Encrypted Computation Parameter Optimization Under Ciphertext Noise
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Solution Overview
Problem
Existing homomorphic encryption schemes face challenges in selecting encrypted computation parameters that balance security, accuracy, and computational efficiency, particularly due to the accumulation of noise during multiple operations, which can render decryption impossible.
Innovation Solution
An automated method optimizes encrypted computation parameters by dividing the computation graph into recurring patterns or subgraphs, using noise constraint functions and cost functions to minimize computational cost while ensuring security and accuracy, allowing for efficient determination of parameters such as polynomial size, GLWE dimension, and key switching/booster keys.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If noise is added to ciphertexts for security reasons, then security against attacks is improved, but decryption accuracy deteriorates when noise accumulates through multiple operations
Solution Approach 1:
The system performs preliminary noise analysis and parameter optimization before executing the encrypted computation. By pre-calculating optimal parameters based on the computation graph and noise constraints, the system ensures that noise accumulation remains within acceptable bounds throughout the computation, thereby maintaining decryption accuracy while preserving security.
Solution Approach 2:
The system dynamically adjusts encryption parameters such as polynomial size, GLWE dimension, and noise distribution characteristics based on the specific computation requirements. By changing these parameters adaptively, the system can maintain sufficient noise for security while preventing excessive noise accumulation that would compromise decryption accuracy.
2Measurement precision
If polynomial size and GLWE dimension are increased to reduce minimal noise, then decryption accuracy is improved, but computational cost increases
Solution Approach 1:
Instead of uniformly increasing polynomial size and GLWE dimension throughout the entire computation, the system applies different parameter settings to different regions of the computation graph based on local noise accumulation characteristics. This allows the system to maintain high decryption accuracy where needed while minimizing computational overhead in less critical regions.
Solution Approach 2:
The system dynamically adjusts polynomial size and GLWE dimension during the computation based on real-time noise analysis. By making these parameters adaptive rather than static, the system can optimize the balance between decryption accuracy and computational efficiency at each stage of the computation.
3Measurement precision
If bootstrapping is performed frequently to reduce noise, then decryption accuracy is maintained, but computational cost increases significantly
Solution Approach 1:
The system implements a feedback mechanism that continuously monitors noise accumulation during encrypted computation. Based on this feedback, the system intelligently determines when bootstrapping is necessary, performing it only when noise levels approach critical thresholds. This prevents unnecessary bootstrapping operations while maintaining decryption accuracy.
Solution Approach 2:
Instead of performing bootstrapping at fixed intervals or overly conservatively, the system applies bootstrapping selectively based on actual noise accumulation patterns. By performing bootstrapping only when necessary rather than excessively, the system maintains decryption accuracy while minimizing the computational overhead associated with frequent bootstrapping operations.
Data Source
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AI summary
Some embodiments are directed to a computer-implemented method of determining encrypted computation parameters for carrying out an encrypted computation on noisy ciphertexts. A computation graph Is divided into multiple subgraphs, defined by a type and by instantiation parameters for the type, Respective sets of encrypted computation parameters are defined for the respective types. An optimization of the encrypted computation parameters is performed to minimize a computational cost of carrying out the encrypted computation according to the encrypted computation parameters. The encrypted computation parameters are constrained to satisfy a noise constraint on ciphertext noise while carrying out the encrypted computation. The noise constraint is based on respective noise constraints for respective subgraphs, defined by a noise constraint function for the type that takes at least the encrypted computation parameters for the type and the instantiation parameters of the subgraph as input.