Matrix-Based Hashing for Brute Force Resistance
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Solution Overview
Problem
Existing hash functions are vulnerable to brute force attacks, particularly when used in distributed attack scenarios, and lack sufficient security measures to prevent collisions and reversibility.
Innovation Solution
A hashing technique that generates a hash from an input string by converting it into a 1 by N input vector, expanding it to an N by N input matrix, adding it to an integer matrix, and then using symbol-encoded vectors and matrices to produce a secure, irreversible, and collision-resistant hash.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional hash functions are used, then computation is efficient, but security against brute force attacks deteriorates
Solution Approach 1:
The patent divides the hashing process into multiple independent stages: converting input string to a 1xN input vector, expanding to an NxN input matrix, adding to an integer matrix, generating symbol-encoded vectors, and producing the final hash. This segmentation increases computational complexity and makes brute force attacks more difficult while maintaining structured efficiency.
Solution Approach 2:
The patent transforms the input from a one-dimensional string into a two-dimensional matrix structure (NxN input matrix), then processes it through multiple dimensional transformations including symbol encoding and matrix operations. This dimensional expansion increases the search space and makes reversal computationally infeasible.
2Reliability
If hash function output size is reduced, then storage efficiency improves, but collision resistance deteriorates
Solution Approach 1:
The patent embeds multiple processing layers within the hashing structure: the input vector is expanded into a matrix, which is then processed through symbol encoding, matrix operations, and multiple transformation stages. This nested structure maximizes the use of computational resources to generate a secure hash output.
Solution Approach 2:
The patent changes parameters dynamically during the hashing process, including the dimensionality of data structures (from 1xN vector to NxN matrix), the complexity of matrix operations, and the encoding schemes used. These parameter changes ensure collision resistance while managing output size efficiency.
3Reliability
If hashing is made irreversible, then security improves, but computational efficiency deteriorates
Solution Approach 1:
The patent performs preliminary transformations during the forward hashing process, including converting the input string to a standardized vector format, expanding to a matrix, and pre-computing intermediate results. These preliminary actions establish a structured foundation that enables efficient irreversible transformation in subsequent stages.
Solution Approach 2:
The patent replaces simple mechanical hashing operations with more complex mathematical transformations including matrix multiplication, symbol encoding, and multi-dimensional data manipulation. These substitutions increase irreversibility while maintaining computational efficiency through optimized algorithms.
Data Source
AI summary
Various examples are directed to systems and methods for hashing an input string. A hashing engine may generate a 1 by N input vector using the input string, where N is a constant number. The hashing engine may expand the input vector to an input matrix, the input matrix having a size of N by N. The hashing engine may access a first integer matrix having a size of N by N and add the first integer matrix and the input matrix to generate an intermediate matrix. The hashing engine may generate a symbol-encoded vector using the intermediate matrix. The hashing engine may also generate a first round output matrix using the symbol-encoded vector and the intermediate matrix and a hash for the input string that is based at least in part on the first round output matrix.