XOR Secret Sharing Encoding for Low-Storage Secure Reconstruction
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Solution Overview
Problem
Existing secret sharing methods require significant storage space and computational power due to the aggregated size of secret shares being 'n' times the secret size, and rely on polynomials for encoding and decoding.
Innovation Solution
Utilize exclusive OR (XOR) operations to generate and decode secret shares using a tetrahedron code model, minimizing storage needs and computational requirements by ensuring the collective size of all shares is only slightly larger than the secret itself.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If polynomial-based secret sharing methods are used, then security and secret distribution are achieved, but storage space and computational power requirements increase significantly
Solution Approach 1:
The patent changes the mathematical operation parameter from polynomial arithmetic to XOR operations. This parameter change reduces the storage space requirement from n times the secret size to a minimal increase over the original secret size, while maintaining security through the cryptographic properties of XOR operations in the tetrahedron code model
2Reliability
If polynomial-based secret sharing methods are used, then security and secret distribution are achieved, but computational power requirements increase significantly
Solution Approach 1:
The patent changes the computational operation from complex polynomial arithmetic to simple XOR operations. This parameter change dramatically reduces computational power requirements and energy consumption, as XOR operations are computationally lightweight compared to polynomial evaluation and interpolation, while still providing secure secret sharing through the tetrahedron code structure
Solution Approach 2:
The patent uses disposable, computationally inexpensive XOR operations instead of expensive polynomial computations. Each XOR operation is a simple, fast, and energy-efficient operation that can be performed repeatedly without significant computational cost, making the secret sharing process more scalable and accessible
3Ease of operation
If traditional secret sharing encoding is used, then secret distribution is achieved, but the aggregated size of secret shares becomes n times the secret size
Solution Approach 1:
The patent segments the secret into multiple parts and distributes them through XOR operations in a tetrahedron code model. This segmentation allows the secret to be split into shares that, when aggregated, occupy minimal space compared to traditional methods, as each share contains only the necessary XOR-ed portions rather than full polynomial representations
Solution Approach 2:
The patent implements a nested structure where secret segments are embedded within shares through XOR operations. The shares are constructed by nesting XOR combinations of secret segments, allowing efficient storage where the total share size is only slightly larger than the original secret, rather than n times the secret size as in traditional schemes
Data Source
AI summary
A system and method for a secret-sharing encoding and decoding using exclusive OR (XOR) operations. A first apparatus includes a data splitting circuit to receive a secret and generate first, second, third, and fourth secret segments based on the secret and a secret share encoding circuit to generate first, second, third, and fourth secret shares by application of XOR operations to the first, second, third, and fourth secret segments. A second apparatus includes a secret share decoding circuit to receive first, second, third, and fourth secret shares and generate first, second, third, and fourth secret segments by application of an XOR operation to share encoded data of the first, second, third, and fourth secret shares, and a data aggregating circuit to: receive the first, second, third, and fourth secret segments; and recreate a secret by combining the first, second, third, and fourth secret segments.