Homomorphic Encryption Bootstrapping with Polynomial Modular Reduction

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Solution Overview

Problem

Conventional fully homomorphic encryption methods face challenges in processing encrypted data efficiently, which hinders effective protection of customer privacy and limits the functionality of customer services.

Innovation Solution

A method and apparatus that generate a ciphertext by encrypting data and perform modular reduction through bootstrapping, utilizing a target approximate polynomial that approximates the modular reduction function, based on selected reference points and Chebyshev polynomials to enhance the efficiency of homomorphic encryption operations.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If conventional encryption methods are used, then security is maintained, but processing efficiency deteriorates

Engineering Contradiction:
ImprovesecurityVSAvoidprocessing efficiency
Core Design Contradiction:
ReliabilityVSProductivity

Solution Approach 1:

The patent replaces conventional decryption-based processing with homomorphic encryption operations that allow direct computation on encrypted data. The bootstrapping mechanism substitutes the need for decryption by performing modular reduction homomorphically, enabling secure and efficient processing simultaneously

Inventive Principle:
Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent changes the parameter representation by using polynomial approximation to represent modular reduction operations. This transformation allows the system to operate in a different mathematical domain where efficient homomorphic computation is possible, resolving the contradiction between security and processing efficiency

Inventive Principle:
Principle #35Parameter changes

2Manufacturing precision

If polynomial degree is increased to improve approximation accuracy, then manufacturing precision improves, but device complexity increases

Engineering Contradiction:
Improveapproximation accuracyVSAvoidpolynomial complexity
Core Design Contradiction:
Manufacturing precisionVSDevice complexity

Solution Approach 1:

The patent applies partial action by using only the necessary degree of polynomial approximation required for adequate accuracy. Instead of using excessively high-degree polynomials, the method selects the minimum sufficient degree to achieve the required approximation quality, balancing accuracy and complexity

Inventive Principle:
Principle #16Partial or excessive action

Solution Approach 2:

The patent creates a universal polynomial approximation framework that can handle various modular reduction operations with a single set of pre-computed polynomials. This multi-functional approach allows the same polynomial structures to serve multiple bootstrapping operations, reducing overall system complexity while maintaining accuracy

Inventive Principle:
Principle #6Universality (Multi-functionality)

Data Source

PatentEP3907926B1Encryption method and apparatus using homomorphic encryption
Publication Date: 2025.08.27 SAMSUNG ELECTRONICS CO LTD
  • EP3907926B1 patent drawingFigure 1
  • EP3907926B1 patent drawingFigure 2A~2B
  • EP3907926B1 patent drawingFigure 2C

AI summary

Disclosed is an encryption method and apparatus. The encryption method using homomorphic encryption may include generating a ciphertext by encrypting data, and bootstrapping the ciphertext by performing a modular reduction based on a selection of one or more target points for a modulus corresponding to the ciphertext.