More "sales pitch" comes from this IETF draft: While the NIST curves are advertised as being chosen verifiably at random, there is no explanation for the seeds used to generate them. In contrast, the process used to pick these curves is fully documented and rigid enough so that independent verification has been done. This is widely seen as a security advantage, since it prevents the generating party from maliciously manipulating the parameters. – ATo Aug 21, 2016 at 7:25
An argument why Ed25519 signature alg & Curve 25519 key exchange alg is more secure; less vulnerable to side attacks since the process that generates is have been purportedly verified and extensively documented.
