Polynomial Homomorphic Encryption via Coefficient Mapping Transform
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Solution Overview
Problem
Existing homomorphic encryption methods require significant computational resources and storage, making them impractical for commercial applications due to vulnerabilities and inefficiencies, such as large ciphertext sizes and rapid noise growth, which complicates data security in cloud computing environments.
Innovation Solution
A polynomial complete homomorphic encryption system based on coefficient mapping transformation that operates directly on ciphertext, using a client-server architecture with key management and operation supporting functions to perform secure homomorphic operations without revealing plaintext, reducing computational and storage requirements through efficient key generation and operation supporting function families.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional homomorphic encryption methods are used, then data security is maintained, but computational resources and storage requirements become excessively large
Solution Approach 1:
The patent changes the mathematical parameters by using polynomial rings with specific modulus values and transforming the encryption scheme to operate on coefficients rather than bits. This parameter transformation reduces the ciphertext size and computational complexity while maintaining security, directly addressing the contradiction between security and resource consumption.
Solution Approach 2:
The patent transitions from bit-level encryption to polynomial coefficient-level encryption, adding a dimensional transformation that allows homomorphic operations to be performed more efficiently. This dimensional change enables the system to reduce computational resources and storage requirements while preserving data security.
2Reliability
If traditional homomorphic encryption methods are used, then data security is maintained, but ciphertext size and expansion rate become excessively large
Solution Approach 1:
The patent changes the encryption parameter from bit-based to polynomial coefficient-based representation. This parameter change fundamentally reduces the ciphertext size by eliminating redundant information and reducing expansion during homomorphic operations, while maintaining security through the underlying polynomial ring structure.
3Reliability
If traditional homomorphic encryption methods are used, then data security is maintained, but noise growth rate becomes excessively rapid
Solution Approach 1:
The patent implements a feedback mechanism through the polynomial ring structure and modulus operations that continuously controls and limits noise growth. The mathematical structure provides inherent feedback that prevents noise from accumulating excessively during homomorphic operations, maintaining both security and operational efficiency.
Data Source
AI summary
A polynomial complete homomorphic encryption method based on the coefficient mapping transformation. A plaintext is expressed as a polynomial consisting of a set of random values, two sets of random coefficient factors and a random constant of a specified mapping function, and in the polynomial: the expression and a set of random coefficient factors of the specified mapping function are taken as a key; another set of random coefficient factors, a set of random arguments and random constants of the mapping function are taken as the ciphertexts for homomorphic operations, so that the part of function key performs three different mappings and then undergoes numerical fitting to obtain the family of operational support functions consisting of three sub-functions respectively, which are used to perform the homomorphic operation of the ciphertext based on the family of operational support functions and return to the locality for decryption by the key.