Page 30 - KVIS Book

MAT02I

Public Key Cryptography Using P X P X P Rubik’s Cube Group

Pasawat Viboonsunti, Sirada Rungruengsakorn
Kamnoetvidya Science Academy, Thailand
Supervisor: Wasanont Pongsawat
Email: sirada_r@kvis.ac.th

Nowadays, the communication is faster and more widespread than before. This means
the security is harder to be maintained. The study of secure communication is called
Cryptography. If the communicators didn’t know each other beforehand, the security
would rely solely on the complexity of computation, this is where mathematics take
place in cryptography.

The purpose of this project is to construct the new cryptography to apply to this case.
Utilizing the group theory, we based our cryptography on p x p x p Rubik’s cube group.
This is to find an alternative cryptosystem and possibly improve or even replace the
current cryptosystems.

We first defined the group by defining faces, moves, set, operation, and exponent
operation. Next, we created an effective algorithm to match every configuration of the
cube to a unique integer. Lastly, we applied the p x p x p Rubik’s cube group to the
Diffie-hellman key exchange protocol. This protocol is for the communicators to agree
on a single move without letting the adversaries knowing it.

In conclusion, we have created a cryptography that works like this. If two people want
to exchange secret message, both have to use the Diffie-hellman protocol to agree on
a secret move. Then, the sender has to change the message into a configuration of a
cube using our algorithm. That configuration will be processed by the secret move and
will be sent to the receiver. The receiver would do the reverse and obtain the message.
Without the secret move, the adversaries will never know the message. For the future
plan, we will test the algorithm and compare it to the existing cryptosystem, then we
will decide whether our cryptosystem should replace existing cryptosystem or not.