Quote from: kTimesG on Today at 10:50:01 AM

Quote from: Valera909 on Today at 08:58:01 AM

Let’s assume we know the private key k lies within a limited range:

k ∈ [-1000, +1000] mod N
...
That’s 1 bit of information recovered via curve symmetry and limited search space.
That’s useful:

In biased brute-force attacks

This only works when you're trying to find the private key of a known public key. For address puzzles, you can't shift the search interval. And for public key puzzles, brute-force is not used because exponentially faster algorithms exist (and some already take advantage of the curve symmetry).

That's a solid and worthy response — agreed.
However, curve symmetry alone reduces the search space by at least 2×, even before taking into account the full stack of optimized algorithms.

As for determining whether a point is the interpreted negative (i.e., reflection) on the curve,
is there a faster method than direct computation for checking it?