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**2001/033**

**Title:**

Dual of New Method for Upper Bounding the Maximum Average Linear Hull Probability for SPNs

**Authors:**
Liam Keliher, Henk Meijer, Stafford Tavares

**Abstract:**

In [3], 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 [4], 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 [3], 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 [3].

**ePrint:**
https://eprint.iacr.org/2001/033

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