Abstract
Compact formulas are derived to represent the Algebraic Normal Form (ANF) of \(f(\bar{x} + \bar{a}~mod~2^{n})\) and \(f(\bar{x} \times \bar{a}~mod~2^{n})\) from the ANF of f, where f is a Boolean function on \(\mathbb{F}^{n}_{2}\) and \(\bar{a}\) is a constant of \(\mathbb{F}^{n}_{2}\). 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 2n 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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Braeken, A., Semaev, I. (2005). The ANF of the Composition of Addition and Multiplication mod 2n with a Boolean Function. In: Gilbert, H., Handschuh, H. (eds) Fast Software Encryption. FSE 2005. Lecture Notes in Computer Science, vol 3557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11502760_8
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DOI: https://doi.org/10.1007/11502760_8
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