I am currently writing a thesis about different cryptographic protocols like DH-Key exchange, TLS or IKE. Most of them rely on a prime number earlier or later, so for security reasons I wondered if this prime number is supplied by the user and if yes that leads to the question if I can manually provide it (for example to use a pseudoprime to break the underlying primitive more easily).

I really tried to search online, but there are very little information about this part of protocols. I hope you can help me with that.

Thank you for your time and answers :)