## Host autoassignment ipv6 » History » Version 3

Victor Oncins, 11/22/2012 11:01 AM

 1 2 3 3 Victor Oncins `h1. Auto-assignment of IPv6 host-oriented prefixes and collision estimation` 1 Victor Oncins 3 Victor Oncins `One of the desired features is qmp nodes are able to offer native IPv6 addressing to final hosts. IPv6 based networks usually assign /64 prefix to each host-oriented interface, subnetted from a bigger /48. This implies the nodes have 2^16 possible /64 prefixes to auto-assign.` 3 Victor Oncins 3 Victor Oncins `If we want to use MAC address numbering as a mapping value, we'll need a mapping function from 48 bits of MAC to 48 bits of IPv6 prefix.` 3 Victor Oncins 3 Victor Oncins `According to this auto-configure addressing philosophy, we deduce that is impossible to avoid ` 3 Victor Oncins `the election of the same prefix /64 (collision) by one or more network interfaces.` 3 Victor Oncins 3 Victor Oncins `Thus the collision probability is greater than 0 if more than one network interface is auto-addressed. Anyway, we` 3 Victor Oncins `could calculate this probability and then estimate the maximum number of network interfaces that can be auto-addresses with ` 3 Victor Oncins `a probability collision less than certain value.` 3 Victor Oncins 3 Victor Oncins `Let l as the last l-LSB of a MAC address, where 1<=l<=24. We left the first 24 bits from OUI. Thus we have a k=2^l possible endings. If ` 3 Victor Oncins `we have in the network N different OUI we'll have p=N*2^(24-l) possible MAC addresses for each possible ending. Obviously n=k*p is the ` 3 Victor Oncins `total space of possible MAC present in a network. If the network randomly includes two or more MAC with the same l-bit ending from ` 3 Victor Oncins `different OUI we'll have a collision, i.e. the same IPv6 /64 prefix will be auto-assigned on different network interfaces.` 3 Victor Oncins 3 Victor Oncins `If we select randomly m < k interfaces (MAC addresses) from N OUI, we obtain ` 3 Victor Oncins 3 Victor Oncins `n!/m!n-m!` 3 Victor Oncins 3 Victor Oncins `different combinations without replacement. This set of m MAC addresses will contain all its MAC addresses with different l-bits ending. These ` 3 Victor Oncins `combinations will generate /64 prefixes without collision. The number of combinations with all different ending is` 3 Victor Oncins 3 Victor Oncins `k!/m!k-m! * p^m` 3 Victor Oncins 3 Victor Oncins `thus the non-collision probability is` 3 Victor Oncins 3 Victor Oncins `Pĉ(m) = k!/n!*n-m!/k-m! * p^m` 3 Victor Oncins 3 Victor Oncins `If only one interface is present in the network Pĉ(1) = kp/n = 1, i.e. the collision is impossible.` 3 Victor Oncins `We can now calculate the maximum number M of interfaces such that the probability of collision was less than certain value. The following table` 3 Victor Oncins `shows this number for a maximum collision probability of 4%.` 3 Victor Oncins 3 Victor Oncins `Prefix l M for N=2 M for N=20 M for N=200` 3 Victor Oncins `----------------------------------------------------` 3 Victor Oncins `/51 13 27 27 27` 3 Victor Oncins `/50 14 38 38 38` 3 Victor Oncins `/49 15 53 53 53` 3 Victor Oncins `/48 16 74 74 74` 3 Victor Oncins `/47 17 105 104 104` 3 Victor Oncins `/46 18 148 147 147` 3 Victor Oncins `/45 19 210 208 208` 3 Victor Oncins `/44 20 298 294 294` 3 Victor Oncins `/43 21 428 416 415` 3 Victor Oncins `/42 22 627 520 587` 3 Victor Oncins `/41 23 957 839 830` 3 Victor Oncins `/40 24 1656 1202 1174` 3 Victor Oncins 3 Victor Oncins `We note that the variation of M with the number of OUI is very small. Thus the maximum number of interfaces in a /48 network with a collision` 3 Victor Oncins `probability 4% is 74.`