## Host autoassignment ipv6 » History » Version 5

Victor Oncins, 11/22/2012 11:46 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 4 Victor Oncins `If we want to use MAC address numbering and grant the non-coincidence of auto-generated prefixes, we'll need a mapping function from 48 bits of MAC to 48 bits of IPv6 prefix. According to this auto-configure addressing philosophy, we deduce that is impossible to avoid the election of the same prefix /64 (collision) by one or more network interfaces.` 1 Victor Oncins 4 Victor Oncins `Thus the collision probability is greater than 0 if more than one network interface is auto-addressed. We` 1 Victor Oncins `could calculate this probability and then estimate the maximum number of network interfaces that can be auto-addresses with ` 4 Victor Oncins `a collision probability less than certain value.` 3 Victor Oncins 4 Victor Oncins `Let 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 ` 4 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 ` 4 Victor Oncins `total space of possible MAC present in that network. If the network randomly includes two or more MAC with the same l-bit ending, we'll have a collision, i.e. the same IPv6 /64 prefix will be auto-assigned on different network interfaces.` 1 Victor Oncins 4 Victor Oncins `If we select randomly m (m < k) interfaces (MAC addresses) from N OUI, we obtain ` 1 Victor Oncins 5 Victor Oncins `n! / m! n-m!` 1 Victor Oncins 3 Victor Oncins `different combinations without replacement. This set of m MAC addresses will contain a subset of combinations where all its MAC addresses have different l-bits ending. These combinations will generate /64 prefixes without collision. The number of such combinations is` 4 Victor Oncins 5 Victor Oncins `p^m * k! / m! k-m! ` 4 Victor Oncins 1 Victor Oncins `thus the non-collision probability is` 4 Victor Oncins 5 Victor Oncins `P_nc(m) = p ^m * k! n-m! / n! k-m!` 4 Victor Oncins 3 Victor Oncins `If only one interface is present in the network P_nc(1) = kp/n = 1, i.e. the collision is impossible.` 4 Victor Oncins `We can now calculate the maximum number M of interfaces such that the probability of collision is less than certain value. The following table` 4 Victor Oncins `shows this number for a maximum collision probability of 4%.` 3 Victor Oncins 3 Victor Oncins 5 Victor Oncins 4 Victor Oncins `|_.Prefix size |_.l |_.M for N=2 |_.M for N=20 |_.M for N=200 |` 4 Victor Oncins `|/51 |13 |27 |27 |27|` 4 Victor Oncins `|/50 |14 |38 |38 |38|` 4 Victor Oncins `|/49 |15 |53 |53 |53|` 1 Victor Oncins `|/48 |16 |74 |74 |74|` 4 Victor Oncins `|/47 |17 |105 |104 |104|` 4 Victor Oncins `|/46 |18 |148 |147 |147|` 4 Victor Oncins `|/45 |19 |210 |208 |208|` 4 Victor Oncins `|/44 |20 |298 |294 |294|` 4 Victor Oncins `|/43 |21 |428 |416 |415|` 4 Victor Oncins `|/42 |22 |627 |520 |587|` 4 Victor Oncins `|/41 |23 |957 |839 |830|` 4 Victor Oncins `|/40 |24 |1656 |1202 |1174|` 5 Victor Oncins 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.`