Partial Modular Exponentiation for Secure Computation
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Solution Overview
Problem
Current secure computation methods for modular exponentiation are inefficient in terms of communication amount and number of communications, particularly when keeping the exponent secret, as they require large communication volumes and frequencies.
Innovation Solution
An information processing apparatus and method that performs partial modular exponentiation calculations using shared exponents, allowing for efficient calculation of modular exponentiation results without revealing the shared exponents, utilizing a (2,3) RSS scheme to minimize communication and maintain secrecy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional secure computation methods are used for modular exponentiation, then security is maintained, but communication amount and number of communications become large
Solution Approach 1:
The exponent a is divided into multiple shares a1, a2, a3 such that a = a1 + a2 + a3 mod p. Each share is distributed to different apparatuses, allowing modular exponentiation to be performed through local calculations without requiring large communication volumes while maintaining security through the secret sharing mechanism
Solution Approach 2:
The patent introduces a modulus p as an intermediary element that enables efficient computation. By performing calculations in the modular field defined by p, the system achieves both security and computational efficiency, reducing communication requirements compared to conventional methods
2Reliability
If conventional secure computation methods are used for modular exponentiation, then security is maintained, but number of communications increases
Solution Approach 1:
The computation is segmented into local operations at each apparatus. Each apparatus performs modular exponentiation on its own share independently, eliminating the need for multiple sequential communications and reducing the number of communication rounds while maintaining security through the distributed share structure
Solution Approach 2:
The shares a1, a2, a3 are prepared and distributed in advance before the modular exponentiation computation. This preliminary distribution allows the actual computation to proceed with minimal communication, as each apparatus already holds the necessary share information to perform local calculations
Data Source
AI summary
An information processing apparatus comprises a partial modular exponentiation calculating part and a partial modular exponentiation synthesizing part. The partial modular exponentiation calculating part is given a base in plaintext and a modulo in plaintext and shared exponents and calculates a partial modular exponentiation that equals a set of shared values according to a modular exponentiation of the base raised by the shared exponent. The partial modular exponentiation synthesizing part calculates shared values of the modular exponentiation from the partial modular exponentiation that equals shared values relating to the modular exponentiation of a sum of shared exponents.