Completion of Computation of Improved Upper Bound on the Maximum Average Linear Hull Probabilty for Rijndael
This report presents the results from the completed computation of an algorithm introduced by the authors in  for evaluating the provable security of the AES (Rijndael) against linear cryptanalysis. This algorithm, later named KMT2, can in fact be applied to any SPN . Preliminary results in  were based on 43\% of total computation, estimated at 200,000 hours on our benchmark machine at the time, a Sun Ultra 5. After some delay, we obtained access to the necessary computational resources, and were able to run the algorithm to completion. In addition to the above, this report presents the results from the dual version of our algorithm (KMT2-DC) as applied to the AES.
Dual of New Method for Upper Bounding the Maximum Average Linear Hull Probability for SPNs
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 .