FHE Key-Switching After ModRaise Using Aggregated Polynomial Sums
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Solution Overview
Problem
Fully Homomorphic Encryption (FHE) schemes face challenges in managing noise accumulation, computational intensity, and memory requirements during key-switching operations, particularly after the ModRaise operation, which hinders their practical application in real-time commercial applications.
Innovation Solution
Optimize key-switching operations by pre-computing aggregated polynomial sums (Sum0 and Sum1) and utilizing pre-multiplied rotation keys, reducing the number of polynomial multiplications and memory usage through techniques like dynamic generation from seed values and parameter adjustments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If traditional key-switching operations are performed after ModRaise in FHE, then security and correctness are maintained, but computational overhead and memory footprint increase significantly
Solution Approach 1:
The patent pre-computes aggregated polynomial sums (Sum0 and Sum1) during key generation or preprocessing phases, storing them for later use during key-switching operations. This preliminary action eliminates the need to compute these sums repeatedly during actual key-switching, significantly reducing computational overhead and improving efficiency without compromising security
Solution Approach 2:
The patent combines multiple polynomial computations into aggregated sums (Sum0 and Sum1) that can be reused across multiple key-switching operations. By merging these computations into pre-computed aggregates, the system reduces redundant calculations and memory access operations, thereby lowering computational overhead while maintaining correctness
2Productivity
If traditional key-switching operations are performed after ModRaise in FHE, then security and correctness are maintained, but computational overhead and memory footprint increase significantly
Solution Approach 1:
The patent extracts and pre-computes the heavy polynomial summation operations (Sum0 and Sum1) separately during key generation, storing only the results. This extraction removes the computational burden from the actual key-switching operation, reducing both computational overhead and the memory footprint required during runtime operations
Solution Approach 2:
The patent performs memory-intensive polynomial computations in advance during key generation, storing the aggregated results for later use. This preliminary computation reduces the memory footprint during actual key-switching operations, as the system only needs to store and access the pre-computed sums rather than performing full polynomial computations in real-time
3Reliability
If bootstrapping is performed to manage noise accumulation, then noise control is achieved, but computational intensity and memory requirements increase
Solution Approach 1:
The patent pre-computes key-switching parameters and aggregated polynomial sums before bootstrapping operations, reducing the computational intensity during the actual bootstrapping process. This preliminary preparation allows the system to manage noise accumulation through bootstrapping while minimizing the additional computational burden imposed by key-switching operations
Solution Approach 2:
The patent integrates key-switching optimizations with bootstrapping operations by using the same pre-computed aggregated sums for both operations. This merging reduces redundant computations and simplifies the overall process, lowering computational intensity and device complexity while maintaining noise control capabilities
Data Source
AI summary
A method and system of the device may include identifying, in an FHE program, key-switching operations occurring after a ModRaise operation. In addition, the device may include determining a first aggregated polynomial sum and a second aggregated polynomial sum; and configuring instructions for performing a MultSum operation based on the determined first aggregated polynomial sum and the second aggregated polynomial sum, the instructions are programmed to be executed during runtime, where the MultSum operation outputs two polynomials, each of which is an inner product between a single cyphertext polynomial and the first aggregated polynomial sum and a single cyphertext polynomial and the second aggregated polynomial sum, thereby reducing memory usage and computational overhead and enhancing key-switching efficiency.