The Exclusive-Or Differential Distribution Of Addition Modulo 2～n With Multiple Inputs

This paper studied the XOR differential distribution of addition modulo 2ⁿ with multiple inputs. It's proved that the XOR differential probabilities depend on the summation bit-wisely in real field of the input differentials, and not depend on their concrete values. This paper also present a recursive formula and a polynomial-time algorithm for the computing of differential probabilities for addition modulo 2ⁿ with multiple inputs, which cut down the computing complexity of the computing XOR differential probabilities for addition modulo 2ⁿ with m inputs from O(2^mn) to O(m⁵n).This paper also took a deep study at the XOR differertial distribution of addition modulo 2ⁿ with three inputs. For the addition modulo 2ⁿ with three inputs, it's proved that the differential probabilities depend on the summation bit-wisely in the real field of the differentials, and not depend on their concret values. It's completely solved the structure of impossible differentials, solved the structure and counting problem of differential correspondences with the differential probility ≥ 1 / 2, solved the structure and counting problem of differential correspondences with the lowest probility of possible differential.