Secret Sharing Device Using Matrix Operations
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Solution Overview
Problem
The Shamir (k, n) threshold scheme requires high computational power due to polynomial interpolation, and existing methods like Fujii and Kurihara's schemes are limited to threshold k values of 2 or 3, restricting their applicability.
Innovation Solution
A secret sharing system that uses a generator matrix G of size k(n-1) x n(n-1) to distribute and recover secret information without polynomial interpolation, allowing for any threshold k value between 2 and n, using a recursive process to create recovery matrices from shared information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If polynomial interpolation is used for secret sharing, then the threshold scheme can work for any k value, but the computational complexity increases significantly
Solution Approach 1:
The patent divides the secret information into multiple blocks and processes each block separately through matrix operations. The generator matrix G is constructed in a segmented manner where different blocks can be processed independently, reducing the overall computational complexity while maintaining support for any threshold k value.
Solution Approach 2:
The patent replaces the polynomial interpolation mechanism with a linear algebra-based matrix operation system. Instead of using polynomial fields and interpolation formulas, the invention uses generator matrices and vector spaces over finite fields, substituting a computationally heavier mathematical mechanism with a more efficient linear algebra approach.
2Productivity
If Fujii method or Kurihara method is used, then the computational speed increases, but the threshold k is restricted to 2 or 3
Solution Approach 1:
The patent creates a universal secret sharing system that can handle any threshold k value (2 ≤ k ≤ n) using the same matrix operation framework. The generator matrix G is designed with a structure that adapts to different k values without requiring fundamentally different algorithms, making the system multi-functional across various threshold requirements.
Solution Approach 2:
The patent changes the parameter k (threshold value) by modifying the structure of the generator matrix G rather than changing the underlying algorithm. The matrix dimensions and construction method are parameterized to accommodate different k values, allowing the same computational approach to work universally across different threshold requirements.
3Reliability
If Shamir (k, n) threshold scheme is used, then secret information can be recovered from any k items, but high-speed computer is required
Solution Approach 1:
The patent uses simple XOR operations and basic matrix multiplications that can be implemented with minimal computational resources. Instead of requiring complex polynomial arithmetic that demands high-speed computers, the invention employs operations that can be performed efficiently on low-grade devices, effectively replacing expensive computational resources with simpler, more accessible hardware.
Data Source
AI summary
A secret sharing device of (k, n) threshold scheme creates a generator matrix G, first divided secret data, and random number data, calculates shared partial data based on the product of matrices with the random number data, the divided secret data, and the generator matrix G, and delivers the shared information formed by the shared partial data and the header information individually to the storage units. The secret sharing device calculates a recovery matrix and multiplies the shared information by the recovery matrix, hence to recover the secret information.