Multiplier Matrix Data Transform for Secure Compression
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Solution Overview
Problem
Current encryption and compression methods for data blocks do not effectively balance encryption for security and compression efficiency, particularly in transforming data to minimize aggregate energy for better compression ratios during storage and transmission.
Innovation Solution
A method and system that utilize a multiplier matrix with diagonally arranged binomial sub-matrices, represented as products of lower, upper factorized matrices, and shift matrices, to transform and encrypt data blocks, generating modified data with reduced aggregate energy for improved compression efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional encryption methods are applied to data blocks, then data security is improved, but compression ratio deteriorates
Solution Approach 1:
The patent applies preliminary action by transforming the data block with a multiplier matrix before encryption is applied. This preprocessing step modifies the data structure to have reduced aggregate energy and improved statistical properties, which enables better compression ratios while maintaining security. The transformation is performed in advance so that subsequent encryption and compression operations work more efficiently on the transformed data.
Solution Approach 2:
The patent employs parameter changes by using a specific multiplier matrix with particular mathematical properties (binomial coefficients arranged in a matrix structure) to transform the data. This changes the statistical parameters of the data, such as its energy distribution and entropy characteristics, making it more amenable to compression algorithms while preserving the security requirements through the reversible nature of the transformation.
2Reliability
If data is encrypted before compression, then security is maintained, but compression efficiency decreases
Solution Approach 1:
The patent reverses the conventional order by performing the multiplier matrix transformation before encryption and compression operations. This preliminary transformation prepares the data in a state that is more efficient for subsequent compression, reducing the computational energy required while maintaining security through the encrypted nature of the final output.
Solution Approach 2:
The patent substitutes the traditional mechanical approach of encrypting then compressing with a transformed approach where mathematical transformation precedes the standard operations. This substitution of the processing sequence reduces the energy expenditure required for compression while maintaining the same security level.
3Productivity
If aggregate energy of transformed data is minimized, then compression ratio is improved, but transformation complexity increases
Solution Approach 1:
The patent segments the transformation process into a structured multiplier matrix operation with specific mathematical properties. By dividing the transformation into discrete matrix multiplication steps with predetermined coefficients, the complexity is made manageable and systematic rather than arbitrary, enabling implementation while achieving reduced aggregate energy for better compression.
Solution Approach 2:
The patent uses specific parameter choices in the multiplier matrix (based on binomial coefficients) that optimize the balance between transformation complexity and compression efficiency. These parameter selections reduce the aggregate energy of the transformed data while keeping the transformation itself relatively simple through the mathematical properties of the chosen parameters.
Data Source
AI summary
A system and method to transform a block of data is disclosed. A block of original data is retrieved from a data store, block of original data including a N number of words, each word including one or more bits of data. A multiplier matrix is provided, the multiplier matrix having N×N words, a plurality of sub matrices arranged diagonally within the N×N matrix, with each of the sub matrix arranged as a binomial matrix. All the words in the multiplier matrix not part of the sub matrix are set to zero. Each of the sub matrix is represented as a product of a plurality of lower factorized matrix, a plurality of upper factorized matrix and a shift matrix. The block of original data is multiplied with the multiplier matrix to generate a transformed block of original data with N number of words.