Truncated differential cryptanalysis was introduced by Lars R. Knudsen at FSE 1994.
The Keccak team provides an summary of this technique as follows:
In truncated differential cryptanalysis one divides the function input, output and intermediate computation values in sub-blocks, typically of equal size (e.g. bytes). Whereas in classical differential cryptanalysis one studies propagation of differences that are fully specified, in truncated differential cryptanalysis one only specifies whether a sub-block is active (has a difference) or is passive (has no difference).
It has been applied by J. Daemen and V. Rijmen on AES, the idea is therefore to indicate if a byte has a been modified or not in order to retrieve a distinguisher.
In the case of a strong alignment, the truncated differences can be easily constrained and followed. In the case of a weak alignment, differences spread extremely fast and it makes really hard for a subdivision of the input space to be found.
On Keccak ($\iota \circ \chi \circ \rho \circ \pi \circ \theta$) we ignore the $\iota$ operation as it is irrelevant from a Xor difference point of view. Lets consider a subdivision of 5 bits (due to the size of the somewhat S-box substitution: the $\chi$ function) and assume we have a difference on that group.
We will ignore $\theta$ due to its operation being difficult to visualize, basically, the active difference is spread over the slice and the slice behind (by $z$ coordinate) in the state.
Then we have $\pi$, if a truncated difference of 5 bit is active then the slice will be set to active.
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So now we have 5 active truncated difference to track.
Then we have $\rho$, which spreads the differences among the $z-axis$ :
Thus, the active truncated differences are now 25.
In other word, the number of active truncated difference in Keccak increases really quickly $\mathcal{O}(25^n)$. This what we call a weak alignment.
