FHE Bootstrapping FFT Reduction via Offline Bootstrap Key Pre-computation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current bootstrapping processes for Fully Homomorphic Encryption (FHE) require a large number of computationally expensive Fast Fourier Transform (FFT) operations, which impede efficient encryption and decryption in security applications.
Innovation Solution
The proposed method reduces the number of FFT operations required for bootstrapping by performing FFT operations on the bootstrap key offline and using a phase vector to eliminate the need for multiple FFT and Inverse FFT operations during the bootstrapping process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a large number of FFT operations are performed during bootstrapping, then the bootstrapping process can be completed, but the computational resources and time required increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-computing the FFT of the bootstrap key offline before the actual bootstrapping operation. This pre-computed FFT key is then reused during bootstrapping, eliminating the need to perform FFT operations on the bootstrap key during the critical bootstrapping path. This resolves the contradiction by ensuring bootstrapping completion while significantly improving computational efficiency.
Solution Approach 2:
The patent extracts the computationally expensive FFT operation on the bootstrap key from the bootstrapping process itself and moves it to an offline pre-computation phase. By separating this operation from the critical bootstrapping path, the patent maintains functional completeness while dramatically reducing the computational burden during actual bootstrapping operations.
2Reliability
If multiple FFT and IFFT operations are performed during bootstrapping, then the cryptographic security is maintained, but the processing time and computational power required increase
Solution Approach 1:
The patent performs the FFT of the bootstrap key in advance during a key generation or setup phase, storing the result for later use. This preliminary computation ensures cryptographic security is maintained while eliminating repeated FFT operations during bootstrapping, thereby reducing processing time significantly.
Solution Approach 2:
The patent changes the computational parameters by transforming the bootstrap key into the frequency domain once offline, then using this transformed representation during bootstrapping. This parameter transformation from time domain to frequency domain representation enables more efficient computations during the actual bootstrapping process.
Data Source
AI summary
A system and method to reduce fast Fourier transforms (FFT) required for bootstrapping in a Fully Homomorphic Encryption process. Ciphertext is separated into a vector of n samples. A fast Fourier transfer (FFT) is performed over a first vector of the samples and a FFT over a bootstrap key. A phase vector of n W(a) terms that are equivalents to the output of a FFT is calculated. A first set of pointwise multiplications of the FFT of the first vector of samples with each of the n W(a) terms in the phase vector is performed. A second set of pointwise multiplications of the results of the first set of pointwise multiplications with the FFT of the bootstrap key is performed. An inverse FFT(IFFT) on the accumulated result of the second set of point-wise multiplications is performed to obtain a bootstrapping result of the ciphertext.