RDF [RDF11-CONCEPTS] describes a graph-based data model for making claims
about the world and provides the foundation for reasoning upon that graph
of information. At times, it becomes necessary to compare the differences
between sets of graphs, digitally sign them, or generate short identifiers
for graphs via hashing algorithms. This document outlines an algorithm for
normalizing RDF datasets such that these operations can be
performed.
Status of This Document
This section describes the status of this
document at the time of its publication. A list of current W3C
publications and the latest revision of this technical report can be found
in the W3C technical reports index at
https://www.w3.org/TR/.
This document describes the URDNA2015 algorithm for canonicalizing
RDF datasets, which was the input from the
W3C Credentials Community Group
published as [CCG-RDC-FINAL].
There are other canonicalization algorithms actively being considered
by the Working Group – notably [Hogan-Canonical-RDF];
future versions of this document may change accordingly.
See Issue 6: Compare the two algorithms, and decide on basis for our work
and Issue 10: C14N choice criteria
for further discussion.
Publication as a Working Draft does not
imply endorsement by W3C and its Members.
This is a draft document and may be updated, replaced or obsoleted by other
documents at any time. It is inappropriate to cite this document as other
than work in progress.
This document was produced by a group
operating under the
W3C Patent
Policy.
W3C maintains a
public list of any patent disclosures
made in connection with the deliverables of
the group; that page also includes
instructions for disclosing a patent. An individual who has actual
knowledge of a patent which the individual believes contains
Essential Claim(s)
must disclose the information in accordance with
section 6 of the W3C Patent Policy.
When data scientists discuss canonicalization,
they do so in the context of achieving a particular set of goals.
Since the same information may sometimes be expressed in a variety of different ways,
it often becomes necessary to transform each of these
different ways into a single, standard representation.
With a standard representation, the differences between
two different sets of data can be easily determined,
a cryptographically-strong hash identifier can be generated for a particular
set of data,
and a particular set of data may be digitally-signed for later
verification.
In particular, this specification is about normalizing
RDF datasets, which are collections of graphs. Since
a directed graph can express the same information in more than one
way, it requires canonicalization to achieve the aforementioned goals
and any others that may arise via serendipity.
Most RDF datasets can be normalized fairly quickly, in terms
of algorithmic time complexity. However, those that contain nodes that do
not have globally unique identifiers pose a greater challenge. Normalizing
these datasets presents the graph isomorphism problem, a
problem that is believed to be difficult to solve quickly. More formally,
it is believed to be an NP-Intermediate problem, that is, neither known to
be solvable in polynomial time nor NP-complete. Fortunately, existing real
world data is rarely modeled in a way that manifests this problem and new
data can be modeled to avoid it. In fact, software systems can detect a
problematic dataset and may choose to assume it's an attempted denial of
service attack, rather than a real input, and abort.
This document outlines an algorithm for generating a canonical
serialization of an RDF dataset given an RDF dataset as input.
The algorithm is called the
Universal RDF Dataset Canonicalization Algorithm 2015 or
URDNA2015.
1.1 Uses of Dataset Canonicalization
There are different use cases where graph or dataset canonicalization are important:
Determining if one serialization is isomorphic to another.
Digital signing of graphs (datasets) independent of serialization or format.
Comparing two graphs (datasets) to find differences.
Communicating change sets when remotely updating an RDF source.
A canonicalization algorithm is necessary, but not necessarily sufficient, to handle many of these use cases. The use of blank nodes in RDF graphs and datasets has a long history and creates inevitable complexities. Blank nodes are used for different purposes:
when a well known identifier for a node is not known, or the author of a document chooses not to unambiguously name that node,
when a node is used to stitch together parts of a graph and the nodes themselves are not interesting (e.g., RDF Collections in [RDF11-MT]),
when someone is trying to create an intentionally difficult graph topology.
Furthermore,
RDF semantics dictate that deserializing an RDF document
results in the creation of unique blank nodes,
unless it can be determined that on each occasion,
the blank node identifies the same resource.
This is due to the fact that blank node identifiers
are an aspect of a concrete RDF syntax
and are not intended to be persistent or portable.
Within the abstract RDF model,
blank nodes do not have identifiers
(although some
RDF store
implementations may use stable identifiers and may choose to make them portable).
