Statistical Properties of Multiplication mod 2
نویسندگان
چکیده
In this paper, we investigate some statistical properties of multiplication mod 2 for cryptographic use. For this purpose, we introduce a family of T-functions similar to modular multiplication, which we call M-functions. We obtain the probability distribution of M-functions as vectorial Boolean functions. At first, we determine the joint probability distribution of arbitrary number of the output of an M-function component bits. Then, we obtain the probability distribution of the component Boolean functions of combination of a linear transformation with an M-function. After that, using a new measure for computing the imbalance of maps, we show that the restriction of the output of an M-function to its upper bits is asymptotically balanced.
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