A function that maps an arbitrary length message to a fixed length message digest is a collision-free hash function if
1. It is a one-way hash function.
2. It is hard to find two distinct messages that hash to the same result . More precisely, any efficient algorithm (solving a P-problem) succeeds in finding such a collision with negligible probability (Russell 1992).
More things to try:
Weisstein, Eric W. "Collision-Free Hash Function." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Collision-FreeHashFunction.html
that maps an arbitrary length message 
to a fixed length message digest 
is a collision-free hash function if
that hash to the same result 
. More precisely, any efficient algorithm (solving
a P-problem) succeeds in finding such a collision with
negligible probability (Russell 1992).
