Secret-Shared Polynomial Approximation for Secure Function Computation
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Solution Overview
Problem
Existing secure computation methods require different schemes for each elementary function, limiting their general applicability.
Innovation Solution
A method for secure computation that uses secret share values and polynomial approximations to support multiple elementary functions by changing parameters, allowing for flexible and efficient computation of functions like reciprocal, square root, and exponential functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If different schemes are selected for each elementary function, then calculation accuracy is maintained, but system complexity and operational difficulty increase
Solution Approach 1:
The patent applies a unified polynomial approximation scheme that can compute multiple elementary functions (reciprocal, square root, exponential, logarithmic) using the same computational framework. By representing functions as polynomials and using secret share values, the system achieves multi-functionality without requiring separate schemes for each function type, thereby reducing system complexity while maintaining calculation accuracy through parameter adjustment.
Solution Approach 2:
The patent utilizes parameter changes by adjusting polynomial coefficients and secret share values to compute different elementary functions using the same base scheme. Instead of changing the computational scheme for each function, the system modifies parameters (polynomial degrees, coefficients, and secret share assignments) to adapt to different function types, resolving the contradiction between accuracy and complexity.
2Adaptability or versatility
If multiple elementary functions are supported by a single scheme, then adaptability improves, but calculation precision may deteriorate
Solution Approach 1:
The unified polynomial approximation scheme provides adaptability by supporting multiple elementary functions through a single computational framework. The system maintains precision by using higher-degree polynomials and adjustable coefficients that can be optimized for each specific function while retaining the same overall scheme, thus achieving both versatility and accuracy.
Solution Approach 2:
The system dynamically adjusts polynomial parameters (degree, coefficients) based on the specific elementary function being computed. This dynamic adaptation allows the single scheme to maintain high precision across different function types by optimizing parameters for each case, rather than using fixed parameters that would compromise precision.
3Ease of operation
If polynomial approximation is used for secure computation, then ease of operation improves, but implementation complexity increases
Solution Approach 1:
The patent replaces complex secure computation operations with polynomial arithmetic operations that are easier to implement and verify. By substituting traditional secure computation mechanisms with polynomial evaluation and secret share manipulation, the system improves ease of operation while the modular polynomial framework actually reduces implementation complexity through standardization.
Data Source
AI summary
A secret share value [y]=[δx2+ax] is obtained through secure computation using a secret share value [x] of a real number x, and a secret share value [func(x)]=[y(ζy+b)+cx] of an elementary function approximation value z=func(x) of the real number x is obtained and output through secure computation using secret share values [x] and [y]. Here, x, y, and z are real numbers, a, b, c, δ, and ζ are real number coefficients, and a secret share value of · is [·].