# CoNTe: A Core Network Temporal Blockchain for 5G
## 3 Federated Byzantine Agreement Consensus
A quorum slice is a grouping of network peers whose pairwise peering is symmetric. Transposed to wireless network context, a quorum slice could consist of all tier-1 mobile network operators (MNO) of a region, who all peer with each other. Within a quorum slice, block additions may be considered final, after a threshold amount of peers confirm the block. However, this functionality on its own does not consist a federation. To form a federation, quorum slices are intended to intersect, such that nodes operating in multiple quorum slices function as relay, extending consensus to the wider network of intersecting slices. In the 5G core network context, this would occur when some portion of regional MNO's within a quorum slice, also peer with MNO's or another region, or internationally. Federated Byzantine Agreement Systems (FBAS) and Quorum are formally defined as [14]:  
* Federated Byzantine Agreement Systems: a federated Byzantine agreement system, or FBAS, is a pair \(\langle V,Q\rangle\) comprising a set of nodes \(V\) and a quorum function \(Q:V\Rightarrow 2^{2^{V}}\setminus\{\emptyset\}\) specifying one or more quorum slices for each node, where a node belongs to all of its own quorum slices--i.e., \(\forall v\in V,\forall q\in Q(v)\,,v\in q\). (Note that \(2^{x}\) denotes a powerset of \(X\).) * Quorum: a set of nodes \(U\subseteq V\) in FBAS \(\langle V,Q\rangle\) is a quorum iff \(U\
eq\emptyset\) and \(U\) contains a slice for each member--i.e., \(\forall v\in U,\exists q\in Q(v)\,,\) such that \(q\subseteq U\). A quorum is a set of nodes that sets the threshold or reaching agreement, and it may be larger than a single quorum slice. Consider Figure 2, which shows two clusters of nodes, each participating in a single quorum slice with symmetric pair-wise connection. Assuming that 100% confirmation is required, node \(v_{5}\) can reach agreement with confirmations from peers \(\{v_{1},v_{2},v_{3},v_{4},v_{6}\}\); however, since node \(v_{6}\) has additional peers \(\{v_{7},v_{8},v_{9},v_{10}\}\), they must also agree to the update before it is accepted; therefore, \(v_{4}\) must agree to an update from \(v_{8}\), etc. Figure 2 represents a worse case scenario of federated agreement. In this example, the pairwise relationship of \(v_{5}\) and \(v_{6}\) represent a single point of failure in reaching consensus. Systems, such as Ripple [30], compensate for this by enforcing, at all times, a minimum connectivity between federated nodes \(\geq\) its maximum fault tolerance (and in turn, making it Byzantine Fault Tolerant). However, doing this again imposes the centralizing requirement of recording and enforcing connectivity among known participants-precluding unmanaged permissionless operation. FBA, as deployed in Conte, instead makes an alternate scenario possible, in which consensus resilience increases as additional unmanaged pair-wise relationships are formed elsewhere in the network-in a manner mirroring that of global internet (Figure 3). which establishes finality without traditional fault-tolerance, to allow its temporal network function deployment, while also not sacrificing consensus safety.