Secret Sharing Method Using XOR and Random Data Combinations
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Solution Overview
Problem
Existing secret sharing methods using XOR operations lack flexibility, allowing third parties to easily reconstruct secret data when they possess more shared data parts than the threshold value, and require significant computational load for polynomial computations.
Innovation Solution
A secret sharing method that allows users to freely incorporate desired algorithms and reduces computational load by creating shared data parts from different combinations of secret and random number data pieces, making it difficult for third parties to reconstruct the secret data even with more shared parts than the threshold value.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polynomial interpolation method is used for secret sharing, then security of secret data is ensured, but computational load increases significantly
Solution Approach 1:
The secret data is divided into multiple shared data parts, where each part contains only a portion of the information needed to reconstruct the secret. This segmentation ensures that no single shared data part reveals the complete secret, maintaining security while allowing for simpler individual computations on each segment.
Solution Approach 2:
Instead of using complex polynomial interpolation to create shares, the invention inverts the approach by using simple XOR operations combined with random number generation. The security is achieved not through computational complexity of the sharing algorithm, but through the information-theoretic security of having insufficient shares below the threshold.
2Productivity
If XOR operation is used for secret sharing, then computational speed increases, but flexibility decreases and security is compromised when more than threshold shares are obtained
Solution Approach 1:
Random number data is generated and incorporated into the shared data parts during the secret sharing process, before any potential reconstruction attempts. This preliminary incorporation of random data ensures that even if an attacker obtains more than the threshold number of shares, they cannot easily reconstruct the secret without the corresponding random number data that was used in the sharing process.
Solution Approach 2:
The invention introduces random number data as an intermediary element that mediates between the secret data and the shared data parts. This random number data acts as an additional layer of protection, ensuring that the relationship between shares and secret remains computationally infeasible to reverse, even when the threshold number of shares is exceeded.
3Ease of operation
If fixed algorithm is used in threshold scheme, then reconstruction is straightforward when threshold shares are obtained, but adaptability to different user requirements decreases
Solution Approach 1:
The invention makes the secret sharing system dynamic by allowing users to select from multiple different algorithms for creating shared data parts. Instead of a fixed algorithm, the system can adapt to user preferences and requirements by choosing from XOR-based methods, polynomial interpolation, or other custom algorithms, while maintaining the core threshold security properties.
Data Source
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AI summary
In a secret sharing process based on an improved threshold scheme, secret data is shared as shared data parts equal to or greater than a threshold value in number such that the secret data cannot be reconstructed from shared data parts less than the threshold value in number. Each of the shared data pieces is created essentially from a different combination of the secret data pieces and the data pieces for secret sharing computation. The secret sharing process allows an algorithm desired by the user to be freely incorporated, and can prevent the secret data to be easily reconstructed even when more shared data parts than the threshold value are acquired by a third party.