Who is Greider's father?

The Dark Valley (orig.: Das finstere Tal) has the American Greider visit a village in the Alps to exert revenge on the local patriarch Brenner for crucifying his mother's husband when they violated the rule that Brenner is the one to lie with every bride in the wedding night. But Greider's ultimate paternity is not entirely clear to me.

From the flashback presented during his "confession" in the church it seems that his mother ran away with her husband before Brenner could sleep with her (which was the whole point of fleeing afterall). Neither does there seem to have been any time for the couple to have sex during their escape and hiding in the tavern until they were captured by Brenner's men. But after the capture things went rather quickly, too, with Greider's mother fleeing the scene right during the crucification of her husband, so Brenner would have to have raped her right there in the snow. So it doesn't seem likely that Greider is either the son of his mother's husband, nor that of Brenner. Yet, it seems less significant for the impact of the story that he would just be the son of some random guy his mother met later in America or on her journey. And at the end, when Greider finally faces the old Brenner the scenery and its emotional presentation might suggest that Brenner is indeed his father. But he still speaks of his killed sons as "his" kin, not implying to also be Greider's.

So is there any definite answer as to who really is Greider's father? Can this be deduced from the movie alone and is Greider aware of it himself? Or was this deliberately left ambiguous? Does the novel maybe present further insight in this regard?