Biometric Key Generation Using Sphere Packing in High Dimensions
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Solution Overview
Problem
Existing biometric encryption methods based on Euclidean distance in high-dimensional spaces suffer from a rapid drop in authentication precision, making them impractical for real-world applications.
Innovation Solution
A key generation apparatus that utilizes sphere packing and sphere covering arrangements with specific densities to generate and restore keys from biometric information, ensuring high precision authentication by selecting points within these arrangements and applying conversion processes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional biometric encryption methods based on Euclidean distance are used in high-dimensional spaces, then the system can process biometric information, but authentication precision rapidly drops exponentially with increasing dimension order
Solution Approach 1:
The patent transforms the authentication approach by changing the distance metric parameter from conventional Euclidean distance to Mahalanobis distance. This parameter change allows the system to account for correlations between different feature dimensions, effectively normalizing the distance measurement in high-dimensional space and preventing the exponential precision drop that occurs with Euclidean distance.
Solution Approach 2:
The patent employs a composite approach by combining multiple technical elements: Mahalanobis distance calculation, feature vector transformation, and a specialized authentication algorithm. This composite methodology integrates statistical analysis (covariance matrix computation) with geometric distance measurement to create a robust authentication system that maintains precision in high-dimensional spaces.
2Measurement precision
If feature data is expressed as vectors in high-dimensional Euclidean space with Euclidean distance, then proximity can be measured, but the methods become inapplicable when using certain distance metrics like Mahalanobis distance
Solution Approach 1:
The patent generalizes the distance measurement by introducing Mahalanobis distance as an alternative to Euclidean distance. This involves changing the metric parameter to include the inverse covariance matrix, allowing the system to adapt to correlated features and non-uniform distributions while maintaining the vector-based representation of biometric data.
Solution Approach 2:
The patent segments the authentication process into distinct computational stages: covariance matrix calculation, feature vector transformation using the covariance information, and distance computation. This segmentation allows the system to handle different distance metrics systematically and makes the methodology adaptable to various statistical models.
3Ease of operation
If triangular lattice is used for biometric encryption based on Euclidean distance, then authentication can be performed, but precision drops exponentially with dimension increase making it impractical
Solution Approach 1:
The patent replaces the triangular lattice structure with a methodology based on Mahalanobis distance in high-dimensional space. This parameter change involves transitioning from a fixed geometric lattice to a statistically-adaptive distance metric that accounts for feature correlations, thereby maintaining authentication capability while preventing precision degradation in high dimensions.
Solution Approach 2:
The patent substitutes the mechanical/geometric approach of triangular lattice with a statistical approach using Mahalanobis distance. This replacement involves using covariance-based transformations and statistical distance metrics instead of fixed geometric structures, enabling the system to adapt to the actual distribution of biometric data in high-dimensional space.
Data Source
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AI summary
A key generation apparatus for accomplishing high precision authentication in biometric encryption and biometric signing based on feature vectors in a high-dimensional Euclidean space, the apparatus: holds a first feature vector indicating a feature of first biometric information, and a parameter for identifying one arrangement out of a sphere packing arrangement with a density less than 1 and more than a predetermined value, or a sphere covering arrangement with a density equal to or more than 1 and less than a predetermined value, identifies one arrangement out of the sphere packing arrangement or the sphere covering arrangement based on the parameter; selects a first point included in the identified one arrangement; generates a first key by predetermined first conversion on the first point; and generates, based on the first feature vector and the first point, a template associated with the first biometric information.