Encrypted Real-Valued Function Evaluation via Univariate Decomposition
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Solution Overview
Problem
Current homomorphic encryption schemes are impractical for transforming a set of ciphertexts corresponding to cleartexts into a set of functions with real-valued variables, as they require complex bootstrapping operations and are limited to binary inputs and simple Boolean circuits, leading to slow computation times and high resource usage.
Innovation Solution
Transform multivariate functions into networks of univariate functions represented as sums and compositions, and optimize evaluations by reusing intermediate results, using homomorphic encryption schemes to evaluate these functions on encrypted data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption schemes are used to transform ciphertexts into functions with real-valued variables, then data confidentiality is preserved, but computation time and resource usage increase significantly
Solution Approach 1:
The patent segments multivariate functions into multiple univariate functions, where each univariate function can be independently evaluated on encrypted data. This decomposition allows the system to process each function separately, reducing the overall computational complexity and time required while maintaining data confidentiality through homomorphic encryption.
Solution Approach 2:
The patent performs preliminary decomposition of multivariate functions into univariate functions before the actual homomorphic evaluation. By pre-processing the function structure and identifying reusable intermediate results, the system prepares optimized evaluation paths that reduce computation time during the actual encrypted data processing phase.
2Measurement precision
If bootstrapping operations are performed to maintain noise levels in ciphertexts, then calculation accuracy is preserved, but resource consumption and computation time increase
Solution Approach 1:
By dividing multivariate function evaluation into separate univariate function evaluations, the patent reduces the depth and complexity of noise accumulation. Each univariate function evaluation is simpler and generates less noise, reducing the frequency and resource intensity of bootstrapping operations needed to maintain calculation accuracy.
Solution Approach 2:
The patent identifies and reuses intermediate calculation results across multiple univariate function evaluations. By recovering and reusing these intermediate values, the system avoids redundant computations that would generate additional noise, thereby reducing the need for frequent bootstrapping operations and associated resource consumption.
3Adaptability or versatility
If multivariate functions are evaluated directly on encrypted data, then functionality is maintained, but computation complexity and resource usage increase
Solution Approach 1:
The patent transforms the evaluation of complex multivariate functions into a sequence of simpler univariate function evaluations. Each univariate function is evaluated independently on encrypted data using homomorphic encryption, which significantly reduces the computational complexity compared to directly evaluating the full multivariate function while preserving the overall functionality.
Solution Approach 2:
The patent creates a universal framework for evaluating any multivariate function by decomposing it into univariate components. This approach provides a multi-functional solution that can handle various types of multivariate functions (polynomials, rational functions, etc.) through a unified methodology, reducing the need for specialized complex evaluation algorithms for each function type.
4Productivity
If intermediate calculation results are reused to optimize evaluation, then resource usage decreases, but system complexity increases
Solution Approach 1:
The patent performs preliminary analysis of the multivariate function structure to identify potential intermediate results that can be reused across multiple univariate function evaluations. By pre-planning the evaluation strategy and identifying reuse opportunities before execution, the system optimizes resource usage without requiring complex real-time decision-making mechanisms during the actual evaluation process.
Solution Approach 2:
The patent creates and stores copies of intermediate calculation results that can be reused in subsequent univariate function evaluations. By maintaining these copied intermediate values in memory, the system avoids redundant computations and reduces resource usage, while the copying mechanism itself remains relatively simple and straightforward to implement.
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.