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Shannon Entropy and Beyond: An Information-Theoretic Framework for Randomness Pre-Screening.
1Faculty of Electronics, Telecommunications and Information Technology, National University of Science and Technology POLITEHNICA Bucharest, 061071 Bucharest, Romania.
Entropy (Basel, Switzerland)
|June 26, 2026
Summary
A single entropy measure is insufficient for assessing data randomness. Combining Shannon, Rényi, permutation, and sample entropy provides a robust diagnostic profile for detecting pseudo-randomness in data sources.
Area of Science:
- Information Theory
- Data Science
- Statistical Analysis
Background:
- Shannon entropy is commonly used to assess data randomness.
- High Shannon entropy values are often misinterpreted as sufficient evidence of randomness.
- Deterministic systems can exhibit high Shannon entropy, masking underlying predictability.
Purpose of the Study:
- To demonstrate the limitations of using Shannon entropy alone for randomness assessment.
- To introduce a multi-entropy diagnostic profile for more accurate randomness evaluation.
- To validate the proposed method using real-world lottery data and pseudo-random number generators.
Main Methods:
- Calculation of Shannon, Rényi, permutation, and sample entropy for various data sources.
- Development of a combined entropy profile for comprehensive data analysis.
- Application of a Random Forest classifier to distinguish between different data generation processes.
Main Results:
- A deterministic logistic map shows high Shannon entropy but low permutation and sample entropy, indicating predictability.
- The Romanian Loto 6/49 lottery data closely resembles a high-quality pseudo-random number generator (PRNG) across all four entropy measures.
- The entropy deficit decay follows a power law, distinguishing predictable systems from random ones.
Conclusions:
- A multi-entropy diagnostic profile is superior to single measures for identifying structured pseudo-randomness.
- The method is effective for RNG certification, cryptographic auditing, and detecting non-random data.
- The approach provides a domain-independent framework for rigorous randomness assessment.
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