6
There function in libsecp256k1 that allows you to directly set the field element to 32 bytes of your choice. Does secp256k1 always return a valid group element for any 32 byte value?
secp256k1_fe_set_b32(&xpoint, bytes)
secp256k1_ge_set_xo_var(ge, &xpoint, 0)
7
The size of secp256k1's coordinate field is 2256 - 232 - 977.
That means there are only 232 + 977 (about 4 billion) possible 32-byte combinations that are not a valid coordinate.
Only slightly less than half (around 2255 - 1.17 * 2127) of those are the X coordinate of a point on the curve (in fact, for every valid X coordinate, there are either exactly 0 or exactly 2 points on the curve).
