[amluto]

> An asymmetric key generation algorithm can't work from a fixed length seed. You need to stretch the seed to an arbitrary length, because the asymmetric key generator requires a random stream.

That may or may not be true for traditional DH. For ECDH it's false. A Curve25519 ECDH private key, for example, is quite literally a handful of random bits. (Depending on how you look at it, it's a 256-bit number with some fixed bits or just 252-ish bits. I say "ish" because I don't remember the exact number of fixed bits off the top of my head.)

Edit: Fixed bogus EdDSA reference. Also, I just looked it up. A Curve25519 private key (http://cr.yp.to/ecdh.html) indeed requires exactly 252 random bits (or the 252-bit output of a secure KDF).