Secure Computation Overflow Prevention via Pre-Shifted Polynomial Approximation
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Solution Overview
Problem
Secure computation faces challenges with overflow issues during right shifting or division based on public values, leading to incorrect calculations and degraded precision.
Innovation Solution
The method involves approximating functions using polynomial approximations, calculating the difference between the original and approximation functions, and then shifting this difference to prevent overflow, maintaining high precision by using secret share values and secure computation techniques.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If right shifting or division based on public value is performed by secure computation, then calculation speed is improved, but overflow occurs leading to incorrect calculation
Solution Approach 1:
The patent applies preliminary action by performing right shifting on the approximation function f'(x) before computing the difference ft(x)−f'(x). This pre-shifting prevents overflow in the subsequent subtraction operation while maintaining calculation efficiency. The approximation function is shifted by a predetermined number of bits before being subtracted from the target function, ensuring that the difference calculation does not overflow.
2Reliability
If right shift is performed to prevent overflow by decreasing bit allocation to decimal area and increasing bit allocation to integer area, then overflow is prevented, but precision is degraded
Solution Approach 1:
The patent applies local quality by making different parts of the computation have different bit allocation characteristics. The approximation function f'(x) is designed with a specific bit allocation (decreasing decimal bits, increasing integer bits) to prevent overflow, while the final result ft(x) maintains high precision through the mathematical relationship ft(x) = f'(x) + (ft(x)−f'(x)). This allows local optimization for overflow prevention without sacrificing global precision.
3Adaptability or versatility
If polynomial approximation is used to represent elementary functions, then secure computation becomes feasible, but overflow occurs during intermediate calculations
Solution Approach 1:
The patent applies preliminary action by pre-shifting the approximation function f'(x) before computing the difference. This ensures that intermediate calculations involving polynomial approximations do not overflow, while still maintaining the versatility of secure computation for elementary functions.
Solution Approach 2:
The patent introduces the approximation function f'(x) as an intermediary that mediates between the target function ft(x) and the final result. By computing the difference ft(x)−f'(x) with pre-shifted f'(x), the intermediary enables secure computation of elementary functions while preventing overflow in intermediate steps.
Data Source
AI summary
A secret share value [ft(x)−f′t(x)] of ft(x)−f′t(x) is obtained through secure computation using a secret share value [x] of a real number x, and a secret share value [ft(x)−f′t(x)]r of (ft(x)−f′t(x))r obtained by right-shifting ft(x)−f′t(x) by the predetermined number of bits is obtained through secure computation using the secret share value [ft(x)−f′t(x)]. Here, [μ] is a secret share value of μ, n is an integer equal to or greater than 1, t=0, . . . , n−1, u=1, . . . , n−1, ft(x) is a function of the real number x, f′t(x) is an approximation function of the function ft(x), a secret share value [f′0(x)] of an approximation function f′0(x) is [f′0(x)]=c0,0+c0,1[x], a secret share value [f′u(x)] of an approximation function f′u(x) is [f′u(x)]=cu,0+cu,1[x]+cu,2[f0(x)]+ . . . +cu,u+1[fu−1(x)], ct,0 is a public value, and ct,1, . . . , ct,n+1 are coefficients.