Secure Exponential Function Computation via Bit Decomposition
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for secure computation, such as those described in NPL 1, are computationally expensive and inefficient for calculating exponential functions.
Innovation Solution
A secure exponential function computation system and method that utilizes a plurality of secure computation apparatuses, each equipped with units for minimum value subtraction, bit decomposition, selective product calculation, upper bit calculation, lower bit calculation, exponential function calculation, and result calculation, to efficiently compute the exponential function by approximating it using an eighth degree polynomial.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If existing secure computation methods are used to calculate exponential functions, then computation security is maintained, but computation speed is slow and computational cost is high
Solution Approach 1:
The patent segments the exponential function computation into multiple discrete steps: minimum value subtraction, bit decomposition, selective product calculation, upper bit calculation, lower bit calculation, and result combination. Each step is handled by a dedicated functional unit, breaking down the complex exponential computation into manageable segments that can be processed efficiently in parallel or sequence.
Solution Approach 2:
The patent transforms the exponential function computation by changing parameters through bit decomposition. The input value is decomposed into bit representations, and the exponential computation is performed by selectively multiplying pre-computed values based on these bits. This parameter transformation converts a complex continuous function into discrete operations that are more efficient to compute.
2Productivity
If existing secure computation methods are used to calculate exponential functions, then computation security is maintained, but computational efficiency is low
Solution Approach 1:
The patent performs preliminary actions by pre-defining the minimum value and performing bit decomposition early in the computation process. The selective product unit pre-calculates mantissa parts for different bit positions, and these pre-computed values are then combined efficiently. This preliminary preparation reduces the computational burden during the main exponential function calculation.
Solution Approach 2:
The computation is segmented into distinct functional units that can operate independently or in parallel. The bit decomposition unit, selective product unit, upper bit calculation unit, lower bit calculation unit, and result calculation unit each handle specific portions of the computation, improving overall computational efficiency through modular processing.
3Reliability
If secure computation is used for advanced statistics or machine learning, then data privacy is protected, but computation speed decreases due to complex operations like inverse, square root, exponent, and logarithm
Solution Approach 1:
The patent applies parameter changes by representing the input value in bit-decomposed form and transforming the exponential function computation into selective multiplication of pre-computed mantissa values. This parameter transformation maintains data privacy through secret sharing while significantly improving computation speed by avoiding direct evaluation of the exponential function.
Solution Approach 2:
The patent substitutes the direct mechanical computation of the exponential function with a different computational mechanism: bit decomposition followed by selective multiplication. This substitution replaces a computationally intensive operation with a series of simpler operations that maintain the same mathematical result but execute much faster in secure computation environments.
Data Source
Figure 1
Figure 2
Figure 3
AI summary
In secure computation, an exponential function is calculated at high speed. A secure exponential function computation system (100) receives [a] as an input and calculates [exp (a)]. The minimum value subtraction unit (11) calculates [a']: = [a] - µ. A bit decomposition unit (12) generates a bit representation [a'0], ..., [a'u - 1] of u upper bits of a' from [a']. A selective product unit (13) calculates a total product [f'] of values that are [a'i?fi:1]. An upper bit calculation unit (14) calculates a total product [ε'] of [a'i?2ε_i:1] for 0 ≤ i < u. A lower bit calculation unit (15) calculates [a'ρ]: = [a'] - ∑2i - t[a'i]. An exponential function calculation unit (16) calculates [w]: = [exp (a'ρ)]. A result calculation unit (17) calculates [w][f'][ε']exp (µ).