On 06/19/2012 02:18 PM, Mark Friedenbach wrote:
> On Tue, Jun 19, 2012 at 10:33 AM, Alan Reiner <etotheipi@gmail.com 
> <mailto:etotheipi@gmail.com>> wrote:
>
>     If we were to use a raw trie structure, then we'd have all the above
>     issues solved:  a trie has the same configuration no matter how
>     elements
>     are inserted or deleted, and accesses to elements in the tree are
>     constant time -- O(1).  There is no such thing as an unbalanced trie.
>     But overall space-efficiency is an issue.
>
>     A PATRICIA tree/trie would be ideal, in my mind, as it also has a
>     completely deterministic structure, and is an order-of-magnitude more
>     space-efficient.  Insert, delete and query times are still O(1).
>     However, it is not a trivial implementation.  I have occasionally
>     looked
>     for implementations, but not found any that were satisfactory.
>
>
> No, a trie of any sort is dependent upon distribution of input data 
> for balancing. As Peter Todd points out, a malicious actor could 
> construct transaction or address hashes in such a way as to grow some 
> segment of the trie in an unbalanced fashion. It's not much of an 
> attack, but in principle exploitable under particular timing-sensitive 
> circumstances.
>
> Self-balancing search trees (KVL, RB, 2-3-4, whatever) don't suffer 
> from this problem.
>
> Mark

I was using "unbalanced" to refer to "query time" (and also 
insert/delete time).  If your trie nodes branch based on the next byte 
of your key hash, then the max depth of your trie is 32.  Period.  No 
one can do anything to ever make you do more than 32 hops to 
find/insert/delete your data.   And if you're using a raw trie, you'll 
always use /exactly/ 32 hops regardless of the distribution of the 
underlying data.  Hence, the trie structure is deterministic 
(history-independent) and cannot become unbalanced in terms of access time.

My first concern was that a malicious actor could linearize parts of the 
tree and cause access requests to take much longer than log(N) time.  
With the trie, that's not only impossible, you're actually accessing in 
O(1) time.

However, you are right that disk space can be affected by a malicious 
actor.  The more branching he can induce, the more branch nodes that are 
created to support branches with only one leaf.