No. DMCA makes most breaking of encryption illegal when used to circumvent copyright. "Most" because it has exemptions even for copyright circumvention. This is a very limited place to make it illegal.

I can probably think of hundreds of places you can still do it and it's not illegal. Some examples: in school classes to learn, at home for practice, researchers attacking each others new algorithms, estate clearance to get dead person assets released, for interoperability in may cases, for archiving old things in many cases, and on and on.

In fact, almost any place I can think of where I might break encryption (which I have done both as a hobby and professionally and as while a PhD student) is perfectly legal. It becomes illegal when used to do something else illegal, like violating copyright, or stealing things.

So no, breaking encryption is not illegal as a whole.

Here, break this: Lbh qvqa'g oernx gur ynj.