Entropass generates site passwords on the fly using a hashing algorithm based on your master passphrase, private key file, and the domain of the site. The private key is saved in your browser, and the domain is automatically populated, so all you have to do is type in your master passphrase each time you login to a site.
Everyone is free to use the Entropass password generation algorithm in their commercial or non-commercial software. It is based entirely on standardized cryptographic technologies that are commonly available in libraries across many languages. This is the pseudocode for the core algorithm:
secret = passphrase + resetCount + sha512(privateKey)
password = b85encode(pbkdf2_hmac('sha512', secret, salt=domain, rounds=100))
The full Python implemenation is just 13 lines of code with no dependencies and is available here.
You can increment the reset count to generate a new password for that site.
You can use any file as a private key, as long as it has never been sent over the internet or shared with anyone else. For example, you could take a picture of yourself or just type a lot of random characters into a text document. Another option is to write a simple program and use the program's output as your private key. The advantage of this is that you can reconstruct your private key if you ever lose all copies of it, as long as you remember how to write the program.