Cheater-Identifiable Secret Sharing Verification via Subset Coherence
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Solution Overview
Problem
Current secret-sharing schemes fail to identify falsified shared information when the number of cheaters exceeds the range k≧3t+1, and they either increase data size or reduce the number of identifiable cheaters, making them inefficient.
Innovation Solution
A verification device using a (k, n) threshold secret-sharing scheme with polynomials of (k−1)th degree on a finite field GF(p) and t-Cheater Identifiable secret-sharing schemes with polynomials of the tth degree on GF(q), generating cheater identification information to identify up to t dishonest shares among n items, by selecting subsets of r items where r≧t+2, and using coherence-judging means to verify dishonest information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the number of cheaters t exceeds the range k≧3t+1, then the ability to identify falsified shares is lost, but increasing k to satisfy k≧3t+1 reduces system flexibility and increases data size
Solution Approach 1:
The patent segments the verification process into multiple rounds, where in each round a subset of shares is verified against a reconstructed secret. This allows progressive identification of cheaters without requiring all k shares to satisfy the strict k≧3t+1 condition simultaneously, thereby maintaining reliability while reducing parameter constraints.
Solution Approach 2:
The patent performs preliminary verification actions by reconstructing the secret from subsets of shares and checking consistency before final secret reconstruction. This preliminary checking identifies cheaters early in the process, preventing them from compromising the final reconstruction, thus maintaining reliability without requiring overly restrictive parameter conditions.
2Quantity of substance
If the data size of shared information is decreased, then storage efficiency improves, but the number of items of falsified shared information that can be identified decreases
Solution Approach 1:
The patent applies partial verification by checking subsets of shares rather than verifying all shares comprehensively. This allows the system to identify cheaters with smaller data sizes by performing verification on representative subsets, balancing storage efficiency with the ability to detect falsified shares.
Solution Approach 2:
The verification process is segmented into multiple rounds with each round verifying a portion of the shares. This segmentation allows the system to maintain cheater identification capability with reduced data size per share, as the collective verification across multiple rounds compensates for the reduced individual share size.
3Reliability
If the threshold k is increased to satisfy k≧2t+2 for better cheater identification, then the number of identifiable cheaters increases, but the requirement for shared information items n increases
Solution Approach 1:
The patent implements dynamic verification where the effective threshold k varies across different verification rounds. In each round, a dynamic subset of shares is selected for verification, allowing the system to adaptively identify cheaters without requiring a permanently high fixed threshold, thus improving cheater identification while reducing the total number of required shared information items.
Data Source
AI summary
A verification device, upon the input of any k items of shared information among n items of shared information and “t”: generates as subsets all combinations that select r items of shared information among the k items of shared information received as input where r satisfies r≧t+2; for each of the subsets, uses the cheater-identification information belonging to the subset to judge whether dishonest shared information is included in the subset; and based on the judgment results, generates and supplies as output a cheater set indicating dishonest shared information among the k items of shared information.