A Formal Foundation for XrML

Vicky WeissmanJoint work with Joe Halpern

The big picture A policy says that under certain

conditions an action, such as downloading a file, is permitted or forbidden.

Digital content providers want to write policies about how their

works may be accessed, and they want their policies enforced.

Diverse apps – same need

Because we can’t regulate access to online content with precision: Digital libraries can’t put certain

content online; it might violate IP laws. The Greek Orthodox Archdiocese of

America is wary of defamation. Cultural traditions aren’t respected.

(Australian Aboriginal communities often restrict access to a clan or gender.)

XrML to the rescue XrML is a language for writing policies. Syntax is XML-based. Semantics is given in 2 ways.

1. An English interpretation of the syntax.2. An English description of an algorithm that

says if a set of XrML policies imply a permission.

Bottom line: write policies in XrML, enforce using the algorithm.

Industry likes XrML XrML endorsed by Adobe, Hewlett-

Packard, Microsoft, Xerox, Barnesandnoble.com, MPEG International Standards Committee…

Microsoft and others plan to make XrML-compliant products.

Will tomorrow’s OS, DVD player, … enforce XrML policies?

XrML Shortcomings No formal semantics.

Policies can be ambiguous. The interpretation of the syntax

doesn’t quite match the algorithm. The algorithm’s behavior on some

(realistic) input is unintuitive and unintended by language designers. E.g. If Alice is a student and every student

may eat lunch, may Alice? Alg. says no.

Improving XrML Fix the algorithm to match developers’

intent. Translate XrML policies to formulas in modal

first-order logic. Lets us compare XrML with languages in CS

literature, borrow complexity results, extensions,…

Formal semantics given in a fairly standard way. Prove our translation matches the

algorithm. Algorithm says policies imply a permission iff

translated policies imply translated permission.

First step: Choose a version

Options: XrML published by ContentGuard, XrML modified by MPEG standards

committee, 2003 version, or Wait for 2004 release, an ISO standard.

We chose the 2003 version. Bugs we find can be fixed. We refer to the 2003 version as XrML.

XrML syntax XrML is an XML-based language.

XrML policies are verbose. So, we present a syntax that is

more concise and easy to map to XrML syntax.

Syntax Principals

Agents (e.g., Alice, Bob) Resources

Digital content (e.g., a movie, an article) Rights

Actions (e.g., play, edit) Properties

Describe a principal (e.g., adult, trusted)

Syntax (cont.) Statements

Stmt ::= Pr(p) | Perm(p, r, s) | true Pr(p) means principal p has property

Pr. Perm(p, r, s) means p is permitted to

exercise right r over resource s.

Syntax (cont.) Statements

Stmt ::= Pr(p) | Perm(p, r, s) | true Pr(p) means principal p has property

Pr. Perm(p, r, s) means p is permitted to

exercise right r over resource s.

Syntax (cont.) Statements

Stmt ::= Pr(p) | Perm(p, r, s) | true Pr(p) means principal p has property

Pr. Perm(p, r, s) means p is permitted to

exercise right r over resource s.

Syntax (cont.) Statements

Stmt ::= Pr(p) | Perm(p, r, s) | true Pr(p) means principal p has property

Pr. Perm(p, r, s) means p is permitted to

exercise right r over resource s.

Syntax (cont.) grant ::=x1…xn(Stmt … Stmt

Stmt)

If condition holds, then conclusion holds. In our fragment, grants are closed

(no free variables). license ::= (grant, principal)

(g, p) means p issues/says g.

Stmt ::= Pr(p) | Perm(p, r, s) | true

condition conclusion

Examples Can write:

`Joe is a professor’ as true Prof(Joe) and Vicky says `Every professor who

gives a talk may have a cookie’ as(x (Prof(x) GivesTalk(x)

Perm(x, eat, cookie)), Vicky).

Examples Can write:

`Joe is a professor’ as true Prof(Joe) and Vicky says `Every professor who

gives a talk may have a cookie’ as(x (Prof(x) GivesTalk(x)

Perm(x, eat, cookie)), Vicky).