See Blank Nodes
in [RDF11-CONCEPTS] for more information.
RDF does have a provision for allowing blank nodes
to be published in an externally identifiable way through the use of
Skolem IRIs,
which allow a given RDF store to replace the use of blank nodes
in a concrete syntax with IRIs,
which then serve to repeatably identify that blank node within that particular RDF store;
however, this is not generally useful for talking about the
same graph in different RDF stores,
or other concrete representations.
In any case, a stable blank node identifier defined for one
RDF store or serialization is arbitrary,
and typically not relatable to the context within which it is used.
This specification defines an algorithm for creating stable blank node identifiers repeatably for different serializations possibly using individualized blank node identifiers of the same RDF graph (dataset) by grounding each blank node through the nodes to which it is connected, essentially creating Skolem blank node identifiers. As a result, a graph signature can be obtained by hashing a canonical serialization of the resulting normalized dataset, allowing for the isomorphism and digital signing use cases. As blank node identifiers can be stable even with other changes to a graph (dataset), in some cases it is possible to compute the difference between two graphs (datasets), for example if changes are made only to ground triples, or if new blank nodes are introduced which do not create an automorphic confusion with other existing blank nodes. If any information which would change the generated blank node identifier, a resulting diff might indicate a greater set of changes than actually exists.
Editor's note
Add descriptions for relevant historical discussions and prior art:
This document is a detailed specification for an RDF dataset
canonicalization algorithm. The document is primarily intended for the
following audiences:
Software developers that want to implement an RDF dataset
canonicalization algorithm.
Masochists.
To understand the basics in this specification you must be familiar with
basic RDF concepts [RDF11-CONCEPTS]. A working knowledge of
graph theory and
graph isomorphism
is also recommended.
1.3 Typographical conventions
This section is non-normative.
The following typographic conventions are used in this specification:
markup
Markup (elements, attributes, properties),
machine processable values (string, characters, media types),
property names,
and file names are in red-orange monospace font.
variable
A variable in pseudo-code or in an algorithm description is italicized.
definition
A definition of a term, to be used elsewhere in this or other specifications,
is italicized and in bold.
References to a definition in this document,
when the reference itself is also a markup, is underlined,
in a red-orange monospace font, and is also an active link to the definition itself.
A reference to a definition in another document,
when the reference itself is also a markup,
is underlined and italicized in a red-orange monospace font,
and is also an active link to the definition itself.
Examples are in light khaki boxes, with khaki left border,
and with a numbered "Example" header in khaki.
Examples are always informative. The content of the example is in monospace font and may be
syntax colored.
Examples may have tabbed navigation buttons
to show the results of transforming an example into other representations.
Code examples are generally given in a Turtle or TriG format for brevity,
where each line represents a single triple or quad.
Additionally, have the following implied directives:
BASE <http://example.com/>
PREFIX : <#>
Following the Turtle/TriG syntax rules, blank nodes always appear in the
`_:xyz` format.
2. Conformance
As well as sections marked as non-normative, all authoring guidelines, diagrams, examples, and notes in this specification are non-normative. Everything else in this specification is normative.
The key word MUST in this document
is to be interpreted as described in
BCP 14
[RFC2119] [RFC8174]
when, and only when, they appear in all capitals, as shown here.
A blank node identifier
as specified by [RDF11-CONCEPTS]. In short, it is a string that begins
with _: that is used as an identifier for a
blank node. Blank node identifiers
are typically implementation-specific local identifiers; this document
specifies an algorithm for deterministically specifying them.
Concrete syntaxes, like [Turtle] or [N-Quads], prepend blank node identifiers with the _: string
to differentiate them from other nodes in the graph. This affects the
canonicalization algorithm, which is based on calculating a hash over the representations of quads in this format.
4. Canonicalization
Canonicalization is the process of transforming an
input dataset to a normalized dataset. That
is, any two input datasets that contain the same
information, regardless of their arrangement, will be transformed into
identical normalized dataset. The problem requires directed
graphs to be deterministically ordered into sets of nodes and edges. This
is easy to do when all of the nodes have globally-unique identifiers, but
can be difficult to do when some of the nodes do not. Any nodes without
globally-unique identifiers must be issued deterministic identifiers.
