Entropy makes it possible to measure the uncertainty about an information source from the distribution of its output symbols. It is known that the maximum Shannon’s entropy of a discrete source of information is reached when its symbols follow a Uniform distribution. In cryptography, these sources have great applications since they allow for the highest security standards to be reached. In this work, the most effective estimator is selected to estimate entropy in short samples of bytes and bits with maximum entropy. For this, 18 estimators were compared. Results concerning the comparisons published in the literature between these estimators are discussed. The most suitable estimator is determined experimentally, based on its bias, the mean square error short samples of bytes and bits.

The analysis of independence between statistical randomness tests has had great attention in the literature recently. Dependency detection between statistical randomness tests allows one to discriminate statistical randomness tests that measure similar characteristics, and thus minimize the amount of statistical randomness tests that need to be used. In this work, a method for detecting statistical dependency by using mutual information is proposed. The main advantage of using mutual information is its ability to detect nonlinear correlations, which cannot be detected by the linear correlation coefficient used in previous work. This method analyzes the correlation between the battery tests of the National Institute of Standards and Technology, used as a standard in the evaluation of randomness. The results of the experiments show the existence of statistical dependencies between the tests that have not been previously detected.

The bit independence criterion was proposed to evaluate the security of the S-boxes used in block ciphers. This paper proposes an algorithm that extends this criterion to evaluate the degree of independence between the bits of inputs and outputs of the stream ciphers. The effectiveness of the algorithm is experimentally confirmed in two scenarios: random outputs independent of the input, in which it does not detect dependence, and in the RC4 ciphers, where it detects significant dependencies related to some known weaknesses. The complexity of the algorithm is estimated based on the number of inputs l, and the dimensions, n and m, of the inputs and outputs, respectively.

This paper presents a criterion, based on information theory, to measure the amount of average information provided by the sequences of outputs of the RC4 on the internal state. The test statistic used is the sum of the maximum plausible estimates of the entropies $H\left(j_t\right|z_t)$, corresponding to the probability distributions $P\left(j_t\right|z_t)$ of the sequences of random variables ${\left(j_t\right)}_{t\in T}$ and ${\left(z_t\right)}_{t\in T}$, independent, but not identically distributed, where $z_t$ are the known values of the outputs, while $j_t$ is one of the unknown elements of the internal state of the RC4. It is experimentally demonstrated that the test statistic allows for determining the most vulnerable RC4 outputs, and it is proposed to be used as a vulnerability metric for each RC4 output sequence concerning the iterative probabilistic attack.

In the last three decades, the RC4 has been the most cited stream cipher, due to a large amount of research carried out on its operation. In this sense, dissimilar works have been presented on its performance, security, and usability. One of the distinguishing features that stand out the most is the sheer number of RC4 variants proposed. Recently, a weakness has been reported regarding the existence of statistical dependence between the inputs and outputs of the RC4, based on the use of the strict avalanche criterion and the bit independence criterion. This work analyzes the influence of this weakness in some of its variants concerning RC4. The five best-known variants of RC4 were compared experimentally and classified into two groups according to the presence or absence of such a weakness.

This study describes the implementation of two algorithms in a parallel environment. These algorithms correspond to two statistical tests based on the bit’s independence criterion and the strict avalanche criterion. They are utilized to measure avalanche properties in stream ciphers. These criteria allow for the statistical independence between the outputs and the internal state of a bit-level cipher to be determined. Both tests require extensive input parameters to assess the performance of current stream ciphers, leading to longer execution times. The presented implementation significantly reduces the execution time of both tests, making them suitable for evaluating ciphers in practical applications. The evaluation results compare the performance of the RC4 and HC256 stream ciphers in both sequential and parallel environments.