Secure Computation Log Mapping for Efficient Division
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing secure computation methods face inefficiencies in performing division operations, particularly in correcting the number of digits and handling numerical ranges during division by secure computation.
Innovation Solution
The analysis device employs secure computation to acquire shares of logarithmic values through mapping, calculates the difference between these shares via subtraction, and then obtains the exponential value of the difference using secure computation, thereby efficiently performing division.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If division is performed by converting to multiplication a×(1/b) using a conversion table, then division can be performed, but the number of digits increases requiring correction and the numerical range is restricted
Solution Approach 1:
The patent transforms the division operation parameters by converting the problem domain from direct division to logarithmic subtraction. By changing the mathematical representation from a/b to log(a) - log(b), the operation benefits from the properties of logarithms where the result naturally maintains appropriate digit length without requiring post-calculation correction, thus resolving the digit correction complexity issue while preserving division efficiency
Solution Approach 2:
The patent introduces logarithmic values as an intermediary representation to facilitate division operations. Instead of directly computing a/b or a×(1/b), the system uses log(a) and log(b) as intermediate forms, performs subtraction on these intermediaries, and then exponentiates the result. This intermediary approach eliminates the need for digit correction that plagues direct multiplication-based division methods
2Productivity
If multiplication is used for division calculation, then division can be performed, but the numerical range is narrower than addition and subtraction
Solution Approach 1:
The patent fundamentally changes the mathematical parameters of the operation by working in the logarithmic domain. Since logarithmic subtraction log(a) - log(b) = log(a/b) has no inherent numerical range restrictions like multiplication, the method inherits the broader range characteristics of addition and subtraction operations while still achieving division functionality, thus resolving the numerical range limitation
Data Source
AI summary
An analysis device includes a memory and processing circuitry configured to acquire a share of a logarithmic value of a first value and a share of a logarithmic value of a second value by mapping of secure computation, calculate a difference between the share of the logarithmic value of the first value and the share of the logarithmic value of the second value by subtraction of secure computation, and acquire an exponential value of the difference by mapping of secure computation.