Secret Sharing Key Management Based on Magic Cube

Abstract

The protection of secret and sensitive data shared through internet network is one of the most important issues that faces internet users. Despite the advance technology emerged lots of solutions to secure secret data sharing, but still the data sharing matter through an open environment is the main challenge. The sharing secret methods play great role in the key management strategy for the sensitive data and the cryptographic keys in terms of generation, exchange and managing in a secure method. The secret sharing scheme built based on proven mathematical concepts that allows the dealer to distribute the secret keys among several participants securely. In this thesis four new mathematical algorithms were proposed which completely based on the magic cube’s principles and the Lagrange mathematical background. The first algorithm relied on generation an odd order folded magic cube that exploits the pivot element of the first magic square in magic cube to be the secret and then embedded in polynomial equation. The pivot element will support in transfer the magic cube properties to the participants to be able to reconstruct the original magic cube again. The Hermite interpolation mathematical method was used in the second algorithm which considers more complex than the Lagrange interpolation method. Because, it depends on the derivative of polynomial and Lagrange derivative in the process of constructing and reconstruction the secret by the dealer and the participants. The third algorithm assumes that the dimension order (N) of the magic cube is the secret key that will be embedded within the polynomial equation and sent to the trusted subscribers. The participants will be able to get the secret (cube dimensions) after using the Lagrange interpolation. The algorithm requires finding the start number and the difference value between the magic cube elements to reconstruct it again. The third algorithm can work with different types of magic cubes of (odd order, singly or doubly even order). The fourth proposed algorithm is newton’s divided difference numerical analysis mathematical method. The newton interpolation was applied on the second polynomial algorithm and showed good results compared with its predecessor in the process of protecting the secret keys. The process of integrating the secret sharing methods with the mathematical characteristics of magic cubes gave a great flexibility in X dealing with different numerical analysis methods. The proposed secret sharing methods have been tested and measured according to some important metrics like the elapsed time and the computational complexity factor. The implemented tests indicated a reasonable and accepted results for the secret computation. All adopted numerical analysis methods provided good results during the process of sharing the secret and gave the necessary protection in trusting the sensitive information. The proposed methods produced distinct results and put the users in front of multi-options in choosing the appropriate way to transfer their confidential and sensitive information to the trusted subscribers in order to protect them from theft, loss or the risk of cryptanalysis. The proposed methods were programmed by Visual Studio 2016 C# programming language under Windows-10 Ultimate version of 64-bit operating system using processor core (TM) i7-77HQ CPU @ 2.80 GHz, Ram 16.0 GB, HD 1TB, and 4GB VGA.