Editor's note
Strictly speaking, the normalized dataset must be serialized to be stable, as within a dataset, blank node identifiers have no meaning. This specification defines a normalized dataset to include stable identifiers for blank nodes, but practical uses of this will always generate a canonical serialization of such a dataset.
In time, there may be more than one canonicalization algorithm and,
therefore, for identification purposes, this algorithm is named the
"Universal RDF Dataset Canonicalization Algorithm 2015"
(URDNA2015).
Editor's note
This statement is overly prescriptive and does not include normative language.
This spec should describe the theoretical basis for graph canonicalization and describe
behavior using normative statements. The explicit algorithms should follow as an informative appendix.
4.1 Overview
This section is non-normative.
To determine a canonical labeling, URDNA2015 considers the
information connected to each blank node.
Nodes with unique first degree information can immediately be issued a canonical identifier
via the Issue Identifier algorithm.
When a node has non-unique first degree information,
it is necessary to determine all information that is transitively connected
to it throughout the entire dataset.
4.7 Hash First Degree Quads defines a
node’s first degree information via its first degree hash.
Hashes are computed from the information of each blank node.
These hashes encode the mentions incident to each blank node.
The hash of a string s, is the lower-case,
hexidecimal representation of the result of passing s
through a cryptographic hash function.
URDNA2015 uses the SHA-256 hash algorithm.
4.2 Canonicalization Algorithm Terms
input dataset
The abstract RDF dataset that is provided as input to
the algorithm.
The canonicalized representation of a quad is based on
canonical N-Triples
defined in [N-Triples].
A quad in canonical n-quads form represents a graph name in the same manner as a subject,
if present, and each quad is terminated with a single new line character (U+000A).
Editor's note
At present, there is no existing definition for a canonicalized [N-Quads] form.
There is a definition for
canonical N-Triples
in [N-Triples], which defines the form of a single triple,
without the terminating EOL.
The set of all quads in a dataset
that mention a node n is called its mention set of n,
denoted Qn.
gossip path
The gossip path between two blank nodes contained within
quads in a dataset, where the path is a sequence
of nodes and quads such that the first quad includes
the starting node as an component, and the last quad includes
the ending node as an component with each quad in the path
containing both the preceding and following nodes.
4.3 Canonicalization State
When performing the steps required by the canonicalization algorithm,
it is helpful to track state in a data structure called the
canonicalization state. The information contained in the
canonicalization state is described below.
Mapping all blank nodes to use this
identifier spec means that an RDF dataset composed of two
different RDF graphs will use different
identifiers than that for the graphs taken independently. This may
happen anyway, due to automorphisms,
or overlapping statements, but an identifier based on the resulting
hash along with an issue sequence number specific to that hash would
stand a better chance of surviving such minor changes, and allow the
resulting information to be useful for RDF Diff.
The identifier prefix is a string that is used at the beginning of an
blank node identifier. It should be initialized to a
string that is specified by the canonicalization algorithm. When
generating a new blank node identifier, the prefix
is concatenated with a identifier counter. For example,
c14n is a proper initial value for the
identifier prefix that would produce
blank node identifiers like c14n1.
An ordered map that relates existing identifiers to issued identifiers,
to prevent issuance of more than one new identifier per existing identifier,
and to allow blank nodes to
be reassigned identifiers some time after issuance.
4.5 Canonicalization Algorithm
Editor's note
At the time of writing, there are several open issues that will determine important details of the canonicalization algorithm.
Issue 4: What is the output of the c14n algorithm?
Following the discussion that just happened at the TPAC joint meeting with the VC.
An option is to return one particular serialization.
An another option is to return a mapping from bnodes to labels.
I prefer the second solution as it is more generic. It does not preclude which serialization to use downstream. It actually does not impose that you serialize the dataset (imagine storing a dataset in a triple store with canonical blank node labels).
Issue 6: Compare the two algorithms, and decide on basis for our work
At TPAC 2022, the RCH WG had a joint meeting with the VC WG, see minutes.
During that meeting, we had two presentations about canonicalization algorithms:
The first algorithm has some track record of incubation in the W3C CCG, and it has an existing specification.
On today's RCH WG meeting, there was a proposal to use the W3C CCG specification as a basis, but OTOH there was also a desire to compare the two algorithms to better understand how they differ, and why one might be used over the other.
