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In this paper we analyse the algebraic properties over the field GF(2) of the addition modulo 2 n. We look at implicit quadratic equations describing this operation, and at probabilistic conditional linear equations. We show that the addition modulo 2 n can be partly or totally linearized when the output is fixed, and this for a large family of outputs. We apply these results to analyse the resistance of the stream cipher Snow 2.0 against algebraic attacks.

Algebraic Description and Simultaneous Linear Approximations of Addition in Snow 2.0.