If the work is a “clean room” reverse engineering job, as in: you didn’t read the original source to produce your version but rather looked at the input and output and wrote new software that had the same behaviour, the this new software is not a derivative work and you can use whatever license you like.

The easy option is public domain, which effectively is a “this belongs to everyone” thing. There’s not much of a practical difference between this or MIT in my understanding.

Another option would be something that preserves the freedoms you attach to the software like the GPL or LGPL if youre feeling less aggressive. These licences compel would-be modifiers to share their changes with everyone else, preventing (for example) companies that want to build their business on top of your work and then charging you for it.

But basically, if you wrote it without referencing the original, it’s your work and you can do as you like. If you were referencing the original source though, then that’s a derivative work and you may be in violation of the copyright holder’s rights.