Numerical Splitting Device Secure Computation Efficiency
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Solution Overview
Problem
Existing secure computation methods require two multiplications and one division for product computation, which is computationally heavy, and are not applicable in moduli without an inverse of 3, limiting their efficiency and versatility.
Innovation Solution
A numerical splitting device and method that generate random numbers and compute segments based on a numerical value and parameter p, allowing for the transmission of shared values to secure computation devices for efficient product computation with only two multiplications, without requiring an inverse calculation and applicable across various moduli.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the existing secure computation method is used for product computation, then the computation can be performed in a split state, but the computational overhead is heavy due to requiring two multiplications and one division in each secure computation device
Solution Approach 1:
The patent changes the computational parameters by introducing a specific mathematical relationship where the sum of three random numbers is set to zero (r1 + r2 + r3 = 0). This parameter constraint transforms the product computation to require only two multiplications instead of two multiplications and one division, reducing computational overhead while maintaining security properties
Solution Approach 2:
The patent segments the computational task by dividing the product computation into separate operations performed by different secure computation devices. Each device performs only two multiplications on its segment of the data, and the results are combined through addition to obtain the final product, avoiding the need for division operations in each device
2Adaptability or versatility
If the existing secure computation method is used, then product computation can be performed, but the method cannot be applied in moduli where no inverse of 3 exists
Solution Approach 1:
The patent changes the mathematical parameters of the computation by eliminating the division operation that requires the inverse of 3. By reformulating the product computation to use only multiplication and addition operations, the method becomes applicable to any modulus regardless of whether the inverse of 3 exists, thereby improving adaptability without sacrificing reliability
3Productivity
If multiplication operations are performed in secure computation devices, then product computation is achieved, but the processing becomes heavy compared to addition and subtraction
Solution Approach 1:
The patent applies partial action by having each secure computation device perform only two multiplications instead of the full set of operations (two multiplications and one division). The remaining computational work is distributed through the addition of results from different devices, reducing the processing load on each individual device while still achieving the complete product computation
Data Source
AI summary
This numerical splitting device: acquires a numerical value w and a parameter p; generates a first random number r1 and a second random number r2; computes a third random number r3 based on the numerical value w, parameter p, first random number r1, and second random number r2 according to an expression, r3=w−r1-r2 mod p; computes first to third segments s1, s2, s3 based on the first to third random numbers r1, r2, r3 and the parameter p according to expressions, s1=r1+r2 mod p, s2=r2+r3 mod p, and s3=r3+r1 mod p; and transmits a pair of the first segment s1 and the second random number r2, a pair of the second segment s2 and the third random number r3, and a pair of the third segment s3 and the first random number r1 to first to third secure computation devices, respectively.