Today I was having a discussion with my cryptography lecturer about the keyspace of a ROT-13 cipher. He argues that the keyspace is 0 because it doesn't have a key.
Could anyone explain to me why the keyspace is 0 and not 1? I could understand if he said that it doesn't have a keyspace but I don't understand why it could have a keyspace of 0.
I was further confused when he said that it was possible for a cryptographic function to have a keyspace of 1. Could someone give me an example of a cryptographic function with a keyspace of 1 and explain how it is different to one with a keyspace of 0?
I feel fairly confused about something that seems like a pretty basic concept.
Thanks for any help.