This repository is my honor thesis in fields of abstract algebra and cryptography under the supervision of Professor Tommy Ratliff at the Mathematics department of Wheaton College.
Rubik’s Cube, estimated to be the world’s besting-selling toy, is a fascinating puzzle that we believe most people have attempted to solve. However, as anyone who has tried knows, Rubik’s Cubes are hard to solve. Cryptography shares the essence with playing Rubik’s Cubes; to fix the scrambled pattern. In this thesis, we discuss the advantages and challenges of using the Rubik’s Cube as the basis of an encryption system.
We start by discussing what cryptography is and listing motivations for us to integrate Rubik’s Cubes with encryption protocols. While presenting the design ideas of the Rubik’s Cube encryption, we consider limitations and make corresponding improvements. Then, under the formal definition of security, we test if our Rubik’s Cube encryption is well designed, and tweak it to make the encryption protocol better under the definition of security. Finally, we illustrate some known structures of the Rubik’s Cube groups and introduce a Rubik’s Cube key exchange protocol, which has a similar structure that the Diffie-Hellman key exchange protocol uses.
Click here to view the thesis itself and click here to download it.
This thesis is licensed under CC-BY-SA-4.0.