The additive differential probability of ARX

Abstract

We analyze adpARX, 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 adpARX 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 adpARX 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 adp 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. © 2011 Springer-Verlag.