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...

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Main Authors: Christoph Lange, Andreas Ahrens, Yadu Krishnan Krishnakumar, Olaf Grote
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Sensors
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Online Access:https://www.mdpi.com/1424-8220/25/12/3825
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author Christoph Lange
Andreas Ahrens
Yadu Krishnan Krishnakumar
Olaf Grote
author_facet Christoph Lange
Andreas Ahrens
Yadu Krishnan Krishnakumar
Olaf Grote
author_sort Christoph Lange
collection DOAJ
description 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.
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spelling doaj-art-fdc51d3d44ea4fea85bf52e4302d1ed72025-08-20T03:29:39ZengMDPI AGSensors1424-82202025-06-012512382510.3390/s25123825Length–Weight Distribution of Non-Zero Elements in Randomized Bit SequencesChristoph Lange0Andreas Ahrens1Yadu Krishnan Krishnakumar2Olaf Grote3School of Engineering—Energy and Information, Hochschule für Technik und Wirtschaft Berlin, University of Applied Sciences, 10313 Berlin, GermanyFaculty of Engineering, Hochschule Wismar, University of Applied Sciences: Technology, Business and Design, 23966 Wismar, GermanyFaculty of Engineering, Hochschule Wismar, University of Applied Sciences: Technology, Business and Design, 23966 Wismar, GermanyEscuela Técnica Superior de Ingeniería y Sistemas de Telecomunicación (ETSIST), Universidad Politécnica de Madrid, Campus Sur, Calle Nikola Tesla s/n, 28031 Madrid, SpainRandomness 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.https://www.mdpi.com/1424-8220/25/12/3825randomized bit sequencesbursttestprobabilitygap processgap distribution
spellingShingle Christoph Lange
Andreas Ahrens
Yadu Krishnan Krishnakumar
Olaf Grote
Length–Weight Distribution of Non-Zero Elements in Randomized Bit Sequences
Sensors
randomized bit sequences
burst
test
probability
gap process
gap distribution
title Length–Weight Distribution of Non-Zero Elements in Randomized Bit Sequences
title_full Length–Weight Distribution of Non-Zero Elements in Randomized Bit Sequences
title_fullStr Length–Weight Distribution of Non-Zero Elements in Randomized Bit Sequences
title_full_unstemmed Length–Weight Distribution of Non-Zero Elements in Randomized Bit Sequences
title_short Length–Weight Distribution of Non-Zero Elements in Randomized Bit Sequences
title_sort length weight distribution of non zero elements in randomized bit sequences
topic randomized bit sequences
burst
test
probability
gap process
gap distribution
url https://www.mdpi.com/1424-8220/25/12/3825
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AT yadukrishnankrishnakumar lengthweightdistributionofnonzeroelementsinrandomizedbitsequences
AT olafgrote lengthweightdistributionofnonzeroelementsinrandomizedbitsequences