I've been looking into elliptic curve cryptography, and have been trying to understand how I can and can't use it. Note that this is a hobby project and I am not making my own crypto systems for anything serious.
I am attempting to create an elliptic curve key pair that is dependent on outputs from other cryptographic functions. As far as I understand it, an key in ECC is based on a single point on the curve, as opposed to RSA which uses a pair of primes.
Does this mean that I can use random bits (or hash outputs) of the correct length as the private key of a curve such as Curve25519?
I've struggled to find information on this topic, but I do know that the soon-to-be released system SQRL (https://www.grc.com/sqrl/crypto.htm, "SQRL's underlying crypto technology") mentions using such a system. If I haven't understood it right, how is this working?