# Decentralized Documentation of Maritime Traffic Incidents to Support Conflict Resolution
## 4 Concept
### TSA Negotiator  
As mentioned in Section 4, the main task of the TSA Negotiator is to ensure that the participants can agree on a common set of timestamping authorities when entering a potentially critical situation. This is realized with a negotiation protocol as is shown in Figure 4. The negotiation protocol is a deterministic protocol so that each participant can run the protocol locally after gathering all information and the results of all participants will be consistent with each other. Therefore, a central instance that coordinates the negotiation can also be avoided here. In the following, we refer to the participants as \(P_{i}\) with \(i=\{1,\ldots,\ n\}\). Furthermore, the local view of a participant is denoted by using \(P_{l}\) for self-references. Initially, each \(P_{l}\) provides a list of trusted TSAs \(\theta(P_{i})\) and a list of trusted organizations \(\phi(P_{i})\). It is assumed that each participant \(P_{i}\) has an internal prioritization of TSAs and wants to maximize the trust by choosing the TSA ranked highest in its local priority list. To ensure that the TSAs with the highest trust from all of the participants are found, the potential TSAs are exchanged in several iterations such as \(j\) (a higher number of iterations, \(j\) means less trust as the lists of possible TSAs are extended with lower prioritized TSAs by each participant). We call a set of TSAs that is trusted by a participant \(P_{i}\) the _trust list_ of \(P_{i}\). Theoretically, any participant can arbitrarily choose trust lists in every iteration. However, we propose the following method for determining the trust list of a participant \(P_{l}\) in iteration \(j\left(\tau_{j}(P_{l})\right)\) of the protocol:  
\[\tau_{j}(P_{l}):=\theta^{*}(P_{l},\min\{j,\ j_{max}(P_{l})\})\]  
with  
\[\theta^{*}(P_{i},n):=\theta\Big{(}\Big{\{}P_{k}|P_{k}\in\cup_{i=1}^{n}\Phi^{( l-1)}(P_{i})\Big{\}}\Big{)}\]  
With \(P\) being a set of participants, \(\theta(P)\) is defined as \(\theta(P):=\cup_{p\in P}\theta(p)\) and \(\phi^{l}(P_{i})\) is the repeated application of \(\phi\) to get the trusted organizations of \(P_{i}\) with \(\phi^{1}\), the union of all trusted organizations of each \(P_{k}\in\phi^{1}\) with \(\phi^{2}\), etc. Note that \(\phi^{0}=\varnothing\). For example, in the first iteration \(j=1\), \(P_{l}\) will only add the TSAs it trusts directly to its trust list \(\pi_{1}(P_{l})\). For \(j=2\), more TSAs will be added by also including the trusted TSAs of organizations or companies that the participant \(P_{l}\) trusts (given by \(\phi^{1}\), e.g., by using the public trusted entities repository, see Section 4.4). Subsequently, this can be continued by  
Figure 4: Negotiation Protocol for the agreement on a trusted TSA between different participants. also adding the TSAs of the trusted organizations of the organizations trusted by \(P_{l}(j=3)\). These transitive relations can thus be continued for the number of iterations in the protocol. In this way, in each iteration, the probability that a commonly trusted TSA is found is increased, as \(\pi_{j}(P_{i})\subseteq\pi_{j+1}(P_{i})\). At the same time, the individual participant's trust in the added TSAs decreases. As this process will not carry on indefinitely, each participant \(P_{i}\) defines locally in how many iterations \(j_{max}(P_{i})\) the own trust list is extended, so that the number of total iterations in the protocol is defined as: \(\max\limits_{1<i<n}(j_{max}(P_{i}))\). Now for each iteration, each participant derives its trust list for the \(j\)-th iteration \(\pi_{j}(P_{l})\) and broadcasts it to all participants over the P2P network. In this way, each participant receives \(n-1\) trust lists in total. Then, it is checked locally (per iteration) if there is an intersection of all trust lists:  
\[\mathop{\cap}\limits_{i=1}^{n}\pi_{j}(P_{i})\mathbin{!}_{\
eq}\varnothing\]  
If an intersection is found, any TSA from the identified intersection can be used by the participants as \( TSA_{selected}\) and utilized to sign the recorded data.