Using RSA to protect license files
===

I want to use RSA to protect license files in an application. The idea is as follows:

1. Create a license file (plaintext).
2. Create an RSA-keypair.
3. Use the public key to encrypt the license file.
4. Put the private key in the binary of the application.
5. The application can then decode the license file and start running.

The thing is that I have to ship the private key with my application. Is that a problem if I keep the public key secret?

If not, what other good (enough) schemes exist to create a license-file system?