Homomorphic Ciphertext Polynomial Bootstrapping for Faster Multiplication
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Solution Overview
Problem
Existing fully homomorphic encryption techniques, such as TFHE, struggle with performing multiplicative operations efficiently due to undefined multiplication on the circle group, limiting high-speed evaluation of complex functions.
Innovation Solution
An encryption processing apparatus that applies a predetermined polynomial to a ciphertext to reduce errors and extract new ciphertexts, enabling high-speed performance of operations between integers without decryption, utilizing Gate Bootstrapping and TRLWE encryption to facilitate multiplicative operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If fully homomorphic encryption based on LWE problem is used to perform operations on encrypted data, then data security is maintained, but computation time becomes excessively long due to error accumulation requiring frequent bootstrapping
Solution Approach 1:
The patent changes the mathematical parameters of the encryption system by using TRLWE (Torus Ring Learning With Errors) encryption instead of standard LWE, and employing Gate Bootstrapping with specific polynomial parameters. This parameter change enables faster computation while maintaining security, reducing bootstrapping time from hours to minutes by optimizing the error reduction mechanism
Solution Approach 2:
The patent applies preliminary error reduction through Gate Bootstrapping before errors accumulate to problematic levels. By periodically reducing errors during computation using pre-prepared bootstrap keys and polynomials, the system maintains decryption capability without requiring complete re-encryption, thus avoiding excessive computation time
2Ease of operation
If TFHE is used for bit-wise homomorphic encryption, then encryption operations can be performed, but multiplicative operations are inefficient due to undefined multiplication on the circle group
Solution Approach 1:
The patent introduces an intermediary mechanism (Gate Bootstrapping with polynomial approximation) that enables multiplicative operations on TRLWE ciphertexts. By using polynomial-based function evaluation as an intermediary, the system can perform multiplication and other complex operations on encrypted integers without requiring direct multiplication on the circle group, thus achieving both operational capability and efficiency
3Measurement precision
If bootstrapping is performed frequently to reduce error components, then decryption accuracy is maintained, but the large amount of computation required makes practical operation difficult
Solution Approach 1:
The patent optimizes bootstrapping computation by changing parameters including using specific polynomial degrees, optimizing bootstrap key generation, and employing efficient modular arithmetic. These parameter changes reduce the computational complexity of each bootstrapping operation while maintaining the ability to reduce error components effectively
Solution Approach 2:
The patent performs preliminary preparation of bootstrap keys and polynomials in advance, storing them for later use during computation. This preliminary action eliminates the need to generate these complex mathematical objects during runtime, significantly reducing the computational burden when bootstrapping is actually needed
Data Source
AI summary
An encryption processing apparatus processes a ciphertext. The ciphertext is a fully homomorphic cyphertext that has, as a plaintext associated with an integer, a value obtained by adding an error with a predetermined variance to a predetermined value and that is able to be subjected to a predetermined operation between integers without being decrypted. The apparatus includes a processor that performs a calculation process of applying a predetermined polynomial to a ciphertext. The calculation process performs a first process of reducing an error of an input ciphertext by using the predetermined polynomial and a second process of extracting the new ciphertext from a ciphertext obtained as a result of the first process. The calculation process computes the new ciphertext that is different in input value at high speed by performing the second process a plurality of number of times on the ciphertext obtained as the result of the first process.