Fig. 3: Probability of identification when the time delay increases.

We plot p_k, the probability of identification within rank 1 for k ∈ {1, 2, 3} when the time delay between the dataset and the attacker’s auxiliary information is equal to D weeks. The auxiliary information is one week long. The 95% confidence interval is shown in light blue. The vertical gray lines correspond to holidays. While p_k decreases slowly with the time delay, our model correctly identifies people p_k=2 = 24.3% of the time even after 20 weeks (k = 2). Even for k = 1, the probability after 20 weeks is as high as p_k=1 = 5.8%. The probability of identification decreases as y = p_k(D = 1)−α_k × (D−1), with α₁ = −0.006, α₂ = −0.017 and α₃ = −0.018.