Figure 5

Realistic effort to identify an anonymous node. (a)–(c) Illustration of the proposed greedy algorithm for deanonymizing a target node T, given identities of source nodes S1 and S2. In (a) we find the shortest path, \(S_{1}\rightarrow I_{1}\rightarrow T\) (links of the shortest path outlined in purple) and interrogate the first node \(I_{1}\). (b) After \(S_{1}\) identifies \(I_{1}\), we reach a dead end as node \(I_{1}\) does not provide information on T. We then again calculate the shortest path to T and find a path \(S_{2}\rightarrow I_{2}\rightarrow I_{3} \rightarrow T\) (with its links highlighted). (c) We interrogate \(I_{2}\) and then \(I_{3}\) (outlined in purple again), who provide information leading to the target. While the optimal path would have taken only \(l=3\) steps, the actual path uses \(\ell _{\mathrm{actual}}=4\) steps due to the extra step from \(S_{1}\rightarrow I_{1}\). (d)–(f) The fraction of nodes reached, \(F_{A}\), for each value of \(\ell _{\mathrm{actual}}\) using our algorithm. Results are from at least 20,000 simulated source-target pairs (for different values of p). (g)–(i) For all three networks the likelihood that continuing to search after \(\ell _{\mathrm{actual}}\) steps will lead to successful identification of a given target node, \(P_{\mathrm{Find}}\). Note that less than 100 nodes have \(\ell _{\mathrm{actual}}>15\) leading to high fluctuations. (j) The mean value of \(\ell _{\mathrm{actual}}\) as a function of the optimal value, ℓ, for the Blockchain Transactions. For lower levels of p, \(\ell _{\mathrm{actual}}\) tends to increase faster with ℓ. In all panels, only target nodes that are not direct neighbors of the source node(s) are considered