Homomorphic Encryption Modular Reduction via Function Composition
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Solution Overview
Problem
Conventional encryption methods are inadequate for processing encrypted data securely, particularly in maintaining customer privacy, and existing homomorphic encryption techniques face challenges in efficient modular reduction operations.
Innovation Solution
The method employs a composition of functions, specifically trigonometric functions, to approximate modular reduction through the generation of approximate polynomials for both the function and its inverse, reducing errors and computational complexity by using a composite function that approximates modular reduction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional encryption methods are used, then implementation is simple, but processing encrypted data is difficult and customer privacy cannot be protected
Solution Approach 1:
The patent introduces an intermediary mechanism (homomorphic encryption scheme) that allows processing of encrypted data without decryption. The encryption scheme acts as a mediator between data protection requirements and processing needs, enabling computations on ciphertext while maintaining security.
Solution Approach 2:
The patent changes the parameter of data representation from plaintext to ciphertext, allowing data to be processed in encrypted form. This parameter change enables both privacy protection and data processing capability simultaneously through homomorphic properties.
2Reliability
If fully homomorphic encryption is used to protect privacy, then customer privacy is preserved, but computational complexity and processing difficulty increase
Solution Approach 1:
The patent segments the complex homomorphic encryption process into manageable components: key generation, encryption, homomorphic operations, and decryption. This segmentation reduces computational complexity by allowing optimized handling of each component separately.
Solution Approach 2:
The patent performs preliminary actions by pre-generating keys and setting up the homomorphic encryption scheme before actual data processing. This preparation reduces computational burden during the actual processing phase.
3Productivity
If bootstrapping is performed to improve homomorphic encryption efficiency, then processing speed improves, but computational overhead increases
Solution Approach 1:
The patent applies partial bootstrapping operations only when necessary, rather than performing full bootstrapping on all ciphertexts. This selective approach improves processing speed for critical operations while minimizing unnecessary computational overhead.
Data Source
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AI summary
An encryption method and apparatus based on homomorphic encryption using a composition of functions. The encryption method includes generating a ciphertext by encrypting data, and bootstrapping the ciphertext by performing a modular reduction based on a composition of a function for a modulus corresponding to the ciphertext.