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Dual of New Method for Upper Bounding the Maximum Average Linear Hull Probability for SPNs
Authors: Liam Keliher, Henk Meijer, Stafford TavaresAbstract:
In , we present a new algorithm for computing an upper bound on
the maximum average linear hull probability (MALHP) for the SPN
symmetric cipher structure, a value required to make claims about
provable security against linear cryptanalysis. This algorithm
improves on existing work in that the resulting upper bound is a
function of the number of encryption rounds (other upper bounds
known to the authors are not), and moreover, it can be computed
for an SPN with any linear transformation layer (the best previous
result, that of Hong et.al , applies only to SPNs with highly
diffusive linear transformations).
It is well known that there exists a duality between linear
cryptanalysis and differential cryptanalysis which allows certain
results related to one of the attacks to be translated into the
corresponding results for the other attack [1,5]. Since this
duality applies to our work in , we immediately obtain an
algorithm for upper bounding the maximum average differential
probability (MADP) for SPNs (required to make claims about
provable security against differential cryptanalysis).
Note: In what follows, we assume familiarity with the notation
and results of .
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