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Quantification of Digital Forensic Hypotheses Using Probability Theory Richard E Overill & Jantje A M Silomon King’s College London Kam-Pui Chow & Hayson.

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Presentation on theme: "Quantification of Digital Forensic Hypotheses Using Probability Theory Richard E Overill & Jantje A M Silomon King’s College London Kam-Pui Chow & Hayson."— Presentation transcript:

1 Quantification of Digital Forensic Hypotheses Using Probability Theory Richard E Overill & Jantje A M Silomon King’s College London Kam-Pui Chow & Hayson Tse 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: “worst-case” probabilitiesFinite ModelInfinite Model Case 1 0.03040.0254 Case 2 0.08070.0435

7 Case 1 - Probability Distributions Finite ModelInfinite Model

8 Case 2 - Probability Distributions Finite ModelInfinite 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 website size. 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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