Length–Weight Distribution of Non-Zero Elements in Randomized Bit Sequences

Randomness plays an important role in data communication as well as in cybersecurity. In the simulation of communication systems, randomized bit sequences are often used to model a digital source information stream. Cryptographic outputs should look more random than deterministic in order to provide an attacker with as little information as possible. Therefore, the investigation of randomness, especially in cybersecurity, has attracted a lot of attention and research activities. Common tests regarding randomness are hypothesis-based and focus on analyzing the distribution and independence of zero and non-zero elements in a given random sequence. In this work, a novel approach grounded in a gap-based burst analysis is presented and analyzed. Such approaches have been successfully implemented, e.g., in data communication systems and data networks. The focus of the current work is on detecting deviations from the ideal gap-density function describing randomized bit sequences. For testing and verification purposes, the well-researched post-quantum cryptographic CRYSTALS suite, including its Kyber and Dilithium schemes, is utilized. The proposed technique allows for quickly verifying the level of randomness in given cryptographic outputs. The results for different sequence-generation techniques are presented, thus validating the approach. The results show that key-encapsulation and key-exchange algorithms, such as CRYSTALS-Kyber, achieve a lower level of randomness compared to digital signature algorithms, such as CRYSTALS-Dilithium.