Homomorphic Encryption Comparison via Composite Polynomial Functions
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Solution Overview
Problem
Current fully homomorphic encryption technologies face limitations in approximating the sign function and require significant non-scalar multiplication and depth consumption for comparison operations, leading to inefficiencies in processing.
Innovation Solution
An electronic apparatus and server system that utilize a composite function composed of multiple polynomials, where each polynomial is optimized through minimax approximation for the sign function, allowing for efficient comparison operations by minimizing non-scalar multiplication and depth consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a single polynomial is used to approximate the sign function, then the approximation is simple, but the accuracy is insufficient
Solution Approach 1:
The patent divides the sign function approximation into multiple segments by using a composite function of multiple polynomials. Each polynomial approximates the sign function over a specific domain, and the composite function combines these approximations to achieve higher overall accuracy. This segmentation approach resolves the contradiction by improving approximation accuracy through multiple specialized polynomials rather than relying on a single complex polynomial.
2Reliability
If comparison operation is performed in homomorphic encryption, then information security is improved, but operation speed deteriorates due to significant non-scalar multiplication and depth consumption
Solution Approach 1:
The patent changes the parameters of the polynomial approximation by optimizing the domains and ranges of the composite function polynomials. By carefully selecting and adjusting these parameters, the system achieves accurate sign function approximation while reducing the number of non-scalar multiplications and depth consumption required for comparison operations in homomorphic encryption, thus improving operation speed without compromising security.
3Adaptability or versatility
If the domain of polynomial is expanded to cover wider range, then the polynomial becomes more versatile, but the approximation accuracy decreases
Solution Approach 1:
The patent applies segmentation by dividing the wide domain into multiple sub-domains, each handled by a separate polynomial in the composite function. This allows each polynomial to maintain high approximation accuracy within its specific sub-domain while the composite function collectively covers a wider overall domain, thus resolving the contradiction between domain versatility and approximation accuracy.
Solution Approach 2:
The patent implements local quality by optimizing each polynomial specifically for its assigned sub-domain rather than using a single polynomial for the entire domain. Each polynomial is tailored to provide the best approximation within its local range, ensuring high accuracy locally while maintaining overall versatility through the composite function structure.
Data Source
AI summary
Disclosed is an electronic apparatus. The electronic apparatus includes a memory storing a composite function in which at least two polynomials are composed and a processor configured to, based on a comparison operation command being received for a plurality of homomorphic ciphertexts, perform operation by reflecting the plurality of homomorphic ciphertexts to the composite function, and obtain a comparison result of the plurality of homomorphic ciphertexts based on the operation result, each of the at least two polynomials may output a value in a preset range for a value in a preset domain, and a domain of one of the at least two polynomials may be determined based on a range of a previous polynomial.