A formal speci cation of the Kademlia distributed hash table

Kademlia is a peer-to-peer distributed hash table (DHT) currently used in the P2P eDonkey le sharing network. The most popular clients used to connect to the Kad network are eMule, aMule and BitTorrent. As other DHT, Kademlia look-up algorithm takes logn steps, which can be reduced to log2b n by increasing the node's routing table size. It also o ers a number of desirable features not o ered by any previous DHT, which makes it the only DHT used in real networks. These features result from the use of a notion of distance between objects introduced by Kademlia. Both nodes and shared les are represented by nbit keys, and their relation depend on the distance between their keys. In this sense, nodes keep information about les close or near to them in the key space and the search algorithm is based on looking for the closest node (or almost closest node, if the information is replicated) to the le key. This paper explains the speci cation of the behaviour of a P2P network that uses the Kademlia DHT in the formal speci cation language Maude. We use the initial description of the Kademlia DHT and ll some open issues with the eMule real implementation. We allow peers to connect to the network and leave it by simulating time using the Real Time Maude facilities.