wang.txt

One might get too swamped with the technicality for deriving such a complicated
differential path. It is helpful to summarize the flow in the main approach:
(1) analyze the propagation of differences, (2) identify wanted and un-wanted
differences, and (3) use the Boolean function and the carry effect to introduce
and absorb these differences.


At this point, it is worth comparing the security of the MD4 family of hash
functions against the best known attacks today. We can see that more complicated
message preprocessing does provide more security. However, even for
SHA-1, the message expansion does not seem to offer enough avalanche effect
in terms of spreading the input differences. Furthermore, there seem to be some
unexpected weaknesses in the structure of all the step updating functions. In
particular, because of the simple step operation, the certain properties of some
Boolean functions combined with the carry effect actually facilitate, rather than
prevent, differential attacks.