So this issue is an invitiation to anyone who can tell us more about the differences between the two algorithms and their potential implications.
It removes restrictions on the type of RDF term that can occur in any slot in a quad tuple - literals as subjects or predicates, blank nodes as predicates etc. By implication, that would include RDF-start quoted triples.
RDF 1.1 separately changed "RDF dataset" to allow blank nodes for in the graph slot.
Generalized RDF does arise - for example, in some rules systems.
Covering generalized RDF gives some future proofing.
I completely agree with the importance of the "herd-privacy" canonicalization proposed in #4 (comment) by @dlongley when we use c14n with selective disclosure. However, if I understand it correctly, we would still have to improve the above algorithm; it seems to me that the following normalized datasets CX1 and CX2 are not modified via the above transformation, i.e., CX1==CY1 and CX2==CY2.
Therefore, even if Alice selectively hides the statement about her spouse, anyone can easily guess whether Bob or Carl is Alice's spouse based on the canonicalized identifiers or the order of unrevealed statement:
In the meeting on 2022-10-12, we discussed criteria that can be used to make a choice between alternative choices in specific steps in the c14n algorithm. The initial list of suggestions is below. We need to formalize this and, IMO, include it in the explainer doc.
ease of implementation
existing incubation / use in the marketplace
time / resource complexity in solving common datasets
time / resource complexity in solving complex (or poison?) datasets
Existence of formal proofs for the algorithms
Demonstration of review of formal proofs for the algorithms
reusing existing primitives that are available on various platforms
cover real life examples
Issue 11: Recording the canonicalization and hashing applied.
In the meeting on 2022-10-12, there was mention of needing to say which choices were made in generating the hash.
We already have the existing URDNA2015 as the canonicalization algorithm. Anything this working group does that makes any change to that will need to have a way to declare which algorithm was used to produce the resultant canonical form.
There may be good reasons for different hashing and signing algorithms.
We need a naming scheme of choices made, together with a way to transmit that information.
Issue 16: Optionally fail on duplicates in Hash N-Degree Quads? question
From the CG spec:
An additional input to this algorithm should be added that
allows it to be optionally skipped and throw an error if any
equivalent related hashes were produced that must be permuted
during step 5.4.4. For practical uses of the algorithm, this step
should never be encountered and could be turned off, disabling
canonizing datasets that include a need to run it as a security
measure.
In §4.5.2, point 5.4.2 defines, as part of the sentence, the identifier variable. This value is used and important in later steps, so I think it would be better to call out its creation (as the first, and in this case only, value of the identifier list) in a separate step.
The main algorithm creates, in (3), a non-normalized identifier list. However, apart from the fact that entries may be removed from it in 5.3, this list is not used. The problematic cases, in step (6) are retrieved based on the hash->bnode[] map, which is also pruned in step 5.4 to remove the simple cases.
Is this a bug somewhere or just an oversight and that list is not necessary?
The Hash N-degre Quads algorithm is defined with a set of specific input parameters (canonicalization state, the identifier for the blank node, and an identifier issuer). However, there is no clear statement in 6.2.4 of the main algorithm on exactly what parameter is used, especially for the the identifier which simply refers to the temporary issuer. The fact that the canonicalization state should be given (the one created in step 1) is fairly obvious but, for example, it is not clear whether the input to the algorithm should be b_n or n. (I presume it is n).
In general, if we define the various algorithms in a functional style (which is fine) then we have to check whether the call of the algorithms follows the same thing, or whether we rely on some "global" values like the canonicalization state.
Actually... the value of b_n in the same step (ie, in 6.2.3 of the main algorithm) isn't used anywhere. I presume that only the "side effect" is used, i.e., that the temporary issues will have a value for n (and may be reused later). If so, we should not assign the value to a variable at this point.
As a more general remark, the explanation/overview in the Hash N-Degree Quad uses different terms, names, etc, then in the real algorithmic part. As a consequence, it really does not help to understand what is happening.
I believe we should have real examples that show, step by step, what is happening in the algorithm itself to help understanding this. To be honest, I converted the (semi-)English text into code but I would not say I understand what is really happening…
URDNA2015 canonically labels an RDF dataset
by assigning each blank node a canonical identifier.
