Random Post Order Based On Category

So I want to be able to display random posts based on their category. I have a sidebar menu setup and have added ONLY categories to it, no pages. When the category is clicked, it currently displays all posts within it. This is all good, except I want it to display the post randomly. I have done this before using Page Templates per category, but I ended up having like 80 page templates. Is there any code that I can include within the index file to obtain the needed results? Thanks!