The problem with fixing a curve is that with enough memory, someone can do some pretty elaborate precomputation. This is part of the problem with NIST's ECC random number generator: you couldn't trust it not to have a back door. Indeed, Juniper found to their horror that their ECC systems did indeed have such a back door, although it isn't clear who else had the backdoor key -- NSA? Chinese? Israeli's? Russians? Better to take the hit on using RSA with seriously large primes, and carefully choosing different ones each time. At 09:03 AM 3/26/2016, Warren D Smith wrote:

It is more of a pain to use elliptic curve systems since you need to find a good curve, etc, which is not trivial. In contrast for RSA, finding suitable primes is pretty easy. However, that only needs to be done once, then the whole world can use just that one curve forever after. Standardize a good one.