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Related Concept Videos

Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

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The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
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The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
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 The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
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While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
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Observation and Analysis of Blinking Surface-enhanced Raman Scattering
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Length-Weight Distribution of Non-Zero Elements in Randomized Bit Sequences.

Christoph Lange1, Andreas Ahrens2, Yadu Krishnan Krishnakumar2

  • 1School of Engineering-Energy and Information, Hochschule für Technik und Wirtschaft Berlin, University of Applied Sciences, 10313 Berlin, Germany.

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|June 27, 2025
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Summary
This summary is machine-generated.

This study introduces a novel gap-based burst analysis to assess randomness in cybersecurity. CRYSTALS-Kyber shows less randomness than CRYSTALS-Dilithium, highlighting differences in cryptographic algorithm security.

Keywords:
burstgap distributiongap processprobabilityrandomized bit sequencestest

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Area of Science:

  • Cybersecurity and Data Communication
  • Information Theory and Cryptography

Background:

  • Randomness is crucial for secure communication and cybersecurity.
  • Cryptographic outputs must appear random to minimize information leakage to attackers.
  • Existing randomness tests often rely on hypothesis testing of element distribution and independence.

Purpose of the Study:

  • To present and analyze a novel gap-based burst analysis for evaluating randomness.
  • To detect deviations from ideal gap-density functions in randomized bit sequences.
  • To quickly verify the randomness of cryptographic outputs.

Main Methods:

  • A novel approach based on gap-based burst analysis is developed.
  • The method focuses on deviations from the ideal gap-density function.
  • The CRYSTALS cryptographic suite (Kyber and Dilithium) is used for testing and verification.

Main Results:

  • The proposed technique effectively verifies randomness in cryptographic outputs.
  • CRYSTALS-Kyber (key-encapsulation/exchange) exhibits a lower level of randomness.
  • CRYSTALS-Dilithium (digital signature) demonstrates a higher level of randomness compared to Kyber.

Conclusions:

  • The gap-based burst analysis is a valid and efficient method for assessing randomness in cryptographic sequences.
  • Different cryptographic algorithms possess varying degrees of randomness.
  • The findings have implications for selecting secure cryptographic primitives.