1) addresses are hashes of public keys, not public keys themselves, so you can't really figure out the private key even with magic / quantum computing.
2) 21 million BTC * 100 million divisions = 2.1 quadrillion < maximum integer uniquely representable by a (double-precision) float (~2^50.9 < 2^53), handy for simpler programming.
3) elliptic curve chosen wasn't one of the dubious NIST ones.
The article is pretty well written, IMO, and does a reasonable job explaining why these are issues in the first place, and how it avoids them. Probably worth a read unless you grok it all from the tl;dr, and even then since it might help you explain things to others.
In essence, apart from 2, which wouldn't take too much hindsight to calculate, both items seem to be the work of a real expert in crypto.
Not the ones that go for the "proven" way "because NIST said so" or the "internet specialists" that cry wolf more often than not (and miss or even suggest security holes)
Not really. The original bitcoin client did what was called direct-to-IP transactions, which didn't use hashed pubkeys, and which was vulnerable to man-in-the-middle attacks (oops).
Bitcoin's ECDSA curve was chosen because it was one of the faster ones, not because of any NIST connection (a "real" cryptographer of the day would have probably advised against the secp256k1 curve used in bitcoin in favor of one of the NIST curves, or DJB's curve which is superior in just about every way.
My point, perhaps too subtle, was that in 2009 there was not sufficient public evidence to suggest such weakening. Rather, the reigning opinion (supported by historical evidence) was that NIST/NSA routinely strengthened standards by selecting parameters so as to make the algorithm secure against publicly unknown mathematical attacks. That is, after all, their stated purpose and what they did with the DES S-boxes.
Turns out, the NSA is a shadow of its former self. But you'd have to have had non-public insider information to have known that with confidence in 2009.
1 is a little hokey because in the common case, the hash is just a weakness -- it doesn't add any security against classical computers, for which ECDSA is already hard enough, and it opens the possibility of hash collisions.
I say "common case" because it only really is a win if _both_ quantum computers are in use _and_ you've never spent from the wallet and never will (except possibly to cash out entirely).
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edit: tl;dr of it all is:
1) addresses are hashes of public keys, not public keys themselves, so you can't really figure out the private key even with magic / quantum computing.
2) 21 million BTC * 100 million divisions = 2.1 quadrillion < maximum integer uniquely representable by a (double-precision) float (~2^50.9 < 2^53), handy for simpler programming.
3) elliptic curve chosen wasn't one of the dubious NIST ones.
The article is pretty well written, IMO, and does a reasonable job explaining why these are issues in the first place, and how it avoids them. Probably worth a read unless you grok it all from the tl;dr, and even then since it might help you explain things to others.