FHE Linear Transformation with Optimized Ciphertext Rotations
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Solution Overview
Problem
Existing FHE schemes, such as CKKS, face challenges in efficiently performing linear transformations due to high computational and memory resource demands, which are not adequately addressed by current methods.
Innovation Solution
Optimizing the linear transformation process by determining a set of optimal rotation parameters and employing techniques like Baby-Step Boosting and Continuous Accumulation for ciphertext rotations, reducing the number of rotations and memory footprint through efficient parameter selection and hardware acceleration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional linear transformation methods are used in FHE schemes, then computational accuracy is maintained, but computational resource consumption and memory footprint increase significantly
Solution Approach 1:
The patent segments the linear transformation process into distinct phases (rotation parameter determination, boosting technique execution, continuous accumulation) that can be independently optimized and executed. This segmentation allows for reducing memory footprint by processing data in smaller chunks rather than loading entire transformation matrices into memory.
Solution Approach 2:
The patent determines optimal rotation parameters dynamically based on input characteristics and transforms the linear transformation into a series of parameterized rotations. By changing the representation from fixed matrices to parameterized operations, memory requirements are reduced while maintaining computational accuracy.
2Measurement precision
If more rotation operations are performed to achieve accurate linear transformation, then transformation precision improves, but execution time and computational overhead increase
Solution Approach 1:
The patent performs preliminary determination of optimal rotation parameters before executing the full linear transformation. By pre-calculating the necessary rotation parameters based on input data characteristics, the system avoids performing unnecessary rotation operations, thereby reducing execution time while maintaining transformation accuracy.
Solution Approach 2:
The patent implements a feedback mechanism where rotation parameters are determined based on the actual state of the ciphertext and transformation requirements. This feedback-driven approach ensures that only the necessary number of rotation operations are performed, optimizing the balance between accuracy and execution time.
3Speed
If hardware acceleration is utilized to speed up linear transformation, then processing speed increases, but initial memory loading requirements and hardware complexity increase
Solution Approach 1:
The patent segments the linear transformation computation into discrete operations that can be efficiently mapped to hardware acceleration units. By breaking down the transformation into rotation and accumulation phases with clearly defined data flows, the hardware complexity is managed while achieving significant speedup.
4Measurement precision
If Rescaling is applied frequently to control noise growth, then decryption accuracy is maintained, but ciphertext size increases and computational overhead increases
Solution Approach 1:
The patent modifies the scaling parameters used in Rescaling operations to achieve noise control with minimal impact on ciphertext size. By carefully selecting scaling factors based on the transformation requirements and noise characteristics, the system maintains decryption accuracy while avoiding excessive ciphertext expansion.
Data Source
AI summary
A method and system for optimizing compute runtime and memory footprint of a linear transformation process are provided. The method includes determining a set of optimal rotation parameters, wherein the optimal rotation parameters provide an optimal tradeoff between runtime compute resources and a memory footprint for a runtime execution of the linear transformation process; initializing the linear transformation process to run a boosting technique with the determined set of optimal rotation parameters, wherein the boosting technique, when executed at runtime as part of the linear transformation process, performs at least one iteration that yields rotated ciphertexts, and wherein the at least one iteration is based on the determined set optimal rotation parameters and at least one key switching key (KSK); and loading the initialized linear transformation process to an internal memory of a hardware accelerator.