University of Luton
In this paper the authors analyze the security of systems based on modular Additions, Rotations, and XORs (ARX systems). They provide both theoretical support for their security and practical cryptanalysis of real ARX primitives. They use a technique called rotational cryptanalysis that is universal for the ARX systems and is quite efficient. They illustrate the method with the best known attack on reduced versions of the block cipher Threefish (the core of Skein). Additionally, they prove that ARX with constants are functionally complete, i.e. any function can be realized with these operations.