加密某些数据与签署某些数据(使用RSA)之间的区别是什么?

它只是颠倒了公共-私有密钥的角色吗?

For example, I want to use my private key to generate messages so only I can possibly be the sender. I want my public key to be used to read the messages and I do not care who reads them. I want to be able to encrypt certain information and use it as a product-key for my software. I only care that I am the only one who can generate these. I would like to include my public key in my software to decrypt/read the signature of the key. I do not care who can read the data in the key, I only care that I am the only verifiable one who can generate them.

签名在这种情况下有用吗?