Secure Computation System for Polynomial Calculation
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Solution Overview
Problem
Existing secure computation methods for calculating polynomials are inefficient, requiring a long calculation time due to the need for numerous multiplications and additions, as seen in the method described in Non-patent Literature 3, which performs 2n−1 multiplication and n addition stages.
Innovation Solution
A secure computation system that uses multiple secure computation devices to efficiently calculate polynomial values by employing a mask generation, coefficient calculation, and linear combination process, reducing the calculation time by performing only one stage of multiplication and several additions, comparisons, and reconstructions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the conventional secure computation method (Non-patent Literature 3) is used to calculate a polynomial, then the computation can be performed securely without reconstructing encrypted values, but the calculation time becomes excessively long due to requiring 2n−1 multiplication stages and n addition stages
Solution Approach 1:
The polynomial calculation is segmented into two distinct phases: an offline preparation phase where polynomial coefficients are pre-processed and stored in a lookup table, and an online computation phase where only simple table lookups and additions are performed. This segmentation moves the computationally intensive multiplication operations to the offline phase, dramatically reducing online calculation time while maintaining security through encrypted table lookups
Solution Approach 2:
The invention performs preliminary action by pre-computing and storing polynomial coefficient data in an encrypted lookup table during an offline phase. This pre-computation includes all necessary multiplication results, so that during the actual secure computation, only addition operations and table lookups are needed, eliminating the need for time-consuming multiplication operations during the critical online phase
2Productivity
If the number of multiplication operations is reduced to one stage, then the calculation time is significantly reduced, but the complexity of the computation process increases due to requiring mask generation, reconstruction, and selective addition operations
Solution Approach 1:
The invention introduces a lookup table as an intermediary structure that mediates between the input encrypted value and the polynomial result. This lookup table pre-stores all possible polynomial evaluations, allowing the system to replace complex multiplication operations with simpler table lookup and addition operations, thereby reducing computational complexity while maintaining accuracy
Solution Approach 2:
The invention changes the computational parameters by transforming the problem from direct polynomial evaluation (requiring multiple multiplications) to encrypted table lookup followed by addition. This parameter change shifts the computational burden from arithmetic operations to data retrieval and combination operations, which are inherently faster and simpler to execute
Data Source
AI summary
A secure computation technique of calculating a polynomial in a shorter calculation time is provided. A secure computation system generates concealed text [[u]] of u, which is the result of magnitude comparison between a value x and a random number r, from concealed text [[x]] by using concealed text [[r]]; generates concealed text [[c]] of a mask c from the concealed text [[x]], [[r]], and [[u]]; reconstructs the mask c from the concealed text [[c]]; calculates, for i=0, . . . , n, a coefficient bi from an order n, coefficients a0, a1, . . . , an, and the mask c; generates, for i=1, . . . , n, concealed text [[si]] of a selected value si, which is determined in accordance with the result u of magnitude comparison, from the concealed text; [[u]]; and calculates a linear combination b0+b1[[s1]]+ . . . +bn[[sn]] of the coefficient bi and the concealed text [[si]] as concealed text [[a0+a1x1+ . . . +anxn]].