Homomorphic Approximation Functions With Error Assignment
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Solution Overview
Problem
Existing homomorphic encryption methods face inefficiencies and accuracy issues when performing operations on approximate polynomials, leading to decreased efficiency and increased error in calculation results.
Innovation Solution
Assigning an error value to encrypted data and performing a homomorphic operation using an approximation function, such as a polynomial, to improve accuracy and efficiency by approximating a target function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a higher-order approximate polynomial is used to improve accuracy, then the accuracy of the calculation result improves, but the computational efficiency decreases
Solution Approach 1:
The patent changes the parameter of the approximation function from high-order to low-order, and compensates for the accuracy loss by introducing error value assignment and homomorphic operations. This transforms the problem from using high-order polynomials (which are computationally expensive) to using low-order polynomials with error compensation (which are efficient but require additional error handling steps).
Solution Approach 2:
The patent introduces an intermediary error value that mediates between the low-order approximation and the target function. By assigning error values to encrypted data and performing homomorphic operations, the system bridges the gap between the simplified low-order polynomial and the actual target function, maintaining accuracy without requiring high-order polynomials.
2Productivity
If a low-order approximate polynomial is used to improve computational efficiency, then the computational efficiency increases, but the accuracy of the calculation result decreases
Solution Approach 1:
The patent applies beforehand cushioning by pre-assigning error values to encrypted data before performing homomorphic operations. This error assignment acts as a cushion that compensates for the inherent accuracy loss from using low-order approximations, ensuring that the final result maintains sufficient accuracy despite the simplified polynomial order.
3Productivity
If approximate polynomials are used to perform non-polynomial operations, then the computational efficiency improves, but the accuracy decreases due to intrinsic limitations in specific ranges
Solution Approach 1:
The patent applies dynamics by making the approximation function adaptive through error value assignment. Instead of using a fixed low-order polynomial that performs poorly in specific ranges, the system dynamically adjusts by assigning error values that compensate for range-specific inaccuracies, allowing the low-order approximation to maintain accuracy across different input ranges while preserving computational efficiency.
Data Source
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AI summary
An apparatus and method for performing an operation using an approximation function are provided. The method for performing an operation according to one embodiment includes assigning an error value to encrypted data; and performing a homomorphic operation for an approximation function, which is obtained by approximating a target function, by using, as an input value, the encrypted data to which the error value is assigned.