# Refusing Incoming Connections

The success probability of double-spending attacks on zero-confirmation transactions heavily depends on the propagation delay of TRy from A to V. Clearly, a direct communication channel between A and V considerably contributes to the success of the attack. For instance, if merchants do not accept incoming connections or are located behind firewalls and NATs, then the success probability of doublespending attacks can be reduced.

Note that it is hard, however, for merchants to ensure that all their current connections are trustworthy. For example, their connections can be compromised by the adversary.

# Increasing the Number of Neighbors

We additionally point out that the number of connections established by V is an important parameter affecting the success of double-spending attacks. That is, the fewer connections of V, the more likely is that all the neighbors of V receive TRy before TRa and thus that V does not receive TRa and therefore cannot detect the attack. Similarly, as the number of connections of V increases, it is more likely that [1]

Table 4.4

Experimental Detection Probability Using 5 Observers 7

 Setting % Observed Europe, 8 connections, 3 helpers 53% Europe, 8 connections, 3 helpers 47% South America, 8 connections, 2 helpers 62% Asia Pacific, 8 connections, 2 helpers 91% North America, 20 connections, 5 helpers 46% North America, 20 connections, 5 helpers 74% North America, 20 connections, 1 helper 78% North America, 20 connections, 4 helpers 78% North America, 20 connections, 2 helpers 60% North America, 20 connections, 1 helper 60% Europe, 20 connections, 3 helpers 87% Europe, 30 Connections, 1 helper 42% Asia Pacific, 40 connections, 1 helper 42% Europe, 40 connections, 1 helper 36% Europe, 40 connections, 2 helpers 36% South America, 40 connections, 1 helper 57% Asia Pacific, 80 connections, 1 helper 18% Europe, 80 connections, 1 helper 28% Asia Pacific, 100 connections, 1 helper 88%

some of these neighbors receive TRa before TRy and forward it to V, who can immediately detect a double-spending attempt.

• [1] In this case, V cannot detect double-spending attacks even if it adopts a very large listening period.Here, ‘Setting’ refers to the location of V, the number of connections of V at the time of the attack,and the number of helpers employed by A.