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

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 Schulte-Geers investigated the problem from another viewpoint and derived a somewhat explicit formula 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 Schulte-Geers presented: our closed formula gives a better insight on these probabilities and more information can be extracted from it.