I told my boss I had an idea for a program that could improve efficiency across much of the business, and he let me build it on company time. In the long term, he wanted to be able to sell it to other companies. However, the program never got implemented due to personnel mismanagement, and I’d rather be able to post it on my github under a free licence so I can use it as a resume item, and at least someone would have the chance to actually use it. It’s all still in my head, and I could write it again if I wanted. If I do, is it illegal to publish it? What if I write it in a different language? Do I need to change the variable names? I did plenty of research and planning on company time to build it, and it’s not like I can research it again, it’s all still in my head.
check carefully what you signed. If you didn’t sign anything saying otherwise, there’s nothing to prevent you from doing it.
If there’s something, you could still work around it (e.g. remove company secrets).
If the resulting product is provable better, then it’s objectively not the same thing you did for your boss.
After checking all of this, your local FSF might give you free legal advice to get going (keep all notes/correspondence secure for later if anything comes up. It proves you tried to act responsibly).