In URDNA2015, an RDF dataset D
is represented as a set of quads of the form < s, p, o, g >
where the graph component g is empty if and only if the
triple< s, p, o > is in the default graph.
This algorithm considers an RDF dataset to be a set of quads.
Two RDF datasets are considered to be isomorphic (i.e., the same modulo blank nodes),
if and only if they return the same canonically labeled list of quads
via URDNA2015.
URDNA2015 consists of several sub-algorithms.
These sub-algorithms are introduced in the following sub-sections.
First, we give a high level summary of URDNA2015.
Initialization.
Initialize the state needed for the rest of the algorithm
using 4.3 Canonicalization State.
Compute first degree hashes.
Compute the first degree hash for each blank node in the dataset using 4.7 Hash First Degree Quads.
Compute N-degree hashes for non-unique nodes.
For each repeated first degree hash (proceeding in Unicode code point order),
compute the N-degree hash via 4.9 Hash N-Degree Quads
of every unlabeled blank node that corresponds to the given repeated hash.
Canonically label remaining nodes.
In Unicode code point order of the N-degree hashes,
issue canonical identifiers to each corresponding blank node using
4.6 Issue Identifier Algorithm.
If more than one node produces the same N-degree hash,
the order in which these nodes receive a canonical identifier does not matter.
This step creates a hash for every blank node in the input document.
Some blank nodes will lead to a unique hash,
while other blank nodes may share a common hash.
This step establishes the canonical identifier for blank nodes having
a shared hash.
This is done by creating unique blank node identifiers for all
blank nodes traversed by the Hash N-Degree Quads algorithm,
running through each blank node without a canonical identifier in the order
of the hashes established in the previous step.
For each result in the hash path list,
code point ordered by the hash in result:
Explanation
The previous step created temporary identifiers for the
blank nodes sharing a common first degree hash,
which is now used to generate their canonical identifiers.
For each blank node identifier,
existing identifier, that was issued a temporary
identifier by identifier issuer in result,
issue a canonical identifier,
in the same order,
using the Issue Identifier algorithm,
passing canonical issuer and existing identifier.
Explanation
In Step 5.2,
hash path list was created with an ordered
set of results.
Each result contained a temporary issuer
which recorded temporary identifiers associated with
a particular blank node identifier in
identifier list.
This step processes each returned temporary issuer,
in order, and allocates canonical identifiers
to the temporary identifier mappings contained
within each temporary issuer,
creating a full order on the remaining blank nodes
with unissued canonical identifiers.
This step populates the normalized dataset with quads
substituting the original blank node identiers,
with the newly established canonical blank node identifiers.
Create a copy, quad copy, of q and replace any
existing blank node identifiern using the
canonical identifiers previously issued
by canonical issuer.
This algorithm issues a new blank node identifier for
a given existing blank node identifier. It also updates
state information that tracks the order in which new
blank node identifiers were issued. The order of issuance is
important for canonically labeling blank nodes that are isomorphic
to others in the dataset.
This algorithm calculates a hash for a given blank node
across the quads in a dataset in which that blank node
is a component.
If the hash uniquely identifies that blank node,
no further examination is necessary.
Otherwise, a hash will be created for the blank node using
the algorithm in 4.9 Hash N-Degree Quads
invoked via 4.5 Canonicalization Algorithm.
4.7.1 Overview
This section is non-normative.
To determine whether the first degree information of a node n is unique,
a hash is assigned to its mention set,
Qn.
The first degree hash of a blank node n,
denoted hf(n),
is the hash that results from 4.7 Hash First Degree Quads
when passing n.
Nodes with unique first degree hashes have unique first degree information.
For consistency, blank node identifiers used in Qn
are replaced with placeholders in a canonical n-quads serialization of that quad.
Every blank node component is replaced with either a or z,
depending on if that component is n or not.
The resulting serialized quads are then code point ordered,
concatenated, and hashed.
This hash is the first degree hash of n, hf(n).
4.7.2 Examples
This section is non-normative.
4.7.3 Algorithm
This algorithm takes the canonicalization state and a
reference blank node identifier as inputs.
Return the hash that results from passing the sorted
and concatenated nquads through the
hash algorithm.
