Secret Sharing System Using Subset Segmentation and Polynomial Interpolation
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Solution Overview
Problem
Existing secret sharing schemes face difficulties in implementing a secure system where share management apparatuses perform independent calculations using different values, leading to issues in reconstruction processing and security concerns due to shared values.
Innovation Solution
A secret sharing system where share management apparatuses within subsets perform common calculations using shared common information, ensuring high security by not sharing values across all apparatuses, and independently secret-sharing basis vectors to generate share secret values.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If share management apparatuses perform independent calculations using different values, then security is improved, but reconstruction processing cannot be properly performed
Solution Approach 1:
The patent divides the share management apparatuses into multiple subsets, where each subset shares common information only within that subset. This segmentation allows independent calculations within each subset while maintaining the ability to reconstruct secrets through polynomial interpolation across subsets, resolving the contradiction between security through independence and reconstructability.
Solution Approach 2:
The patent introduces share information as an intermediary that is distributed to multiple subsets. Each subset uses this share information along with their own common information to perform independent calculations, yet the share information acts as a mediator that enables reconstruction processing by providing a common reference point across all subsets.
2Ease of operation
If a single common value is shared across all share management apparatuses, then reconstruction processing is simplified, but security is compromised
Solution Approach 1:
The patent segments the common information into multiple subset-specific common values (first common information, second common information, etc.). Each subset uses its own common information independently, eliminating the security risk of a single shared value while maintaining reconstruction capability through the structured relationship between subset common informations and share information.
Solution Approach 2:
The patent applies local quality by giving each subset its own specific common information tailored to that subset's needs. This allows each subset to perform calculations with locally optimized parameters while the overall system maintains security through the distributed nature of these local common informations, rather than relying on a single global common value.
3Ease of operation
If linear calculation is performed on share information, then reconstruction is straightforward, but the result leaks information about the secret
Solution Approach 1:
The patent changes the parameters of the calculation by introducing non-linear operations through polynomial evaluation and interpolation. Instead of simple linear calculations on share information, the system uses polynomial functions where the shares are evaluations of a secret polynomial at different points. This non-linear transformation maintains reconstructability through polynomial interpolation while preventing information leakage about the secret from linear relationships.
Data Source
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Figure 3A~3B
AI summary
A sharing apparatus independently shares a value corresponding to each element θ(ψ, i, β) · g2 of basis vectors bi*(θ) among each subset SUB(α) consisting of H(α) share management apparatuses PA(α, 1), ..., PA(α, H(α)) to generate share information SH(ψ, i, β, α, h(α)) corresponding to each element θ(ψ, i, β) · g2. The share management apparatus PA(α, h(α)) generates a share secret value DSH(ψ, α, h(α)) by performing a common calculation common in the subset SUB(α) on common information shared in the subset SUB(α) and the share information SH(ψ, i, β, α, h(α)). An acquisition apparatus generates reconstructed secret values SUBSK(ψ, α) for each subset SUB(α) by performing a reconstruction processing for the subset SUB(α) and generates generation information D*(ψ) from the reconstructed secret values SUBSK(ψ, α).