Simplification of Frequency Test for Random Number Generation Based on Chi-Square

Abstract

This paper presents the simplified method of random test suite based on the frequency (block) test. The test is used to check the first property of random numbers which is to have the same probabilities of being "1" and "0". Random numbers are used for the secret key generation which is an essential part for cryptographic system. Before encryption, secret keys need to pass the random test in order to make it harder for outsiders to predict the pattern of the secret keys. Basically, the decision making of whether the secret keys are truly random, is based on the test statistics computation. Due to the motivation that the classical method based on the NIST statistical test suite (NIST STS) is complex and redundant, the reduction of this random testing procedure is then proposed. The introduced technique does not need to compute the incomplete gamma function (Igamc) nor the P-value for the decision making of test results unlike that of the classical method. Thus, it results to the reduction in the testing decision time. In this technique, the decision making and conclusion can be determined from the critical value of chi-square (chi2) directly. Its results without having to compute Igamc is compared to that of the classical method. In the test, the significance level (a) is set to be 0.01 or 0.05 in order to obtain the critical values and the critical regions. Resulting to the confidence of 99% or 95% respectively. Next, overall performance is evaluated by computing the percentage difference in order to demonstrate that the proposed value gives the same result as that of the classical method. Therefore, this proposed technique can be applied as that of the conventional based on the frequency (block) test.