Homomorphic Function Evaluation Using Univariate Decomposition
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Solution Overview
Problem
Existing homomorphic encryption schemes are impractical for evaluating functions with real-valued variables due to high computational complexity and the need for frequent bootstrapping operations, which are slow and resource-intensive, especially when dealing with multivariate functions.
Innovation Solution
Transform multivariate functions into networks of univariate functions through sums and compositions, optimizing calculations by identifying and reusing intermediate values, and representing functions as tables rather than Boolean circuits.
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 multiple univariate functions through variable substitution and decomposition. Each univariate function can be independently evaluated on encrypted data, reducing the overall computational complexity while maintaining data confidentiality through homomorphic encryption.
Solution Approach 2:
The patent employs nested computational structures where univariate function evaluations are embedded within a larger multivariate function evaluation framework. Intermediate results from univariate evaluations are combined through homomorphic operations to produce the final result, creating a nested evaluation architecture.
2Measurement precision
If bootstrapping operations are performed frequently to maintain ciphertext validity, then calculation accuracy is preserved, but computation time increases
Solution Approach 1:
The patent performs preliminary decomposition of multivariate functions into univariate components before encryption. This pre-processing step allows the system to evaluate simpler univariate functions that require fewer bootstrapping operations, thereby reducing computation time while maintaining accuracy through controlled noise management.
3Adaptability or versatility
If multivariate functions are evaluated directly on encrypted data, then functionality is maintained, but resource consumption increases
Solution Approach 1:
The patent divides multivariate function evaluation into separate univariate function evaluations. Each univariate function processes one variable at a time, reducing the computational resources required for each individual evaluation while maintaining the overall functionality through combination of results.
Solution Approach 2:
The patent discards intermediate plaintext values during the evaluation process, working exclusively with encrypted data and intermediate ciphertexts. Only the final result is decrypted, minimizing resource consumption by avoiding unnecessary plaintext conversions while recovering the necessary information through homomorphic operations.
Data Source
AI summary
The disclosed embodiments are directed toward cryptographic methods and variants thereof based on homomorphic encryption enabling the evaluation of real-valued functions on encrypted data, in order to allow carrying out homomorphic processing on encrypted data more broadly and efficiently.