Homomorphic Encryption Rebooting via Multi-Degree Polynomials

Resolve Bottlenecks,
Find Innovative SolutionsGenerate Solutions

Solution Overview

Problem

Conventional rebooting methods for homomorphic encryption require high computational resources and have low accuracy, making them inefficient for maintaining secure communication environments.

Innovation Solution

The method involves linear transformation of homomorphic encryption using multi-degree polynomials and approximate modulus operations with block diagonal matrices to optimize calculations, reducing complexity and improving accuracy.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If conventional rebooting methods are used for homomorphic encryption, then the encryption can be maintained, but the computational resources required are high and accuracy is low

Engineering Contradiction:

Improveencryption maintenanceVSAvoidcomputational resources

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The patent changes the mathematical parameters by using multi-degree polynomials (7th to 80th degree) instead of conventional rebooting methods. This parameter change enables the system to achieve both high reliability in encryption maintenance and reduced computational complexity through optimized polynomial operations

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces the conventional mechanical rebooting process with a mathematical substitution using multi-degree polynomials and approximate modulus operations. This substitution reduces the computational burden while maintaining encryption reliability, effectively replacing a complex mechanical process with a more efficient mathematical approach

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Reliability

If conventional rebooting methods are used for homomorphic encryption, then the encryption can be maintained, but the calculation accuracy is low

Engineering Contradiction:

Improveencryption maintenanceVSAvoidcalculation accuracy

Core Design Contradiction:

ReliabilityVSMeasurement precision

Solution Approach 1:

The patent employs multi-degree polynomials (7th to 80th degree) as mathematical parameters to achieve high calculation accuracy. These polynomials provide precise approximation capabilities that significantly improve measurement precision while maintaining encryption reliability

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent introduces multi-degree polynomials as intermediary mathematical tools between the encryption process and the rebooting operation. These polynomials serve as mediators that enable accurate calculation and precise modulus operations, bridging the gap between encryption maintenance and calculation accuracy

Inventive Principle:

Principle #24Intermediary (Mediator)

3Productivity

If homomorphic encryption operations proceed continuously, then processing can be performed, but q is reduced making further operations impossible

Engineering Contradiction:

Improveprocessing capabilityVSAvoidoperation sustainability

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The patent performs preliminary rebooting operations using multi-degree polynomials before the encryption operations exhaust their capacity. This preliminary action restores the encryption parameters (q) to sustainable levels, enabling continuous processing capability to be maintained over extended periods

Inventive Principle:

Principle #10Preliminary action

Solution Approach 2:

The patent establishes a continuous cycle of encryption operations followed by rebooting operations using multi-degree polynomials. This continuous action ensures that the encryption parameter q is constantly maintained at sustainable levels, allowing uninterrupted processing capability to proceed indefinitely

Inventive Principle:

Principle #20Continuity of useful action

Data Source

PatentUS11239995B2Apparatus for processing approximately encrypted messages and methods thereof

Publication Date: 2022.02.01 CRYPTO LAB INC

AI summary

A method for processing an encryption is provided. The method for processing an encryption includes the steps of linearly transforming a homomorphic encryption for an approximate message including an error, performing an approximate modulus operation for the linearly transformed homomorphic encryption by using a multi-degree polynomial set such that input values within a predetermined range are approximate to an integer point, and linearly transforming the homomorphic encryption which was approximately modulus operated into a form of encryption.