1. A mathematical function that maps values from a large (or very large) domain into a smaller range, and that reduces a potentially long message into a "message digest" or "hash value" or that is sufficiently compact to be input into a digital signature algorithm. Note: A "good" hash function is one that results from applying the function to a (large) set of values that are evenly (and randomly) distributed over the range. 2. A function that maps values from a (possibly very) large set of values to a smaller range of values. 3. A (mathematical) function which maps values from a (possibly very) large set of values into a smaller range of values.