I'm thinking about the evaluation of a cipher or separate cipher round as a PRNG. In general, we can encrypt consecutive natural numbers and check them with some randomness test. But PRNGs don't work like this. They use their output like a new input.
Shouldn't it be like that the ciphers should have long periods in such a test? Do they have long periods? If not, they should not be considered good PRNGs, correct? And is it possible that a cryptographically secure PRNG will have a short period for some inputs?