The ANF of the composition of addition and multiplication mod 2n with a Boolean function

Compact formulas are derived to represent the Algebraic Normal Form (ANF) of f ((x) over bar + (a) over bar mod 2(n)) and f ((x) over bar x (a) over bar mod 2(n)) from the ANF of f, where f is a Boolean function on F-2(n) and (a) over bar is a constant of F-2(n). We compare the algebraic degree of the composed functions with the algebraic degree of the original function f. As an application, the formula for addition modulo 2(n) is applied in an algebraic attack on the summation generator and the E-0 encryption scheme in the Bluetooth keystream generator.