Homomorphic Encryption Modulus Refresh via Blind Rotation
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Solution Overview
Problem
Conventional modulus refresh methods in homomorphic encryption suffer from low precision bits in output values due to approximate polynomial representations, leading to small modulus values when a high-order polynomial is used, which limits the number of ciphertext operations.
Innovation Solution
A processor-implemented method for modulus refresh that performs blind rotation on the ciphertext, using homomorphic operation-based preprocessing and Learning with Error (LWE) vectors to generate a target ciphertext with a larger modulus, thereby increasing the modulus value and enhancing operational precision.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If approximate polynomial operations are used for modulus refresh, then the decryption process can be homomorphically operated, but the output value has low precision bits compared to existing ciphertext
Solution Approach 1:
The decryption process is divided into multiple independent circuit blocks (first circuit block for modulus operation, second circuit block for rotation, third circuit block for addition). Each block performs a specific function with controlled precision requirements, allowing the overall system to achieve high precision output while maintaining homomorphic operability.
2Manufacturing precision
If a high-order approximate polynomial is used, then the modulus operation can be more accurately approximated, but the value of modulus obtained in the modulus refresh process becomes small
Solution Approach 1:
A rotation factor (intermediary element) is introduced to transform the relationship between the approximate polynomial output and the final modulus value. The rotation operation mediates between the low-precision polynomial result and the high-precision modulus requirement, allowing the system to use simple approximate polynomials while still achieving accurate modulus values through the intermediate rotation step.
Data Source
AI summary
Disclosed is a method and apparatus for modulus refresh, where the method for modulus refresh of a ciphertext in homomorphic encryption includes receiving a first ciphertext corresponding to a first modulus, generating a second ciphertext by performing a blind rotation on the first ciphertext, and generating a target ciphertext corresponding to a second modulus greater than the first modulus based on the first ciphertext and the second ciphertext.