Recoverable Data Transformation with Galois Field Redundancy
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Solution Overview
Problem
Existing data processing systems lack effective methods for transforming plaintext data into redundant forms that provide protection and recovery capabilities, especially in scenarios where data loss occurs, and they often fail to protect data from unauthorized access.
Innovation Solution
The system employs Galois field operations and a generator matrix to transform input data into multiple output data streams, ensuring that the original data can be recovered from any subset of the output streams, while maintaining confidentiality by not storing plaintext directly.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If plaintext data is stored and handled in a readily accessible manner, then ease of operation is improved, but data security deteriorates as plaintext is exposed to unauthorized access
Solution Approach 1:
The patent segments plaintext data into multiple data streams through transformation, where no single stream contains the complete original data. This segmentation allows the data to be distributed and stored across multiple locations, improving accessibility while preventing unauthorized access since reconstructing the original data requires collecting and processing multiple streams simultaneously.
Solution Approach 2:
The patent introduces transformed data streams as intermediaries between the original plaintext and its storage locations. These intermediary streams undergo mathematical transformation (e.g., using Galois field operations) that obscures the original data, allowing safe distribution and storage while maintaining the ability to reconstruct the original data through the inverse transformation process.
2Reliability
If data is transformed into redundant forms for recovery capability, then reliability is improved, but device complexity increases due to transformation processes
Solution Approach 1:
The patent applies parameter changes by using mathematical transformations (such as Galois field operations and matrix multiplication) to convert plaintext data into transformed data streams. These transformations modify the data representation while preserving the ability to reconstruct the original data, achieving redundancy and recovery capability through systematic parameter modification rather than complex physical mechanisms.
Solution Approach 2:
The patent replaces complex mechanical or procedural recovery mechanisms with mathematical transformations. By using algebraic operations (such as matrix inversion or Galois field arithmetic) to reconstruct data, the system achieves reliable data recovery without requiring complex mechanical systems, physical media manipulation, or intricate procedural steps.
3Reliability
If additional output data streams are generated from input data, then data redundancy is improved for loss recovery, but loss of substance increases due to additional data generation
Solution Approach 1:
The patent applies partial action by generating exactly the number of redundant data streams needed for recovery (H-W streams where H is total streams and W is minimum required streams). This avoids generating excessive redundancy while ensuring that any W streams can reconstruct the original data, optimizing the balance between recovery capability and storage overhead.
Solution Approach 2:
The patent uses mathematical transformations to generate redundant data streams that are efficiently related to the original data through parameter changes (such as linear combinations using Galois field arithmetic). This allows the system to create H output streams from W input streams with controlled overhead, where the redundant streams contain just enough information for recovery without duplicating all original data.
Data Source
AI summary
Systems and methods are disclosed for processing data. In one exemplary implementation, there is provided a method of generating H output data from W data input streams produced from input data. Moreover, the method may include generating the H discrete output data components via application of the W data inputs to one or more transforming components or processes having specified mathematic operations and/or a generator matrix functionality, wherein the W data inputs are recoverable via a recovery process capable of reproducing the W data inputs from a subset (any W members) of the H output data streams. Further exemplary implementations may comprise a transformation process that includes producing an H-sized intermediary for each of the W inputs, combining the H-sized intermediaries into an H-sized result, and processing the H-sized result into the H output data structures, groups or streams.