Integral and Multidimensional Linear Distinguishers with Correlation Zero

Zero-correlation cryptanalysis uses linear approximations holding with probability exactly 1/2. In this paper, we reveal fundamental links of zero-correlation distinguishers to integral distinguishers and multidimensional linear distinguishers. We show that an integral implies zero-correlation linear approximations and that a zero-correlation linear distinguisher is actually a special case of multidimensional linear distinguishers. These observations provide new insight into zero-correlation cryptanalysis which is illustrated by attacking a Skipjack variant and round-reduced CAST-256 without weak key assumptions.