Homomorphic Ciphertext Encoding With Half-Size Embedding Matrix
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Solution Overview
Problem
Existing homomorphic encryption methods require significant computational resources for polynomial transformation operations due to the large size of matrices used in encoding and decoding processes, leading to inefficiencies and potential security vulnerabilities.
Innovation Solution
The method employs a matrix with half the size of the canonical embedding function and utilizes inverse Discrete Fourier Transform (iDFT) for encoding and Discrete Fourier Transform (DFT) for decoding, reducing computational complexity by using a matrix with only half the elements of the canonical embedding function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If a full-size canonical embedding function matrix is used for polynomial transformation, then encoding and decoding accuracy is maintained, but computational complexity and resource consumption increase significantly
Solution Approach 1:
The patent divides the full canonical embedding function matrix into multiple sub-matrices, each handling a portion of the polynomial transformation. This segmentation allows the system to process data in smaller chunks, reducing the computational burden of each individual operation while maintaining the overall transformation accuracy through coordinated processing across all sub-matrices.
Solution Approach 2:
The patent applies partial action by using a reduced-size matrix that processes only the essential components of the polynomial transformation. Rather than applying the complete canonical embedding function, the invention identifies and processes the critical subset of transformations needed, achieving sufficient accuracy with significantly reduced computational resources.
2Measurement precision
If a full-size canonical embedding function matrix is used for polynomial transformation, then transformation accuracy is preserved, but operation speed decreases
Solution Approach 1:
The patent segments the polynomial transformation process into multiple smaller operations using sub-matrices. This allows parallel processing of different segments, significantly improving operation speed while the coordinated results maintain the required transformation accuracy.
Solution Approach 2:
The invention performs partial action by executing only the necessary subset of transformation operations required for adequate accuracy. This selective processing eliminates redundant computations, thereby increasing operation speed without compromising the essential transformation quality.
3Ease of operation
If decryption is performed to enable calculation on the message, then calculation capability is achieved, but security risk and resource waste increase
Solution Approach 1:
The patent introduces an intermediary approach by performing calculations on encrypted data through controlled polynomial transformations. This intermediary method allows mathematical operations to be executed on ciphertext without full decryption, maintaining security while enabling necessary calculations through homomorphic properties and controlled transformations.
Solution Approach 2:
The invention applies preliminary action by pre-processing the encryption and establishing a framework that allows future calculations to be performed without decryption. The initial setup creates a structure where subsequent operations can be executed on the encrypted form, eliminating the need for repeated decryption and re-encryption cycles.
Data Source
AI summary
Disclosed is an operation device. The operation device includes a memory storing at least one instruction; and a processor configured to execute the at least one instruction, and the processor, by executing the at least one instruction, may perform encoding or decoding for an approximate homomorphic ciphertext using a predetermined matrix having only a half of an element of a matrix corresponding to a canonical embedding function.