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Originally Posted by xyz987
Okay, but they still have a problem. There are millions of subtrees, picking a ramdon root key for each of them is not and efficient method. Also, I have not read yet NNL paper but you are always talking about a unique tree for everything, so subtrees should be part of this unique tree (the 30 level tree)
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Yes, subtrees are part of the 31 level tree (edited from references to 30 level - see below). The paper says to choose a different random key for every node in the tree. I agree, it is a large number. I came up with 64 Gb of data in random numbers. (32 levels counting from 0 level at bottom to level 31 at top times 16 bytes for each 128 bit key).
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Furthermore arnezami's soft player has received 22 device keys for one of the 22 level trees (the first one). However, any player also has 231 more keys (253 - 22 = 231). So the next 21 keys may be located at the second 22 level tree (at one of the two 21 level trees it has), the next 20 keys at the third 22 level tree, and so on. This order is just an example, in fact I am saying that subtrees are also using keyspace of the 30 level tree (order is not important).
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Yes, I agree. [edit: I think I read your intent here incorrectly. The 22 device keys for one subtree tell you nothing about the 22 keys for another adjacent one of the 512 subtrees, nor anything about either of the two sets of 21 device keys for the same one of the 512 subtrees. Device keys come from the random number assigned to the root node of a subtree. That's why all nodes get a random number assigned in a master 31 level tree - so knowing some device keys from one subtree tells you nothing about other subtrees.]
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Not so isolated, read above.
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I'm not sure how the above makes them not isolated.
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BTW, it should be 31 level tree. 30 - 22 = 8 and 2^8 = 256, not 512
Edit: Also, there are up to 31 bits available for the path.
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Yes, that makes sense, I'm always messing up at the boundaries. I edited this post to change my references to a 31 level tree for the large tree. I edited the random number data size too, but I still may be off by a factor of two.
Notice that the processing keyspace size is larger than the 31 level tree of random number master keyspace. Every node gets only one random number from the master keyspace, but it gets a processing key from every other node above it. (Well actually only from the nodes up to the 22 level.) Fortunately devices can calculate all the processing keys they need from the device keys they get. So far only one of those processing keys has been found!