We had the objective of minimizing the surface area for attack, so we did not want to expand the scope to include non-ECDSA algorithms. Utilizing the same curve as Bitcoin (secp256k1) has a number of advantages, not the least of which is incentivizing the verification of its security (not to mention, the integrity of the secp256r1 curve is in doubt).
Furthermore, the path to building a clean user experience around a clean Javascript library that runs [and performs] well in all browsers is much less tenuous than getting browser support for a new algorithm — lending to faster innovation.
For other readers, here is some discussion of secp256k1 security. (You mention r1 above, but BitAuth references k1?)
http://blog.cr.yp.to/20140323-ecdsa.html https://bitcointalk.org/index.php?topic=380482.0 http://lists.randombit.net/pipermail/cryptography/2014-Janua...
The attacker can't imitate you because the site has your public key already.
And if all authentication is done client-side with javascript, the attacker could steal your private key and use it to attack other sites.
The point I'm trying to make is that if you can trust SSL to protect a BitAuth signature, you can also trust it to protect a password. So claiming "passwords may travel over plaintext" as a relative advantage of this scheme is disingenuous; in both cases, you need to provide that protection at a lower protocol level.
Also, it seems a little questionable to claim "passwords may travel over plaintext" as a benefit of BitAuth over password authentication. My initial impression is that when not using HTTPS, BitAuth is more secure than password authentication against a passive adversary, but that both are equally vulnerable to MITM attacks.