qgis - Connect points and store point info in line attributes

I have a point shapefile where I want to connect all points (25 points that makes 600 pairs).

As a result, I need a line shapefile with attribute table that contains points lying on the line.

e.g.

lineID    pointID1    pointID2
  1          25          16

I've tried few plugins including points2one, MMQGIS, etc., but none of them worked.