At 02:19 AM 7/7/03 -0700, Sarad AV wrote: or how are we supposed to

find collision free hash functions?What exactly is the difficulty in finding collision free hash functions?

Because there are no collision *free* hash functions, there will always be several domain elements that map to the same range element. Assuming more domain elements than range elements, which is generally what people mean by hashing. You're not asking the right question, you need more constraints on the type of hash functions and their resistance to collisions. You're probably looking for functions that make it hard to intentionally find arguments that produce hashes identical to a given one. There's an incredibly dry taxonomically-inclined downloadable text on this somewhere but the margin of my screen is too small to contain the url. You'll first have to use language more precisely to get any use out of it.