Examples Can write:

`Joe is a professor’ as true Prof(Joe) and Vicky says `Every professor who

gives a talk may have a cookie’ as(x (Prof(x) GivesTalk(x)

Perm(x, eat, cookie)), Vicky).

Principals – in some detail Set of principals is the set of

primitive principals (e.g., Alice, Bob) closed under union. E.g., Alice Bob is a principal. Often written as {Alice, Bob}.

According to the XrML doc, {p1,.., pn} represents p1, …, pn “acting together as one holistic identified entity”. But what does this mean?

Groups/members relationship Suppose that Alice has property PrA

and the group {Alice, …} has property Prg.

What should we infer? Option 1: nothing. Option 2: {Alice, …} has property

PrA. Option 3: Alice has property Prg.

Groups/members relationship Suppose that Alice has property PrA and

group {Alice, …} has property Prg. What should we infer?

Option 1: nothing. Option 2: {Alice, …} has property PrA. Option 3: Alice has property Prg.

XrML chooses each of these options (at different points in the specification).

Groups/members relationship Suppose that Alice has property PrA and

group {Alice, …} has property Prg. What should we infer?

Option 1: nothing. Option 2: {Alice, …} has property PrA. Option 3: Alice has property Prg.

XrML chooses each of these options (at different points in the specification).

No formal semantics language is inconsistent!

Our fix Since XrML is inconsistent…

We do not assume that a group has the properties of its members or vice-versa.

But can easily write policies to force either relationship (or both).

The syntax given here is a fragment of XrML. (See paper for details.)

XrML Algorithm Query(s,L,G) algorithm

s is a closed statement. L is a set of licenses. G is a set of grants that implicitly

hold. Returns true if s “follows” from L and

G. Query calls Auth and Holds.

Auth Algorithm Recall

s is a closed statement. L is a set of licenses. G is a set of grants that implicitly hold. A condition is a conjunction of

statements. Auth(s, L, G) returns a set D of

closed conditions; s “follows” from L and G if a condition in D “holds”.

Holds Algorithm Holds(d,L) algorithm

d is a closed condition. L is a set of licenses. Returns true if d “follows” from L.

Query(s, L, G) overviewQuery(s, L, G)

Set D to the output of Auth(s, L, G)

Return dD Holds(d, L)

s is a closed statement, L is a set of licenses, and G is a set of grants that hold implicitly.

s “follows” from L and G if a condition in the output of Auth(s, L, G) “holds”.

Holds(d, L) returns true if d “follows” from L.

Problem Let g = true Student(Alice),

g’ = x (Student(x) Perm(x, eat, lunch))

May Alice eat lunch? Query(Perm(Alice, eat, lunch), , {g, g’})

Problem Let g = true Student(Alice),

g’ = x (Student(x) Perm(x, eat, lunch))

May Alice eat lunch? Query(Perm(Alice, eat, lunch), , {g, g’})

Query calls Auth(Perm(Alice, eat, lunch), , {g, g’}).

Auth returns {Student(Alice)}.

Problem Let g = true Student(Alice),

g’ = x (Student(x) Perm(x, eat, lunch))

May Alice eat lunch? Query(Perm(Alice, eat, lunch), , {g, g’})

Query calls Auth(Perm(Alice, eat, lunch), , {g, g’}). Auth returns {Student(Alice)}. Query calls Holds(Student(Alice), ).

lost g!

Problem Let g = true Student(Alice),

g’ = x (Student(x) Perm(x, eat, lunch))

May Alice eat lunch? Query(Perm(Alice, eat, lunch), , {g, g’})

Query calls Auth(Perm(Alice, eat, lunch), , {g, g’}). Auth returns {Student(Alice)}. Query calls Holds(Student(Alice), ). Holds returns false; so, Query returns false.

lost g!

The fix To correct the problem, pass G to

Holds and modify Holds to use the new info.

Bug is easy to find and easy to fix, but still made it into the released March 2003 version of the spec.

Another bug Query(s, , {x (Perm(p, issue, x) s)})

Query calls Auth on same input. Auth returns {Perm(p, issue, g) | g is a

grant}. Recall: Auth output is a set of closed

conditions. Query calls Holds on each returned

condition.