4.8 Hash Related Blank Node
This algorithm generates a hash for some
blank node component of a quad,
considering its position within that quad.
This is used as part of the
Hash N-Degree Quads algorithm
to characterize the blank nodes related to some particular blank node
within their mention sets.
4.8.1 Overview
This section is non-normative.
An identifier for a blank node, related,
which is a component of some quad, is used along
with information describing its position within the quad to create
a representation of that blank node within the quad,
which is then hashed.
The identifier is first found from the following:
Set the identifier to use for related, preferring
first the canonical identifier for related if issued, second
the identifier issued by issuer if issued, and last, if
necessary, the result of the
Hash First Degree Quads algorithm,
passing related.
Explanation
If a canonical identifier was already issued for related,
it will be in the canonical issuer contained within
canonicalization state.
Otherwise, the temporary issuer instance may already
have a mapping for related.
Lastly, if no identifier, canonical or temporary, has already been issued,
a new identifier is created using the
Hash First Degree Quads algorithm.
Initialize a stringinput to the value of
position.
If position is not g, append
<, the value of the predicate in
quad, and > to input.
Append the string _:, followed by identifier, to input.
Explanation
This resulting string is used to generate a hash; in this respect, it is similar to
the Hash First Degree Quads algorithm which
uses the serialization of quads in nquads for hashing. For the sake of consistency, the
nquad representation of identifier is used in this step, hence the
appearance of the _: string.
Return the hash that results from passing input
through the hash algorithm.
4.9 Hash N-Degree Quads
This algorithm calculates a hash for a given blank node
across the quads in a dataset in which that blank node
is a component for which the hash does not uniquely identify that blank node.
This is done by expanding the search from quads directly referencing that
blank node (the mention set), to those quads
which contain nodes which are also components of quads in the mention set,
called the gossip path.
This process proceeds in every greater degrees of indirection until
a unique hash is obtained.
Editor's note
The 'path' terminology could also be changed to better
indicate what a path is (a particular deterministic serialization for
a subgraph/subdataset of nodes without globally-unique identifiers).
4.9.1 Overview
This section is non-normative.
Usually, when trying to determine if two nodes in a graph are
equivalent, you simply compare their identifiers. However, what if the
nodes don't have identifiers? Then you must determine if the two nodes
have equivalent connections to equivalent nodes all throughout the
whole graph. This is called the graph isomorphism problem. This
algorithm approaches this problem by considering how one might draw
a graph on paper. You can test to see if two nodes are equivalent
by drawing the graph twice. The first time you draw the graph the
first node is drawn in the center of the page. If you can draw the
graph a second time such that it looks just like the first, except
the second node is in the center of the page, then the nodes are
equivalent. This algorithm essentially defines a deterministic way to
draw a graph where, if you begin with a particular node, the graph
will always be drawn the same way. If two graphs are drawn the same way
with two different nodes, then the nodes are equivalent. A
hash is used to indicate a particular way that the graph
has been drawn and can be used to compare nodes.
When two blank nodes have the same first degree hash,
extra steps must be taken to detect global,
or N-degree, distinctions.
All information that is in any way connected to the blank node n
through other blank nodes, even transitively, must be considered.
To consider all transitive information,
the algorithm traverses and encodes all possible paths of incident
mentions emanating from n, called gossip paths,
that reach every unlabeled blank node connected to n.
Each unlabeled blank node is assigned a temporary identifier
in the order in which it is reached in the
gossip path being explored.
The mentions that are traversed to reach
connected blank nodes are encoded in these paths via related hashes.
This provides a deterministic way to order all paths coming from n that
reach all blank nodes connected to n without relying on input blank
node identifiers.
This algorithm works in concert with the main canonicalization algorithm
to produce a unique, deterministic identifier for a particular blank
node. This hash incorporates all of the information that
is connected to the blank node as well as how it is connected. It does
this by creating deterministic paths that emanate out from the blank
node through any other adjacent blank nodes.
Ultimately, the algorithm selects a shortest gossip path,
distributing canonical identifiers to the unlabeled blank nodes
in the order in which they appear in this path.
The hash of this encoded shortest path,
called the N-degree hash of n,
distinguishes n from other blank nodes in the dataset.
