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Quantification of Digital Forensic Hypotheses Using Probability Theory

This paper presents the application of probability theory to assess the plausibility of the Inadvertent Defence (ID) in child pornography possession cases. It compares two actual cases from Hong Kong, employing probabilistic models to analyze outcomes under varying assumptions regarding image downloads. The results indicate that a criminal prosecution remains feasible under both infinite and finite model scenarios. Our findings contribute to understanding how simple probability theories can effectively evaluate legal defenses in digital forensic contexts.

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Quantification of Digital Forensic Hypotheses Using Probability Theory

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  1. Quantification of Digital Forensic Hypotheses UsingProbability Theory Richard E Overill & Jantje A M Silomon King’s College London Kam-Pui Chow & HaysonTse University of Hong Kong

  2. Synopsis • Introduction & Background • Probabilistic Models • Simplifying Assumptions • Results& Interpretation • Summary & Conclusions • Questions & Comments?

  3. Introduction & Background • Possession of Child Pornography (CP) is a serious offence in HK, UK and elsewhere • Under prosecution, 2 common defences are: • Trojan Horse (when many CP images are recovered) • Inadvertent (when a few CP images are recovered amongst many non-CP images) • We used complexity theory to quantify the plausibility of the THD (ICDFI-2012, ICDFI-2013) • Here we use probability theory to quantify the plausibility of the Inadvertent Defence (ID)

  4. Probabilistic Models • Greedy download – every image on website • the probability distribution is trivially singular. • Selective download – a representative sample of images on website • Infinite website: probabilities do not change as download proceeds – use the Binomial Theorem; • Finite website: probabilities change as images are downloaded – use the “Urn/Bag of balls” model.

  5. Simplifying Assumptions • Random browsing behaviour. • Random distribution of CP images on website. • No duplicates in download. • Single download session. • Single website. • Single computer. • One individual.

  6. Results & Interpretation • 2 actual HK cases: • Case 1: 248/30,000 images were CP (2010); • Case 2: 84/714,430 images were of CP (2013). • “worst case” (prosecution) results:

  7. Case 1 - Probability Distributions Finite Model Infinite Model

  8. Case 2 - Probability Distributions Finite Model Infinite Model

  9. Summary & Conclusions • Infinite model worst-case results (2.5% & 4.3%) suggest a criminal prosecution is feasible. • Finite model worst-case results (3% & 8%) also suggest a criminal prosecution is feasible but are influenced by assumptions of websitesize. • Non-worst-case probabilities fall off rapidly: σ≈√μ • Simple probability models can be used to quantify the plausibility of the Inadvertent defence (ID) against possession of CP.

  10. Questions & Comments? richard.overill@kcl.ac.uk www.inf.kcl.ac.uk/staff/richard/

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