Brainsteem Mathematics Challenges: Powers of 2018

Haven't published in ages, so let's have a few warm-up questions over the next days.

Question

Find the last two digits of 2018²⁰¹⁸

(If you cannot see the superscript, this is 2018^2018.)

This is supposed to be done with just pen and paper; the actual number is too large for most programs anyway.

The first correct answer and further interesting comments will be rewarded with an upvote.

Enjoy!

More Brainsteems coming soon...