Quantum impossible differential and truncated differential cryptanalysis

We study applications of BV algorithm and present quantum versions of impossible differential cryptanalysis and truncated differential cryptanalysis based on it. Afterwards, we analyze their efficiencies and success probabilities rigorously. In traditional impossible differential attack or truncated differential attack, it is difficult to extend the differential path, which usually limits the number of rounds that can be attacked. By contrast, our approach treats the first $r-1$ rounds of the cipher as a whole and applies BV algorithm on them directly. Thus extending the number of rounds is not a problem for our algorithm.