We propose a new lightweight BCH code corrector of the random number generator such that the bitwise dependence of the output value is controllable. The proposed corrector is applicable to a lightweight environment and the degree of dependence among the output bits of the corrector is adjustable depending on the bias of the input bits. Hitherto, most correctors using a linear code are studied on the direction of reducing the bias among the output bits, where the biased input bits are independent. On the other hand, the output bits of a linear code corrector are inherently not independent even though the input bits are independent. However, there are no results dealing with the independence of the output bits. The well-known von Neumann corrector has an inefficient compression rate and the length of output bits is nondeterministic. Since the heavy cryptographic algorithms are used in the NIST’s conditioning component to reduce the bias of input bits, it is not appropriate in a lightweight environment. Thus we have concentrated on the linear code corrector and obtained the lightweight BCH code corrector with measurable dependence among the output bits as well as the bias. Moreover, we provide some simulations to examine our results.

Recently, NIST has published the second draft of SP 800-90B used for entropy estimations of random number generators. It is conducted within the framework of a cryptographic module validation program (CMVP) for the entropy source. The official evaluation criteria such as CMVP should be supported by rigorous and theoretical foundations so as to achieve the credibility and reliability of the evaluation process. For the theoretical background of the entropy estimation, it is assumed in SP 800-90B that the distribution of the entropy source is unknown since we cannot obtain an appropriate hypothesis about the distribution of the noise source which is a component of the entropy source. In this case, the nonparametric statistical method is commonly used. The test suite of SP 800-90B is divided into two major steps. The first step is to determine the track, IID(independent and identically distributed) or Non-IID, and the second step is to estimate the entropy of the given source. The permutation tests and additional chi-square tests are used to test IID assumption for entropy source in the first step, and when all tests in the first step are passed, the given source is determined as IID. Depending on whether the given data is determined as IID or Non-IID, the entropy estimation is conducted using different estimators in the second step. In this paper, we concentrate on the additional chi-square tests and analyze them from the view point of the nonparametric statistical method. We find out several defects of the degrees of freedom in the tests of independence for binary and non-binary data. We correct the degrees of freedom based on our analysis, and it solidifies the theoretical basis of SP 800- 90B. Furthermore, we provide some experimental results with the corrected degrees of freedom which show that the corrected tests are more effective.