Homomorphic Encryption Bootstrapping via Odd Function Modular Reduction
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Solution Overview
Problem
Conventional encryption methods are inadequate for processing encrypted data securely, particularly in maintaining customer privacy through fully homomorphic encryption, as they face challenges in efficiently performing logical and mathematical operations on encrypted data.
Innovation Solution
The proposed solution involves generating a ciphertext by encrypting data and bootstrapping it using a modular reduction based on an odd function property, which includes transforming an approximate polynomial to reduce the degree and domain of the polynomial, thereby optimizing the modular reduction process through the use of Chebyshev polynomial bases and algorithms like Paterson-Stockmeyer or baby-step giant-step, to enhance the efficiency of homomorphic encryption operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional encryption methods are used, then data security is maintained, but the ability to process encrypted data is lost
Solution Approach 1:
The patent introduces homomorphic encryption as an intermediary mechanism that allows processing operations to be performed on encrypted data without decryption. The encryption scheme acts as a mediator between data security requirements and processing needs, enabling computations on ciphertexts while maintaining confidentiality through mathematical properties of the encryption function.
Solution Approach 2:
The patent transforms the encryption approach by changing the mathematical parameters and structure of the encryption function to support homomorphic properties. Specifically, it uses polynomial-based encryption schemes where the algebraic structure allows operations on encrypted values, fundamentally changing how encryption parameters are selected and how cryptographic operations are performed.
2Reliability
If fully homomorphic encryption is implemented, then privacy preservation is improved, but computational complexity increases
Solution Approach 1:
The patent segments the complex homomorphic encryption process into distinct modular components including key generation, encryption, decryption, and bootstrapping operations. Each component is independently optimized using polynomial arithmetic and number theoretic transforms, allowing the system to manage computational complexity through structured decomposition of the overall encryption scheme.
Solution Approach 2:
The patent replaces traditional mechanical or algorithmic encryption operations with mathematically efficient polynomial-based computations. By substituting conventional cryptographic primitives with homomorphic polynomial arithmetic and fast number theoretic transforms, the system reduces computational overhead while maintaining security guarantees.
3Reliability
If bootstrapping is performed using conventional methods, then ciphertext renewal is achieved, but processing time increases
Solution Approach 1:
The patent performs preliminary preparation of polynomial approximations and pre-computes certain transformation matrices that are needed for bootstrapping operations. By pre-processing and caching these mathematical structures, the actual bootstrapping operation during runtime is significantly accelerated, reducing the time penalty associated with ciphertext renewal while maintaining security.
Data Source
AI summary
An encryption method and apparatus based on homomorphic encryption using an odd function property. The encryption method includes generating a ciphertext by encrypting data, and bootstrapping the ciphertext by performing a modular reduction based on an odd function property for a modulus corresponding to the ciphertext.