The paper "High-speed high-security signatures" by Bernstein et al. introduces the Edwards curve Ed25519.
Concerning the base point $B$, it says that
- $B$ is the unique point $(x, 4/5)\in E$ for which $x$ is positive, and
- $B$ corresponds to the basepoint used on the birationally equivalent curve Curve25519.
The actual coordinates of $B$ are: [15112221349535400772501151409588531511454012693041857206046113283949847762202, 46316835694926478169428394003475163141307993866256225615783033603165251855960]
I'm not sure I fully understand the choice of this point:
I can't really see that $B$ is unique and that '$x$ is positive'. (What does positive mean here?)
Does this point have any special security properties that other points do not have, or is it just a 'rigid' choice to convince us that no backdoor was built-in?
If you know anything about this point, please tell me! Many thanks!