Homomorphic Encryption Polynomial Domain Extension
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Solution Overview
Problem
Existing homomorphic encryption-based machine learning algorithms face limitations in calculating non-polynomial operations due to narrow approximation domains, leading to potential model failures when dealing with new datasets or hyperparameters, as they are not adaptable to varying input ranges.
Innovation Solution
A method is introduced to compute an approximate polynomial with a wider domain by extending a first approximate polynomial function to a second range, using a second approximate polynomial function that maintains preset accuracy, which is achieved by determining the number of iterations and basic functions based on the initial and extended ranges, and applying domain extension functions like the r-domain extension function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a first approximate polynomial function is used for non-polynomial operations in homomorphic encryption, then computation can be performed within a limited range, but the domain range is restricted and the model may fail when input ranges exceed the first range
Solution Approach 1:
The domain range is divided into multiple segments (first range and second range). The first approximate polynomial function handles computations within the first range, while the second approximate polynomial function extends coverage to the second range. This segmentation allows the system to maintain reliability within each segment while achieving broader adaptability through multiple segments.
Solution Approach 2:
The patent extends the domain range by introducing a new dimension of approximation - the second approximate polynomial function. This is achieved by determining coefficients for the extended range based on the first polynomial function and additional computational steps, effectively adding a dimensional extension to the approximation capability.
2Adaptability or versatility
If the domain range is extended to accommodate various datasets and hyperparameters, then adaptability improves, but computational complexity and intermediate value issues increase
Solution Approach 1:
The patent performs preliminary determination of the second approximate polynomial function coefficients before actual homomorphic computations. By pre-calculating the extended range polynomial based on the first polynomial and specified accuracy requirements, the system avoids complex real-time computations during inference, reducing operational complexity while maintaining extended domain adaptability.
Data Source
AI summary
A method of operating a homomorphic ciphertext is disclosed. The method of operating a homomorphic ciphertext includes receiving a non-polynomial operation command with respect to a homomorphic ciphertext, computing an approximate polynomial function corresponding to the non-polynomial operation, performing an operation of the homomorphic ciphertext using the computed polynomial function, and outputting the operated homomorphic ciphertext, wherein the approximate polynomial function is a second approximate polynomial function which is obtained by extending a first approximate polynomial function to have a second range wider than the first range having a preset accuracy with the non-polynomial operation within a first range.