Is it possible to "crack" an ASIC?
It is quite possible to reverse engineer an ASIC and there really isn't much you can do about it.  Basically the main way you do it is physically by removing each layer of the ASIC and using a specialized computer program to recover the schematic.  It is very difficult to understand all the functions of the ASIC and you can obfuscate it in various ways but there isn't anything you can really do to prevent it.  Randomly sending inputs and seeing what would happen would not be very fruitful (although it can be done effectively in limited circumstances, such as Compaq's reverse engineering of IBM's BIOS chip).

One of the leading companies that does this type work is called Chipworks.  Reverse engineering a chip is one of the main ways a company can tell (and get evidence) that a competitor has violated their patented IP.