Re: History: Question on C14N list of nodes instead of subtrees

Hi John,

>Your point on the complexity of the expression to be evaluated is
>well-taken.  One point of interest however, is that the bound is not,
>strictly speaking, O(log n).  In the worst case it can be very much
>worse, but cases in practice it is likely to be very much better than
>O(log n).  The reason is that XML documents tend to lack depth relative
>to the number of nodes.  The O(log n) rating would only apply in cases
>where a constant branching factor is guaranteed in the parse tree,
>whereas nodes in real XML documents tend to have lots more siblings than

Right, I was talking in terms of a "mathematically average"
document, whatever that means. FWIW, a "simple" signature
has 21 nodes and depth 6.

>Perhaps more to the point, Donald Eastlake's recent communications with
>me are most instructive.  In them, he pointed out alternatives to some
>of my earlier expressions, which were a bit kludgy because I knew a lot
>less about XPath back when they were created.  The predicate you
>  count(id('to-be-signed') | ancestor-or-self::node()) =
>    count(ancestor-or-self::node())
>permits only those nodes whose ancestor count is equal to the ancestor
>count plus a particular node identified by id.  In other words, the
>predicate permits a node identified by id and the node's descendants.  I
>came up with this before I really understood the issues in capturing
>namespace and attribute nodes (in the ancestor direction, namespace and
>attribute nodes take element parents, but these types of nodes do not
>register as 'children' of that element so the descendant-or-self::node()
>test does not match them).  Only later did I discover the //@* and
>//namespace::* notation when trying to find some way of expressing the
>default expression for canonicalization, which should be default include
>all nodes.  Donald combined this with the notion of using the id
>function to obtain a subtree root, resulting in the logically equivalent
>	(id('to-be-signed')//. | id('to-be-signed')//@* |
>id('to-be-signed')//namespace::* )
>Presumably, the id function will be backed by a hash table, providing
>constant expected time lookup of the subtree root.  The next step after
>each id() function invocation calls for a linear time traversal of the
>subtree, performing a constant time test at each node.  Finally, as long
>as the union operations are done intelligently as merge operations, the
>whole thing comes out as worst case O(n) where n is the number of nodes
>in the subtree (not in the document!).  This should be remarkably

The problem is that XMLDSIG does not utilise XPath in this
manner; it uses the XPath expression as a boolean test for
each node in the input set, so the expression above will
evaluate to true for every node in the document (presuming
there exists an element of such ID).

If we formulate a new XMLDSIG XPath intersection transform
then we can use these expressions to solve some problems
more efficiently.

>As for the other larger expression you included below, I could benefit
>from a thorough description of its context as there *may* be a way to do
>it more efficiently, but I'm a little short of time and it is not
>immediately obvious exactly what it is doing.  Give me a bit more
>context, and I'll bang around in the XPath spec a bit more and see if
>something pops out.  It looks like you are trying to exclude a subtree
>rather than include a subtree, in which case it may be hard to come up
>with something because XPath has no native support for set subtract or
>intersect.  We may have to get creative (add a function or something).

I believe that the earlier expression is trying to sign
a portion of the XML document relative to the signature:

count((here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//. |
here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//@* |
here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//namespace::*) |
self::node()) =
count((here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//. |
here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//@* |
ere()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//namespace:: *))

Here he is trying to sign just the aida:signedContent element
and its children without using IDs. There is no way to formulate
this given our current XPath filter without an "average" cost
of log(n) per node in the input set because you'll always
have to check each node's ancestry.


>John Boyer
>PureEdge Solutions Inc.
>>>Finally, as to the speed issue that the originator is experiencing, I'd
>>>say he is suffering from a non-optimized implementation.  The reason is
>>>that an O(n) traversal of the nodes of a parse tree is sufficient for
>>>including all such nodes in a node-set.  Since all members of the
>>>node-set will be rendered in a serialization, the cost is O(n).  Thus,
>>>the cost of putting all nodes in a node-set should (or can at least) be
>>>commensurate with serialization.  If it is taking progressively longer
>>>to calculate the node-set as the XML document grows, then the XPath
>>>implementation needs to be optimized.  Alternately, we only require
>>>behavior equivalent to the evaluation of the (//. | //@* |
>>>//namespace::*) expression.
>>The cost is more like O(n log(n)) because our use of XPath
>>as a per-node filter often requires evaluating, for each
>>node in the document, something along the lines of:
>>  count(id('to-be-signed') | ancestor-or-self::node()) =
>>   count(ancestor-or-self::node())
>>Here, ancestor-or-self is going to be an O(log(n)) operation.
>>In the originator's case he is trying to do an XPointer
>>and winding up with:
>>URI="", XPath=
>>. |
>>here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//@* |
>>ce::*) |
>>self::node()) =
>>. |
>>here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//@* |
>>e:: *))
>>This is O(log(n)) per node in the document (and you have to admit
>>that there is going to be a hefty constant in front of that O),
>>which is painful as the document size grows.
>>One option (off the top of my head, so I've not given it mich
>>thought) would be to introduce a new XPath intersection transform:
>>  <XPath>
>>here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//. |
>>here()/ancestor::aida:eDocument[1]/child::aida:signedContent[1]//@* |
>>  </XPath>
>>The result of this would be the intersection of the input node
>>set and the node set that results from evaluating the transform.
>>This would be entirely XPath based (no need for XPtr), and
>>would drop things to O(n) (with a significantly-reduced
>>constant) for doing signature-relative operations.

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Received on Thursday, 24 January 2002 15:03:47 UTC