The answer is that no, there isn't a secure license key algorithm that doesn't require a mathematical diploma to understand.
The best license keys are the ones digitally signed with an asymmetric encryption algorithm. You sign the key data with a private encryption key and embed the signature in the key, and the key validation (which implies signature verification among other things) is done with a public key. This way, no one can create license keys unless they have access to the private key which is...private. The problem is that there are very few (and difficult) algorithms which have sufficiently short signature sizes to be embedded in a product key. RSA is not one of them (signature size for RSA512 is 1024 bits - too much).
You can check out SoftActivate Licensing SDK it uses elliptic curve cryptography to generate short, digitally signed license keys (C++/C# source code is available).
