An interactive server implements a login challenge with a variant of Diffie-Hellman (for non-commutative groups) on the group of permutations of the Rubik’s cube. After computing a discrete logarithm on this (non-abelian) group, we can compute the handshake to log in as admin and obtain the flag.
![Can you extract admin’s private key from this cube?](https://duksctf.github.io/resources/2017/googlectf/rubik/admin.png)
See the link for a complete writeup with more graphics.