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Erschienen in:
2011 | OriginalPaper | Buchkapitel
The Additive Differential Probability of ARX
verfasst von : Vesselin Velichkov, Nicky Mouha, Christophe De Cannière, Bart Preneel
Erschienen in: Fast Software Encryption
Verlag: Springer Berlin Heidelberg
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We analyze
$\mathrm{adp}^\texttt{ARX}$
, the probability with which additive differences propagate through the following sequence of operations: modular addition, bit rotation and
XOR
(
ARX
). We propose an algorithm to evaluate
$\mathrm{adp}^\texttt{ARX}$
with a linear time complexity in the word size. This algorithm is based on the recently proposed concept of S-functions. Because of the bit rotation operation, it was necessary to extend the S-functions framework. We show that
$\mathrm{adp}^\texttt{ARX}$
can differ significantly from the multiplication of the differential probability of each component. To the best of our knowledge, this paper is the first to propose an efficient algorithm to calculate
$\mathrm{adp}^\texttt{ARX}$
. Accurate calculations of differential probabilities are necessary to evaluate the resistance of cryptographic primitives against differential cryptanalysis. Our method can be applied to find more accurate differential characteristics for
ARX
-based constructions.