Parametric Search Tree Pruning Under Fully Homomorphic Encryption
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Fully homomorphic encryption introduces significant computational burdens and complexity, making parametric searching on encrypted data slow and difficult to parallelize, especially in large datasets or complex systems.
Innovation Solution
A computer-implemented method for identifying a leaf in a tree using parametric searching with fully homomorphic encrypted data, where each node represents a subset of points with a bounding simplex, and a processor set traverses the tree to identify the nearest point by generating parameters and selecting subsets of child nodes based on ranges, repeating steps until the leaf is found.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fully homomorphic encryption is applied to parametric searching, then data security is improved, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent segments the parametric searching process into discrete tree traversal steps, where each node evaluation is independently encrypted and processed. The search space is divided into hierarchical levels, allowing incremental processing of encrypted data without requiring full decryption at each step, thereby reducing overall computational complexity while maintaining security.
Solution Approach 2:
The patent performs preliminary encryption of the dataset and tree structure before the searching operation begins. Homomorphic encryption keys are pre-generated and the data is pre-processed into encrypted form, allowing the parametric search to proceed directly on encrypted data without repeated encryption operations during the search itself, reducing real-time computational burden.
2Reliability
If fully homomorphic encryption is used for parametric searching, then data privacy is protected, but processing speed decreases
Solution Approach 1:
The search process is segmented into parallelizable tree traversal operations where multiple nodes at the same level can be evaluated simultaneously. Each node's encrypted bounding simplex parameters are processed independently, enabling parallel computation that offsets the inherent slowness of homomorphic encryption operations and improves overall processing speed.
Solution Approach 2:
The patent evaluates only the necessary subset of tree nodes required to find the nearest point, rather than traversing the entire tree. By using the encrypted parametric search to prune branches that cannot contain the nearest point, the system performs partial action on the data structure, significantly reducing the number of expensive homomorphic operations required.
3Reliability
If parametric searching is performed on encrypted data, then security is maintained, but the ability to parallelize computations is reduced
Solution Approach 1:
The patent structures the encrypted parametric search as a hierarchical tree traversal where levels can be processed in parallel. Each node contains encrypted information about its bounding simplex, allowing independent evaluation of multiple nodes at the same depth level without requiring sequential decryption, thus restoring parallelization capability while maintaining security.
Solution Approach 2:
The patent introduces encrypted parametric representations (bounding simplexes) as intermediaries that carry spatial information in encrypted form. These intermediaries enable comparison and filtering operations between encrypted data points without requiring direct decryption, allowing parallel processing of multiple candidates while preserving security through the intermediary encrypted structures.
Data Source
AI summary
A computer-implemented method for identifying a leaf in a tree is provided. A processor set receives a first point representing one or more values within a d-dimensional space for identifying the leaf in the tree. The processor set generates a parameter for identifying the leaf in the tree. The processor set identifies a node at highest depth of the tree. The processor set determines a first value of the parameter for generating a range. The processor set selects a subset of child nodes from the number of child nodes associated with the node at the highest depth of the tree based on the range. The processor sets the subset of child nodes as the node at the highest depth of the tree. The processor set traverses the tree by repeating the identifying step, the determining step, the selecting step, and setting steps until the leaf in the tree is identified.