Multiple-chi-square tests and their application on distinguishing attacks

Chi-square tests are vastly used for distinguishing random distributions, but extra care must be taken when using them on several independent variables. We noticed, the chi-square statistics, in some previous works, was computed half of its real value. Thus, to avoid possible future confusions, we formulize multiple-chi-square tests. To show the application of multiple-chi-square tests, we introduce two new tests and apply them to Trivium as a special case. These tests are modifications of ANF monomial test and, when applied to Trivium with the same number of rounds, the data complexity of them is roughly 2
⁴
times smaller than that of previous ANF monomial test.