The alternative approach for the strong distinguishing attack

The strong distinguishing attack is normally constructed based on Pearson´s chi-square test. It uses several samples for increasing the correctness level. The number of samples is usually estimated to 1/ε², where e is the random bits´s bias. However, it lacks the method for verifying the accuracy of the strong distinguisher´s advantage, given the number of samples. It may not obtain high advantage as expected if the number of samples is underestimated. This paper proposes the new framework for strong distinguishing attack, which is solely based on Binomial hypothesis test instead of Pearson´s chi-square test. The proposed strong distinguishing attack can calculate the precise number of samples and verify the advantage when the number of samples is limited. Moreover, this work also shows that the commonly used estimation method always under estimate the number of samples.