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We show that addition mod 2 n is CCZ-equivalent to a quadratic vectorial Boolean function. We use this to reduce the solution of systems of differential equations of addition to the solution of an equivalent system of linear equations and to derive a fully explicit formula for the correlation coefficients, which leads to enhanced results about the Walsh transform of addition mod 2 n . The results have direct applications in the cryptanalysis of cryptographic primitives which use addition mod 2 n .