In what way does a hash provide a better message integrity check than a checksum (such as the Internet checksum)?
One requirement of a message digest is that given a message M, it is very difficult to find another message M’ that has the same message digest and, as a corollary, that given a message digest value it is difficult to find a message M’’ that has that given message digest value. We have “message integrity” in the sense that we have reasonable confidence that given a message M and its signed message digest that the message was not altered since the message digest was computed and signed. This is
not true of the Internet checksum, where we saw in Figure 7.18 that it easy to find two messages with the same Internet checksum.