Someone correct me if I'm wrong here, but I always thought the right vs. left hand thing dated back to Roman culture. You were taught to carry daggers in your right hand so greeting someone by shaking with your right hand was a show of no aggression. If you could shake hands with your right, then you didn't have a dagger at the ready. So shaking hands with your left was looked down on as dishonest.
I never thought about eastern cultures dealing with it separately, but it makes sense to greet each other with your "food" hand as opposed to your other... It could be random luck that they chose their right hand like the Romans did (or maybe being left handed is genetically recessive and all cultures tend to choose the right hand). Of course, Russian engineers use the "Left Hand Rule" where we in the west use the "Right Hand Rule" so I guess take my speculations with a pillar of salt :blahblah: