Secure Batch Approximation Using Segmented Low-Order Polynomials

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Solution Overview

Problem

In secure computation, calculating complicated functions through polynomial approximation requires high-order polynomials to maintain accuracy, leading to increased calculation time.

Innovation Solution

Divide the function into sections and approximate each section using a lower-order polynomial, allowing for batch calculation with reduced polynomial order without degrading accuracy.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Measurement precision

If the order of the polynomial is increased to improve approximation accuracy, then the approximation accuracy is improved, but the calculation time is increased

Engineering Contradiction:

Improveapproximation accuracyVSAvoidcalculation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent divides the function into multiple sections and creates separate low-order polynomial approximations for each section. By segmenting the function domain and applying localized polynomial approximations, the system achieves high approximation accuracy without requiring high-order polynomials, thus reducing calculation time while maintaining precision.

Inventive Principle:

Principle #1Segmentation

2Measurement precision

If the order n of a polynomial is increased, then the approximation accuracy is improved, but the number of times of addition-and-subtraction and multiplication is increased in O(n)

Engineering Contradiction:

Improveapproximation accuracyVSAvoidcalculation efficiency

Core Design Contradiction:

Measurement precisionVSProductivity

Solution Approach 1:

The function is divided into multiple sections with separate low-order polynomial approximations for each. This segmentation allows the system to achieve high overall approximation accuracy while keeping the polynomial order (and thus the computational complexity) low for each segment, improving calculation efficiency.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Different low-order polynomial approximations are used for different sections of the function, optimized for local characteristics. This local optimization allows accurate approximation without requiring high-order polynomials globally, reducing the number of operations while maintaining accuracy.

Inventive Principle:

Principle #3Local quality

Data Source

PatentUS12341885B2Secret batch approximation system, secure computation device, secret batch approximation method, and program

Publication Date: 2025.06.24 NIPPON TELEGRAPH & TELEPHONE CORP

AI summary

Calculation time is reduced without degrading approximation accuracy in calculation of a complicated function through secure computation. A secret batch approximation system calculates a concealed text [z] of an approximate value z for a function value y satisfying yj=f(xj) by using a concealed text [x] of a value x as input. g is defined as a polynomial for approximating each section of m sections into which the function f is divided. A parameter acquisition unit acquires a concealed text [a] of a parameter a corresponding to the value x for each integer j that is not less than 1 and not more than n, where aj is defined as a parameter pi corresponding to a section Ri including a value xj. A polynomial calculation unit calculates a polynomial g([x], [a]) by using the concealed text [x] of the value x as input based on the concealed text [a].