Paper 2019/848

Observations on the DLCT and Absolute Indicators

Anne Canteaut, Lukas Kölsch, and Friedrich Wiemer


Recently Bar-On et al. proposed the DLCT for a tighter analysis of probabilities for differential-linear distinguishers. We extend the analysis of the DLCT, and gain new insights about this notion. The DLCT entries correspond to the autocorrelation spectrum of the component functions and thus the DLCT is nothing else as the ACT. We note that the ACT spectrum is invariant under some equivalence relations. Interestingly the ACT spectrum is not invariant under inversion (and thus not under CCZ equivalence), implying that it might be beneficial to look at the decryption for a differential-linear cryptanalysis. Furthermore, while for Boolean functions a lower bound for the maximal absolute autocorrelation, the absolute indicator, is not known, the case for vectorial Boolean functions is different. Here, we prove that for any vectorial Boolean function, its absolute indicator is lower bounded by $2^{n/2}$. Eventually, for APN functions we show a connection of the absolute indicator to the linearity of balanced Boolean functions, and exhibit APN permutations with absolute indicator bounded by $2^{(n+1)/2}$.

Available format(s)
Secret-key cryptography
Publication info
Preprint. MINOR revision.
boolean functionsDLCTACTautocorrelationabsolute indicatordifferential-linear attack
Contact author(s)
anne canteaut @ inria fr
lukas koelsch @ uni-rostock de
friedrich wiemer @ rub de
2019-07-22: received
Short URL
Creative Commons Attribution


      author = {Anne Canteaut and Lukas Kölsch and Friedrich Wiemer},
      title = {Observations on the DLCT and Absolute Indicators},
      howpublished = {Cryptology ePrint Archive, Paper 2019/848},
      year = {2019},
      note = {\url{}},
      url = {}
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