Rubie-Cubeman

Symmetric-key cryptography requires that both the sender and recipient of a secure communication share the same private key. Symmetric-key cryptography relies on the use of a trusted third party to share the private key between the communicating parties. Unfortunately, the use of a shared private key is the main drawback of the symmetric-key system. This is because the private key is susceptible to attacks when it is being shared. Asymmetric, or public key exchange protocols address this issue by implementing the use of public-private key pairs.

The Rubie-Cubeman public-key exchange protocol is a new tool for visualizing the asymmetric key-exchange relationship applied by the Diffie-Hellman key exchange, but in a simplified and interactive manner that makes for an excellent educational tool. It is currently being developed by Dr. Ryan Henry for an academic paper he is writing. The Rubie-Cubeman protocol bears similarity to the Diffie-Hellman protocol but with a second consecutive round of public key sharing to address the non-commutativity of the Rubik’s Cube group. We’ve created the Rubie-Cubeman public-key exchange protocol visualizer to demonstrate this protocol.

It is important to note that the cubes can be extrapolated far beyond the complexity of the 3x3 cube shown here. To increase security against brute force attacks one could use a 100x100 or even a 1000x1000 cube, for example. This is analogous to increasing cryptographic constructions and security parameters. Further, the paper details one-way functions that include Binary Rubik’s Cube Exponentiation and Baby-Twists/Giant Twists that can significantly increase security against cryptographic attacks. These are complex and mathematically intensive functions which will not be demonstrated in our model.

Let’s say both Alice and Bob each start with a solved Rubik’s Cube.

Alice and Bob establish a shared secret in the form of the cube move sequences, G and H.
Alice and Bob also establish their own pair of secret values, [a_o, a₁] and [b_o, b₁] respectively, which they will not share.
Alice and Bob each apply the first shared sequence of moves, G, to their solved cubes. Alice applies G, a_o number of times, and Bob applies G, b_o number of times.
The cubes are then exchanged between Alice and Bob. Eve, a potential eavesdropper, could observe this interaction and what the cubes look like in this state, but not the sequence of moves to get to that state.
With the cube Alice received from Bob, Alice applies move set G, a_o number of times, and then applies move set H, a₁ number of times. Similarly, Bob applies move set G, b_o number of times, and then applies move set H, b₁ number of times to the cube Bob received from Alice.
The cubes are exchanged once again, also observable by Eve.
Now, Alice applies H, a₁ number of times to the cube Alice received back from Bob, and Bob applies H, b₁ number of times to the cube Bob received from Alice.

If done correctly, both cubes should result in identical configurations, which is the shared secret key between Alice and Bob. Fortunately for Alice and Bob, Eve has no way of finding out what their private keys, [a_o, a₁] and [b_o, b₁], are from the cubes.

About