Compact formulas are derived to represent the Algebraic Normal Form (ANF) of f(x + a mod 2~n) and f(x x a mod 2~n) from the ANF of f, where f is a Boolean function on F_2~n and a 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.
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机译：导出紧凑型公式，以表示来自F的ANF的F（x + A mod 2〜n）和f（xxa mod 2〜n）的代数正常形式（ANF），其中f是f_2〜n上的布尔函数a是f_2〜n的常数。我们将组成功能的代数程度与原始函数F的代数进行比较。作为应用，添加模数2〜n的公式应用于在蓝牙键盘发生器中的求和发生器上的代数攻击和E_0加密方案中。
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