Homomorphic Evaluation of Real-Valued Functions With Univariate Decomposition
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Solution Overview
Problem
Existing homomorphic encryption methods are impractical for evaluating functions with real-valued inputs due to high computational complexity and resource requirements, particularly in bootstrapping operations, limiting their applicability to binary inputs and simple Boolean circuits.
Innovation Solution
Transform multivariate functions into networks of univariate functions represented as sums and compositions, optimizing calculations by reusing intermediate values and employing homomorphic encryption schemes, such as LWE and RLWE, to reduce complexity and computation time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption schemes are used to evaluate functions on encrypted data, then data confidentiality is preserved, but computational complexity and time increase significantly
Solution Approach 1:
The patent segments multivariate functions into networks of univariate functions, where each function is represented as a composition of simpler univariate functions. This decomposition allows the evaluation to be performed through a series of manageable steps rather than as a single complex operation, reducing the overall computational burden while preserving homomorphic encryption properties
Solution Approach 2:
The patent employs pre-computation of lookup tables for univariate functions during an offline phase. These tables store pre-evaluated results that can be directly applied during online evaluation, eliminating the need to perform complex homomorphic operations during actual data processing. This preliminary action significantly reduces computational complexity and time during runtime while maintaining data confidentiality
2Measurement precision
If bootstrapping operations are performed to reduce noise in ciphertexts, then calculation accuracy is maintained, but computation time and memory usage become impractical
Solution Approach 1:
The patent breaks down the bootstrapping process into segmented operations on univariate functions. Instead of performing a single complex bootstrapping operation on multivariate functions, the system performs multiple simpler bootstrapping steps on individual univariate functions, each requiring less computational resources and time
Solution Approach 2:
The patent pre-computes and stores lookup tables containing results of bootstrapped univariate function evaluations. During actual evaluation, these pre-computed values are retrieved and applied directly, avoiding the need to perform time-consuming bootstrapping operations in real-time while maintaining calculation accuracy
3Adaptability or versatility
If multivariate functions are evaluated directly on encrypted data, then functionality is preserved, but resource requirements become excessive
Solution Approach 1:
The patent transforms multivariate functions into networks of univariate functions, decomposing complex multivariate operations into compositions of simpler univariate functions. This segmentation reduces the computational resources required for each individual operation while preserving the overall functionality of the original multivariate function through mathematical composition
Solution Approach 2:
The patent performs pre-computation of univariate function networks and stores them as lookup tables. During evaluation, these pre-computed structures are utilized to minimize real-time computational resources required, allowing the system to handle complex multivariate functions with reduced memory and processing requirements
Data Source
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AI summary
The invention relates to a cryptographic method and variants thereof based on homomorphic encryption enabling the assessment of true value functions on encrypted data, in order to enable homomorphic processing to be performed more widely and efficiently on encrypted data.