Is it illegal to work for a completing company owned by former employees of my current employer?

I would like to leave my current employer and work for a competitor. The competing company was started by my current employer's former VP and one other former employee. Both former employees lost their jobs and had at no point in time signed a non-compete agreement. I have not signed a non-compete agreement. I do not believe that my current employer can claim that I will violate any trade secret agreements, as almost everything produced in this industry is copied from someone's old design and the designs are, for the most part, easily available to anyone who wants to produce them. It seems to me that I would be able to work for any competitor regardless of who they were formerly employed by. Is that true or will I run into legal problems if I make this move?