Homomorphic Encryption Distance Analytics via Finite Decryption Table
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Solution Overview
Problem
Conventional 2DNF homomorphic encryption schemes have inefficient decryption algorithms, limiting their use in distance-based operations due to slow decryption and the need for small decryption tables that restrict the domain of encrypted values.
Innovation Solution
Generating multiple versions of a data point in different Euclidean spaces, encrypting them, and storing across multiple databases using a finite decryption table for distance-based operations, allowing for efficient computation of distance-based analytics like k-nearest neighbors and k-means clustering.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional 2DNF homomorphic encryption schemes are used, then data can be encrypted and processed, but decryption is slow and inefficient
Solution Approach 1:
The patent pre-computes and stores decryption results in a decryption table during an offline phase. When a decryption request occurs, the system performs a quick table lookup instead of executing the slow decryption algorithm in real-time. This preliminary preparation resolves the contradiction by making decryption fast (improving productivity) while maintaining security through the homomorphic encryption scheme (preserving reliability).
Solution Approach 2:
The patent uses a finite decryption table that covers only a subset of all possible encrypted values rather than computing all possible decryptions. This partial approach is sufficient for distance-based operations where only relative comparisons are needed, not absolute decryption of all values. It improves decryption speed by limiting the table size while still achieving the operational goal.
2Productivity
If a decryption table is used to speed up decryption, then decryption speed improves, but the decryption domain is limited to a small sub-set of encrypted values
Solution Approach 1:
The patent transforms the problem from decrypting individual values to comparing relative distances between encrypted values. Instead of extending the decryption table to cover all possible values (which would require exponential space), the system operates in the distance domain where only relative differences matter. This dimensional shift allows the finite table to handle a much broader range of practical scenarios.
Solution Approach 2:
The patent changes the operational parameter from absolute value decryption to relative distance computation. By working with encrypted distance metrics rather than attempting to decrypt all possible value combinations, the system achieves both fast decryption (through the finite table) and broad applicability (to any distance-based operation). The parameter change from 'value domain' to 'distance domain' resolves the contradiction.
3Productivity
If multiple versions of data points are generated and stored across multiple databases, then distance-based operations become efficient, but storage complexity increases
Solution Approach 1:
The patent segments the data storage into multiple specialized databases, each handling specific aspects of the data (e.g., different Euclidean spaces, different data point versions). This segmentation allows each database to be optimized for its specific purpose and enables parallel processing of distance-based operations. The complexity is managed by creating modular, independent storage units rather than a monolithic complex system.
Solution Approach 2:
The patent creates multiple copies of data points in different representations (different Euclidean spaces, different encryptions) and stores them across multiple databases. These copies enable efficient distance-based operations without requiring complex real-time transformations. The copying approach simplifies the storage mechanism by using redundant but specialized representations rather than a single complex structure.
Data Source
AI summary
Methods, systems, and computer program products for enabling distance-based algorithms on data encrypted using a 2DNF homomorphic encryption scheme with inefficient decryption are provided herein. A computer-implemented method includes generating multiple versions of a data point, wherein each of the multiple versions of the data point comprises a distinct value corresponding to a distinct Euclidean space; encrypting each of the multiple versions of the data point; storing the multiple encrypted versions of the data point across multiple databases; and executing one or more distance-based algorithms on the multiple encrypted versions of the data point by using a finite decryption table across the multiple databases, wherein the finite decryption table stores a set of plaintext-ciphertext mappings between (i) multiple plaintext values and (ii) multiple encrypted ciphertext values corresponding to the multiple plaintext values.