Analysis of the Noise Functions of Macrocosm Approximation of Binary Addition and Triple Addition Modulo 2n with XOR

Macrocosm approximation is a class of attacks to ciphers by replacing a strong cipher function with a weak cipher function.The XOR of the two functions is called the noise function of this macrocosm approximation. This paper studies the probability distributions of the noise functions produced by macrocosm approximation of binary addition and triple addition modulo 2n with XOR,and gives the computation formulae of the probability distributions of the corresponding noise functions and the square sums of the probabilities, which is helpful to recognize the ability of resistance to macrocosm approximation of binary addition and triple addition modulo 2n with XOR.