Integral and multidimensional linear distinguishers with correlation zero

Authors:
Andrey Bogdanov;Gregor Leander;Kaisa Nyberg;Meiqin Wang
Affiliations:
ESAT/SCD/COSIC and IBBT, KU Leuven, Belgium;Technical University of Denmark, Denmark;Aalto University, Finland;Key Laboratory of Cryptologic Technology and Information Security, Ministry of Education, Shandong University, Jinan, China
Venue:
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Year:
2012

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Abstract

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.