For clarity, we consider a gossip path encoded via the string s
to be shortest provided that:
The length of s is less than or equal to the length
of any other gossip path string s′.
If s and s′ have the same length (as strings),
then s is code point ordered less than or equal to s′.
For example, abc is shorter than bbc,
whereas abcd is longer than bcd.
The following provides a high level outline for how the N-degree hash of n
is computed along the shortest gossip path.
Note that the full algorithm considers all gossip paths,
ultimately returning the hash of the shortest encoded path.
Compute related hashes.
Compute the related hash Hn set for n,
i.e., all first degree mentions between n and another blank node.
Note that this includes both unlabeled blank nodes and those
already issued a canonical identifier (labeled blank nodes).
Explore mentions.
Given the related hash x in Hn,
record x in the data to hash Dn.
Determine whether each blank node reachable via the mention with related hash x
has already received an identifier.
Record the identifiers of labeled nodes.
If a blank node already has an identifier,
record its identifier in Dn once for every
mention with related hash x.
Skip to the next related hash in Hn
and repeat step 2.
Distribute and record temporary identifiers to unlabeled nodes.
For each unlabeled blank node,
assign it a temporary identifier according to the order in which it is reached in the gossip path,
recording its given identifier in Dn (including repetitions).
Add each unlabeled node to the recursion list Rn(x)
in this same order (omitting repetitions).
Recurse on newly labeled nodes.
For each ni in Rn(x)
Record its identifier in Dn
Append < r(i) > to Dn
where r(i) is the data to hash that results from returning to
step 1,
replacing n with ni.
Compute the N-degree hash of n.
Hash Dn to return the N-degree hash of n,
namely hN(n).
Return the updated issuer In
that has now distributed temporary identifiers to all unlabeled blank nodes connected to n.
As described above in step 2.3,
HN recurses on each unlabeled blank node
when it is first reached along the gossip path being explored.
This recursion can be visualized as moving along the path from n
to the blank node ni that is receiving a temporary identifier.
If, when recursing on ni,
another unlabeled blank node nj is discovered,
the algorithm again recurses.
Such a recursion traces out the gossip path from n
to nj via ni.
The recursive hash r(i) is the hash returned from
the completed recursion on the node ni
when computing hN(n).
Just as hN(n) is the hash of Dn,
we denote the data to hash in the recursion on ni
as Di.
So, r(i) = h(Di).
For each related hash x ∈ Hn,
Rn(x) is called the recursion list on
which the algorithm recurses.
4.9.2 Examples
This section is non-normative.
Editor's note
Add some examples ranging from simple to complicated and resource consuming.
4.9.3 Algorithm
Issue 16: Optionally fail on duplicates in Hash N-Degree Quads? question
An additional input to this algorithm should be added that
allows it to be optionally skipped and throw an error if any
equivalent related hashes were produced that must be permuted
during step 5.4.4. For practical uses of the algorithm, this step
should never be encountered and could be turned off, disabling
canonizing datasets that include a need to run it as a security
measure.
Add a mapping of hash to the
blank node identifier for component
to Hn, adding an entry
as necessary.
Create an empty string, data to hash.
For each related hash to blank node list mapping in
Hn, code point ordered
by related hash:
Explanation
This loop explores the gossip paths for each
related blank node sharing a common hash to identifier
finding the shortest such path (chosen path).
This determines how canonical identifiers for
otherwise commonly hashed blank nodes are chosen.
Each path is represented by the concatenation of the
identifiers for each related blank node
– either the issued identifier,
or a temporary identifier created using a copy of issuer.
Those for which temporary identifiers were issued are later
recursed over using this algorithm.
Create a recursion list, to store
blank node identifiers that must be
recursively processed by this algorithm.
For each related in p:
If a canonical identifier has been issued for
related by canonical issuer, append the string _:, followed by
the canonical identifier for related, to path.
Explanation
A canonical identifier may have been generated before calling this algorithm,
if it was issued from an earlier call to Hash First Degree Quads algorithm.
There is no reason to recurse and apply the algorithm to any related blank node that has already been assigned a canonical identifier.
Furthermore, using the canonical identifier also further distinguishes it from any temporary identifier, allowing for even greater efficiency in finding the chosen path.
Otherwise:
If issuer copy has not issued
an identifier for related, append
related to recursion list.
