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*Victor Oncins, 11/22/2012 11:46 AM *

# Auto-assignment of IPv6 host-oriented prefixes and collision estimation¶

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.

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.

Thus the collision probability is greater than 0 if more than one network interface is auto-addressed. We

could calculate this probability and then estimate the maximum number of network interfaces that can be auto-addresses with

a collision probability less than certain value.

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

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

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.

If we select randomly m (m < k) interfaces (MAC addresses) from N OUI, we obtain

n! / m! n-m!

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

p^m * k! / m! k-m!

thus the non-collision probability is

P_nc(m) = p ^m * k! n-m! / n! k-m!

If only one interface is present in the network P_nc(1) = kp/n = 1, i.e. the collision is impossible.

We can now calculate the maximum number M of interfaces such that the probability of collision is less than certain value. The following table

shows this number for a maximum collision probability of 4%.

Prefix size | l | M for N=2 | M for N=20 | M for N=200 |
---|---|---|---|---|

/51 | 13 | 27 | 27 | 27 |

/50 | 14 | 38 | 38 | 38 |

/49 | 15 | 53 | 53 | 53 |

/48 | 16 | 74 | 74 | 74 |

/47 | 17 | 105 | 104 | 104 |

/46 | 18 | 148 | 147 | 147 |

/45 | 19 | 210 | 208 | 208 |

/44 | 20 | 298 | 294 | 294 |

/43 | 21 | 428 | 416 | 415 |

/42 | 22 | 627 | 520 | 587 |

/41 | 23 | 957 | 839 | 830 |

/40 | 24 | 1656 | 1202 | 1174 |

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

probability 4% is 74.