Fast Algorithm of Multiplied by Constant on Modulo 2^n Operation´s Differential Transformation Probability

Multiplied by constant on modulo 2ⁿ operation, a code link, is first used in the cipher algorithm Sosemanuk, which has been selected in the eSTREAM final portfolio. This code link is recognized as a permutation with strong nonlinear property and fine realization efficiency. But there is no published paper analyzed it with differential cryptanalysis. In this paper, the differential property of the operation is studied. And from the recursive connection of its carries´ counts, an algorithm of this operation´s differential transformation probability is given, which time complexity is O(n) on average.