So how can we find out if our addresses are "weak"?
You can't.
I'm no expert on elliptical curves, but basically it seems to come down to this:
- Every address is a point on the elliptical curve, described by a triplet.
- Evil has mapped 768 by himself, and is currently mapping thousands more of rendezvous points - fixed points on the curve.
- Your address might, or might not be "close" to any given rendezvous point.
- If it is, he can crack it in a short time, by using an arc-attack. That is, he can figure out a tiny portion of the curve, and attack it.
- If your address is within this tiny arc, it's weak.
- As he adds more rendezvous points (i.e. platforms of attack), every address potentially falls into his attackable zones.
A few things:
1. We do not know how far from a rendezvous point he can reasonably attack.
2. We have no context on how many rendezvous points make a problem - i.e. 768 points could be a serious issue for a large portion of the namespace, or 150 million could be non-serious. We just don;t know this.
3. The namespace is ENORMOUS.
4. The chances of any given address falling in an attackable space appears to be very small.
5. The addresses in use are (we must assume) randomly distributed
6. This means any address could be weak or strong, and we cannot know this either.
Until Evil can do two things, nobody can know if this is a threat:
a. Actually crack an address. He's given a script which should generate a weak address. So anything output by that should have been cracked quickly. i.e. by now.
b. Publish how far from any given rendezvous point his attack can go, and the portion of the curve in total he can attack.
To expand that last point a bit:
Total namespace: 2^160.
Rendezvous points: 768 (at this time)
Divide the namespace by the points and that's a hell of a lot of black space which cannot be attacked.
If he can go 50 trillion points to either side of the points, this might not be a very big portion of the namespace at all.
On the other hand, if Evil has figured out a way to work with only the used namespace, then Bitcoin is in serious shit.
Rit.
PS: I might have alot of the above surmises wrong. I'm no mathematician, and I'm certainly no cryptographer.
