... problem of preserving the integrity of a potentially large message is thus reduced to that of a small fixed-size hash- value. Since the existence of collisions is guaranteed in many-to-one mappings, ... security of a subset of the MDCs subsequently discussed in this section. Similar to the case of block ciphers for encryption (e.g. 8- or 1 2- round DES vs. 16-round DES), security of MDCs often comes ... decryption of y using k yields x. (However, a “black-box” which computes f(x, k) for fixed, externally-unknown k is a one-way function of x.) In contrast, f(x, k) is a one-way function of k;giveny...