Host autoassignment ipv6 » Historial » Versió 3
Victor Oncins, 22-11-2012 11:01
1 | 3 | Victor Oncins | h1. Auto-assignment of IPv6 host-oriented prefixes and collision estimation |
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2 | 1 | Victor Oncins | |
3 | 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. |
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5 | 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. |
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7 | According to this auto-configure addressing philosophy, we deduce that is impossible to avoid |
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8 | the election of the same prefix /64 (collision) by one or more network interfaces. |
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10 | Thus the collision probability is greater than 0 if more than one network interface is auto-addressed. Anyway, we |
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11 | could calculate this probability and then estimate the maximum number of network interfaces that can be auto-addresses with |
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12 | a probability collision less than certain value. |
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14 | 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 |
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15 | 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 |
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16 | 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 |
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17 | different OUI we'll have a collision, i.e. the same IPv6 /64 prefix will be auto-assigned on different network interfaces. |
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19 | If we select randomly m < k interfaces (MAC addresses) from N OUI, we obtain |
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21 | n!/m!n-m! |
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23 | different combinations without replacement. This set of m MAC addresses will contain all its MAC addresses with different l-bits ending. These |
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24 | combinations will generate /64 prefixes without collision. The number of combinations with all different ending is |
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26 | k!/m!k-m! * p^m |
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28 | thus the non-collision probability is |
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30 | Pĉ(m) = k!/n!*n-m!/k-m! * p^m |
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32 | If only one interface is present in the network Pĉ(1) = kp/n = 1, i.e. the collision is impossible. |
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33 | We can now calculate the maximum number M of interfaces such that the probability of collision was less than certain value. The following table |
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34 | shows this number for a maximum collision probability of 4%. |
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36 | Prefix l M for N=2 M for N=20 M for N=200 |
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37 | ---------------------------------------------------- |
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38 | /51 13 27 27 27 |
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39 | /50 14 38 38 38 |
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40 | /49 15 53 53 53 |
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41 | /48 16 74 74 74 |
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42 | /47 17 105 104 104 |
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43 | /46 18 148 147 147 |
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44 | /45 19 210 208 208 |
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45 | /44 20 298 294 294 |
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46 | /43 21 428 416 415 |
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47 | /42 22 627 520 587 |
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48 | /41 23 957 839 830 |
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49 | /40 24 1656 1202 1174 |
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51 | 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 |
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52 | probability 4% is 74. |