New Short Binary Sequence Test Algorithm: First Interval Test

The randomness test is particularly important in the evaluation of encryption algorithms. The ciphertext generated by the encryption algorithm should have a certain degree of randomness, otherwise the security of the algorithm cannot be guaranteed. Besides, block cipher algorithm and hash function algorithm cannot generate a long binary sequence, up to 512 bits, and the detection results of traditional detection algorithms are not ideal when detecting short fixed length sequences. Therefore, a new detection algorithm is proposed for the randomness of short binary sequences, which is named as the First Interval Test. It focuses on checking whether the length of the interval between the first element and its nest position is random, using the first interval, FI, as a new statistic, and transforming the detection sequence, so that this algorithm can be applied to the randomness detection of integer sequences and binary sequences. The specific probability distribution at each length is given, the parameter selection of the algorithm is defined, and the real p-value distribution is derived to further apply the chi-square goodness of fit test. Taking the correlation between plaintext and ciphertext as the standard, a comparative experiment was carried out on block cipher algorithm and hash function algorithm. The results show that the First Interval Test improves the accuracy of the randomness test.