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Comment: Spelling correction  trough => through. Revert was me as well.

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NTK_RFC 0001
Subject: Gnode contiguity
This text describes a change to the Npv7 about the collision of IPs. It will be included in the final documentation, so feel free to correct it. But if you want to change the system here described, please contact us first.
The real problems
A collision of IPs happens when two gnodes with the same ID are born separately, so when they meet each through a direct link or through other nodes many problems arise since there are some ambiguities:
 In the first case there can be nodes which have the same IP.
 In the second:
A <> B <> D <> A
 After a qspn_round the node B will have two routes to reach the gnode A. But in this case the gnode A isn't a contiguous gnode, so when B wants to reach a node which belongs to A, it will send the packet using only one route which may lead to the A gnode which hasn't the wanted node.
So these are the real problems. In order to solve them it is necessary that every time two gnodes meets each other for the first time, one of them will redo the hook, in fact, this was the cause of all. When a gnode meets for the first time another gnode is like when a new node joins the network: it hooks with the other nodes. The same must be done for the gnode.
Hook of gnodes
The hook of two gnodes works in this way: only the gnode which has less nodes than the other will change (let's call the first gnode X and the second Y). If X and Y have the same number of nodes, the gnode which has the smaller gnode_id will change. The bnodes of X will start to rehook, the other nodes will rehook when they notice that a new rnode which belongs to Y comes up. Summing up: the bnodes rehook first, then their rnodes, then the rnodes of the rnodes of the bnodes... and so on, all the nodes of the gnode have rehooked.
It doesn't matter that a gnode composed by 2^24 nodes changes all its IPs, since it will happen only very few times, i.e. when the gnode of the Europe meets that of the America.
Gnode count
This method requires that the number of nodes present in a gnode has to be known, therefore the qspn_pkt which traverse gnodes stores also the number of nodes of each traversed gnode.
No first tracer_pkt
While rehooking, the first tracer_pkt won't be sent like in the normal hook 'cause if all the nodes of the gnode which is rehooking send it, there would be a broadcast pkt for each node. The next qspn_round will let the other know the routes to reach them.
Rehook of two equal, not contiguous gnodes
When there are two nodes with the same ip, or gnodes with the same gid, one of them will rehook, following the same rules we've described, but all the packets that the two (g)nodes will send each other will be routed by the daemons. For example if A wants to send a packet to A' it stores in the pkt the route it received with the last qspn_pkt, the other nodes will forward the packet to A' using that route, this is to avoid the problem described above.
Rehook details
The gnode X is rehooking at the gnode Y.
If the gnode Y hasn't enough free nodes for all the nodes of the gnode X then the situation evolves in this way:
 maxYnodes = maxmimum number of nodes in Y; curYnodes = current number of nodes in Y (gnode count of Y). diff = maxYnodes  curYnodes;
`diff' is the number of new nodes which the gnode Y can accept inside. The bnodes of X will say to `diff'# nodes in X to rehook in the gnode Y, all the other noninformed nodes will create a new gnode.
Let's analyse the two cases.
informed nodes
Remembering how the nodes rehook (first the bnode, then its rnodes, then the rnodes of its rnodes, etc..) we adopt this strategy:
 join_rate=diff/number_of_X_bnodes  1;
Each bnode of X knows it can inform `join_rate'# nodes, so when its rnodes try to rehook at it, they'll know that:
 they will become part of the gnode Y
 they can inform other `(join_rate1)/(number_of_links1)'# nodes
The same procedure holds for recursively the rnodes of the rnodes of the bnode.
When `join_rate' becomes zero the node becomes noninformed.
noninformed nodes
The gid of the new gnode they create is based on the hash of their previous gid. In this way all the noninformed nodes will be in the same new gnode, cause they all generates the same hash. If the new gid is already taken in the map they'll increment it by one until they choose a nontaken gnode.
Counting the nodes
At this point all seems to be solved, but it is not. Anyone can modify the qspn, so for example the X which has less nodes than Y can fake the number, and Y will be forced to rehook. It this happens anyone can easily force a gnode of 2^24 nodes to change its IPs! Therefore the problem to be solved now is: how can the gnode Y verify that the gnode X has really more nodes?
What is the main property of a network which has more nodes than another? The computability power!
We assume that the average computability power for a gnode of the second level or greater is constant. (a gnode of the second level can have 2^16 nodes, in the third level 2^24). Therefore the gnode of level 1 won't be checked.
Each node of the gnode which has to rehook (in this case the gnode Y, since the gnode X is faking the qspn_pkt) will send a problem to solve to the other gnode and it wait for a very small time the reply with the solution in it. If the solution is right the node receiving it will rehook, otherwise the gnode X will be banned and excluded from all the qspn floods. Only one challenge each T time can occur, where T is proportional to the size of the Y gnode. So say that Y has 16milions IPs, if it has already sent a challenge it will send another after 10 minutes.
Computability power
But this system leaves opened another kind of attack: the gnode X can target a single node in Y, replying only to its reply and making it rehook. In order to prevent this the nodes act in this way:
 When a node hooks it creates a RSA key pair, then its rnodes get its public key.
 When a node receives a reply to the problem, it broadcasts the reply inside its gnode,
signing it with its public key. When its rnodes receive the pkt, check the signature. If it is valid they update the counter of received replies for the problems sent, then they substitute the signature with their own. The packet will propagate until it reaches all the nodes of the gnode.
 The nodes will start to rehook only when all the replies will be
received (during the wait time). Since it is not possible that all the reply are received it is allowed that 10% of replies are lost.
The problem to solve sent by the nodes is:
 f(x) mod k
where k is a random number between 2^{16 and 2}32.
f(x) is a function which is not easily computable with mod k. When x gets bigger the computation time increases. We are still deciding on what f() function using.
Dumb machines
Generating the problem doesn't require a high computability power, in fact, the daemon will keep 8 or 16 problems cached, generated while the cpu isn't used.
The machines which have a very low computability power won't reply and even try to solve the problems they receive (but only if they can't take the computability of the problem).
ANDNA changes
If a same hostname is registered in two separeted gnodes what happens when they meet? Which node will mantain the hostname?
The node which is in the greater gnode wins: the hash_nodes of the smaller gnode, which rehooks, will reset their uptime counter, in this way when they receive the update request from the node (which has changed its IP and must update its hname), they ask to the other gnode for the old andna_caches.
Moreover the ANDNA_MIN_UPDATE_TIME (the minum amount of time to be waited before sending an update os the hname) has to be reduced to NEW_HOOK_WAIT_TIME, which is the minimum amount of time to be waited before rehooking. This is necessary, because all the hname updates sent before ANDNA_MIN_UPDATE_TIME seconds have elapsed since the last update rejected. If a gnode rehooked, the hostname of its nodes has to be updated, therefore the update request must be accepted.
And that's all
That's all folks.
Alpt, Katolaz, Mancausoft, Uscinziatu