Another bug Query(s, , {x (Perm(p, issue, x) s)})

Query calls Auth on same input. Auth returns {Perm(p, issue, g) | g is a grant}.

Recall: Auth output is a set of closed conditions. Query calls Holds on each returned condition.

The set of grants is infinite. g0 = true Student(Alice) gi = true Perm(Bob, issue, gi-1), i = 1, …

D is an infinite set; so, Query doesn’t terminate.

Our fix Restrict the grants in the language.

If a grant g has a condition d, d mentions a resource variable x, and x is free in d, then x is free in g’s conclusion.

Easy to prove that if the restriction is met, then Auth always returns a finite set.

Can make an empirical argument for why this restriction is okay.

But that’s not all…

In this small fragment of XrML, there are 2 other bugs. See paper for details.

The translation The translation is fairly straightforward. Two points worth noting:

Query assumes that a grant g holds, if it’s issued by some trusted principal (i.e., a principal whose permitted to issue g).

Holds(d, L, G) returns true iff d logically follows from L and G. So, a condition d holds iff d logically follows from L and G.

The translation depends on L and G.

Correctness

Thm: the fixed Query(s, L, G)

returns true iff lLl L,G gG gL,G sL,G is true in every model that satisfies the union properties (p1p2 = p2p1, …). tL,G is the translation of t wrt L and G.

Complexity The XrML alg. runs in exponential

time. The XrML document says that the

language implementers are responsible for optimizations.

But using the translation, we can prove that…

Complexity Determining if a set of XrML grants

imply a statement is NP-hard. This is because the language supports

sets of primitive principals. If we remove from the language…

XrML translates (essentially) to Datalog, which is a well-known tractable language.

Given the translation, finding a tractable, fairly expressive fragment is easy.

Summary Industry wants to implement XrML but … XrML has no formal semantics

and needs them! We give formal semantics to a

representative fragment of XrML. Even a small fragment is intractable.

We can leverage results in the CS literature to find fairly expressive, tractable options.

Next step: Add negation to XrML. This is critical for merging policies.

Two minor bugs in paper (don’t effect results); corrected version online.

talk ends on preceding slide

Sample XrML policy Consider the policy `anyone may

play the movie `Big Hit’ for $2 (per use)’.

We could write this policy in XrML as…

<license><grant>  <forAll varName="anyone" />

<!-- This is saying that anyone can use this grant.  -->   <principal varRef="anyone" /> <!-- The right to play the movie is granted  -->   <cx:play />

<!-- This is the movie that we are giving access to.   -->

<cx:digitalWork> <cx:title>Big Hit </cx:title>  

</cx:digitalWork><!-- $2.00 each  --> <sx:fee>

<sx:paymentPerUse>  <sx:rate currency="USD">2.00</

sx:rate> </sx:paymentPerUse

</sx:fee>  </grant> 

</license>

The translation We now translate XrML licenses and grants to

“equivalent” formulas in modal first-order logic.

The translation relies on which licenses have been issued and which grants implicitly hold.

Let sL,G be the translation of any string s wrt the input parameters L and G.

Translation (cont.) Except for licenses and grants,

translation is easy. We assume a constant cg for each grant g Perm(p, issue, g)L,G = Perm(p, issue, cg)

(d1 d2)L,G = d1L,G d2

L,G, Pr(p)L,G = Pr(p), and trueL,G = true

Translating licenses Recall: (g, p) means p said g. According to Query,

if p may issue g, then (g,p) means that g holds otherwise, (g, p) is meaningless

Option 1: (g, p)L,G = Said(p, cg), restrict to models satisfying the axiom scheme

Said(p, cg) Perm(p, issue, cg) gL,G

Option 2: (g, p)L,G = Perm(p, issue, cg) gL,G

Translating grants x1…xn(d e)L,G =

x1…xn (Holds(d, L, G) eL,G) Holds(d, L, G) returns true iff d is a

logical consequence of L and G. Define a modal operator Val, where

Val() is true in a model m iff is true in all models.

Holds(d, L, G)=Val(lL l L,G gG gL,G dL,G )