Explanation
Temporarily labeled nodes have identifiers recorded
in issuer copy,
which is later used to recursively call this algorithm,
so that eventually all nodes are given canonical identifiers.
Use the
Issue Identifier algorithm,
passing issuer copy and related, and
append the string _:, followed by the result, to path.
If chosen path is not empty and the length
of path is greater than or equal to the length
of chosen path and path is
greater than chosen path when
considering code point order,
then skip to the next
permutationp.
Explanation
If path is already longer than
the prospective chosen path,
we can terminate this iteration early.
Explanation
path is used to generate a hash at a later step; in this respect, it is similar to
the Hash First Degree Quads algorithm which
uses the serialization of quads in nquads for hashing. For the sake of consistency, the
nquad representation of blank node identifiers is used in these steps, hence the
usage of the _: string.
For each related in recursion list:
Explanation
The propective path is extended with
the hash resulting from recursively calling this algorithm
on each related blank node issued a temporary identifier.
Set result to the result of recursively executing
the
Hash N-Degree Quads algorithm,
passing related for identifier and
issuer copy for path identifier issuer.
Use the
Issue Identifier algorithm,
passing issuer copy and related; append the string _:, followed by
the result, to path.
If chosen path is not empty and the length
of path is greater than or equal to the length
of chosen path and path is
greater than chosen path when considering code point order,
then skip to the next p.
Explanation
If path is already longer than
the prospective chosen path,
we can terminate this iteration early.
If chosen path is empty or path is
less than chosen path when considering code point order,
set chosen path to path and chosen issuer
to issuer copy.
Append chosen path to data to hash.
Replace issuer, by reference, with
chosen issuer.
Return issuer and the hash that results from
passing data to hash through the
hash algorithm.
5. Privacy Considerations
Editor's note
TBD
6. Security Considerations
Editor's note
TBD
7. Use Cases
This section is non-normative.
Editor's note
TBD
8. Examples
This section is non-normative.
Editor's note
TBD
A. URGNA2012
This section is non-normative.
A previous version of this algorithm has light deployment. For purposes of identification,
the algorithm is called the
"Universal RDF Graph Canonicalization Algorithm 2012"
(URGNA2012),
and differs from the stated algorithm in the following ways:
In 4.9 Hash N-Degree Quads, the position parameter passed to
the Hash Related Blank Node algorithm
was instead modeled as a direction parameter, where it could have
the value p, for property, when the related blank node was a
subject and the value r, for reverse or reference, when
the related blank node was an object. Since URGNA2012 only normalized
graphs, not datasets, there was no use of the graph name position.
C. Changes since the First Public Working Draft of 24 November 2022
This section is non-normative.
The algorithm, and the examples, have been changed to systematically
use the xyz format for blank node identifiers, instead of
_:xyz. See Issue 46
for the discussion.
4.7 Hash First Degree Quads
was simplified to remove the simple flag,
which was unused in existing implementations.
The original design of the algorithm was to use the
assigned canonical blank node identifier,
if available, instead of _:a or _:z,
similar to how it is used in
the related hash algorithm, but this text never made it into the spec
before implementations moved forward.
Therefore, the hashes never change,
making the loop based on the simple
flag that calls this algorithm unnecessary.
See Issue 23 for the discussion.
Removed issue marker for
Issue 15
in 4.5 Canonicalization Algorithm,
adding a note that
literal
components of quads are not normalized,
and two literals with different syntactic representations
remain distinct resources.
Changed the way Blank Node identifiers are described
(see Issue 46),
generally omitting the leading _: which is a serialization artifact.
This is still required in the algorithms, but the distinction
between what is an identifier, and the serialzation form
is clarified.
D. Acknowledgements
This section is non-normative.
The editors would like to thank Jeremy Carroll for his work on the
graph canonicalization problem, Gavin Carothers for providing valuable
feedback and testing input for the algorithm defined in this
specification, Sir Tim Berners Lee for his thoughts on graph canonicalization
over the years, Jesús Arias Fisteus for his work on a similar
algorithm.
Editor's note
Acknowledge CCG and RCH WG. Consider using .publ_ack.json.
Issue 19: Add history of the development of the c14n work
It's important for both patent and person credit reasons to include the full history.