Abstract:
Modular inversion is a frequent and time-consuming operation in cryptography and algorithmic number theory. Since modular inversion requires many operations on large numbers, resource-constrained clients like mobile devices and IC cards cannot directly perform it.
This project proposes a novel unimodular matrix transformation technique to secure modular inversion outsourcing. This method gives our algorithm amazing properties. To our knowledge, it is the first secure outsourcing computation algorithm that supports arbitrary and variable modulus, eliminating the restriction in previous work that the protected modulus must be a fixed composite number.
Second, our algorithm avoids the multi-server non-collusion assumption by using the single untrusted program model. Third, modular inversion only requires one round of client-cloud server interaction and allows the client to verify the cloud server’s results with optimal probability 1. We also propose a multi-variable modular inversion secure outsourcing algorithm.
Our algorithms save local-client computations, according to theoretical and experimental results. Finally, the outsourced RSA key generation and Chinese Reminder Theorem are two important and useful applications of our algorithms.
Note: Please discuss with our team before submitting this abstract to the college. This Abstract or Synopsis varies based on student project requirements.
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