This intermediary step allows the RSA accumulator method (which requires prime numbers) to handle composite number inputs while maintaining mathematical correctness.
Solution Approach 2:
The patent changes the parameter type by converting composite number parameters into prime number parameters through a systematic transformation process. This parameter change enables the use of RSA accumulator-based proofs which are mathematically defined for prime numbers only.
2Adaptability or versatility
If RSA accumulator-based proof of membership method is used, then lookup argument is enabled, but duplicate elements cannot be processed
Solution Approach 1:
The patent performs preliminary deduplication processing on the index vector before applying the RSA accumulator-based lookup argument. By removing duplicate elements in advance, the system simplifies the subsequent proof verification process while maintaining the ability to handle the original data set.
Solution Approach 2:
The patent extracts and removes duplicate elements from the index vector, keeping only unique elements for the lookup argument process. This extraction of problematic duplicate elements allows the RSA accumulator method to function correctly without modification.
3Adaptability or versatility
If conversion of composite numbers to prime numbers is performed, then applicability to composite number tables is enabled, but additional processing steps are required
Solution Approach 1:
The conversion of composite numbers to prime numbers is performed in advance during a setup phase, separate from the actual proof verification process. This preliminary action allows the transformation to be cached or pre-computed, minimizing its impact on the speed of subsequent lookup arguments.
Solution Approach 2:
The patent segments the overall process into distinct phases: a setup phase where composite-to-prime conversion occurs, and a verification phase where lookup arguments are performed. This segmentation allows the computationally intensive conversion to be separated from the faster verification operations.
Data Source
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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.