Paper 2015/026

A More Explicit Formula for Linear Probabilities of Modular Addition Modulo a Power of Two

S. M. Dehnavi and A. Mahmoodi Rishakani and M. R. Mirzaee Shamsabad

Abstract

Linear approximations of modular addition modulo a power of two was studied by Wallen in 2003. He presented an efficient algorithm for computing linear probabilities of modular addition. In 2013 Sculte-Geers investigated the problem from another viewpoint and derived a somewhat explicit for these probabilities. In this note we give a closed formula for linear probabilities of modular addition modulo a power of two, based on what Schlte-Geers presented: our closed formula gives a better insight on these probabilities and more information can be extracted from it.