1. 1st PKI Research Workshop, NIST, Gaithersburg 20021 A Note On SPKI’s Authorisation Syntax Olav Bandmann* Industrilogik L4i AB Mads Dam KTH/IMIT *Work done while at SICS, Swedish Institute of Computer Science. Supported by Microsoft Research, Cambridge

2. 1st PKI Research Workshop, NIST, Gaithersburg 20022 SPKI SPKI: Approach based on binding names and authorisations to keys SPKI authorisation certificate (issuer, subject, propagate, tag, validity) Tags (= authorisation expressions) given in special S-expression (LISP-like) syntax

3. 1st PKI Research Workshop, NIST, Gaithersburg 20023 Tuple Reduction Decisions resolved by tuple reduction –Cert vs cert –Request vs cert For tags, compute Z = AIntersect(X,Y), the most inclusive authorisation granted by both X and Y

4. 1st PKI Research Workshop, NIST, Gaithersburg 20024 Contributions Problem: AIntersect is not suitable for space/time critical applications In this paper: Restricted syntax which –Conforms with SPKI ”practice” (we think) –Has n log n procedure Other contributions: –Authorisation preorder  –Sound and complete axiomatisation for Standard syntax Restricted syntax

5. 1st PKI Research Workshop, NIST, Gaithersburg 20025 Objections But: –SPKI authorisation expressions (tags) are small –Requests do not involve the set construction It depends... –For hand-crafted certs and standard usage, maybe so –For e.g. macros, precomputation, richer delegation logics, maybe not More on this later

6. 1st PKI Research Workshop, NIST, Gaithersburg 20026 Authorisation Trees Rivest S-expressions – example: x = (object person (conds (group ”admin”) (unit ”finance”)) (op income read)) Authorisation and request in same syntax: y = (object person (conds (group ”admin”)) (op income read)) z = (object person (conds (group ”admin”) (unit ”finance”)) (op income)) Both y and z would grant x –”Being authorised by” = lists are extended to right

7. 1st PKI Research Workshop, NIST, Gaithersburg 20027 Authorisation Order Authorisation trees: t ::= a | (a t 1... t n ) where a is an atom, n ≥ 1 Authorisation order t 1  t 2, t 1 authorised by t 2 : –a ≤ t iff t ≤ a iff t=a –(x 1... x n ) ≤ (y 1... y m ) iff n ≥ m and x i ≤ y i (1 ≤ i ≤ m) Can show that: t 1 =AIntersection(t 1,t 2 ) iff t 1  t 2

8. 1st PKI Research Workshop, NIST, Gaithersburg 20028 Star Forms * forms abbreviate sets of S-expressions: –(*) : The wildcard –(* set X 1... X n ): Union of X 1,...,X n –(* range ) –(* prefix ) Example: t = (object person (conds (group ”admin”) (* set (unit ”finance”) (type ”Managers”))) (op income (* set read write)))

9. 1st PKI Research Workshop, NIST, Gaithersburg 20029 S-Expressions Set constants b, Val(b) nonempty set of atoms X ::= (*) | a | b | (a X 1... X n ) | (* set X 1... X m ) Semantics: || b || = Val(b) || (X 1... X n ) || = {(t 1... t k ) | k  n,  i:1  i  n t i  || X i ||} || (* set X 1... X m ) || = || X 1 || ...  || X m || Obs: || X || is lower closed: t 1  t 2  || X ||  t 1  || X ||

10. 1st PKI Research Workshop, NIST, Gaithersburg 200210 S-Expression Preorder Def. X ≤ Y iff || X ||  || Y || ||. || not suitable for algorithm Computes all paths through a tree Set constants (range, prefix) may give infinite sets Task: Decide - without computing ||. ||: Given t and X is t  X? Given X and Y, is X  Y?

11. 1st PKI Research Workshop, NIST, Gaithersburg 200211 Weak Preorder Let X ≤ w Y iff one of: 1 - 4.... 5.X=b 1, Y=b 2 and Val(b 1 )  Val(b 2 ) 6.X = (X 1... X m ), Y = (Y 1... Y n ), m≥n, and X i ≤ w Y i, 1≤i≤m 7.X = (* set X 1... X m ), X i ≤ w Y for all 1≤i≤m 8.X = b, Y = (* set...) and... 9.X not b nor (* set...) form, Y = (* set Y 1... Y n ) and X ≤ w Y i for some i: 1≤i≤n

12. 1st PKI Research Workshop, NIST, Gaithersburg 200212 Weak Preorder Let X ≤ w Y iff one of: 1 - 4.... 5.X=b 1, Y=b 2 and Val(b 1 )  Val(b 2 ) 6.X = (X 1... X m ), Y = (Y 1... Y n ), m≥n, and X i ≤ w Y i, 1≤i≤m 7.X = (* set X 1... X m ), X i ≤ w Y for all 1≤i≤m 8.X = b, Y = (* set...) and... 9.X not b nor (* set...) form, Y = (* set Y 1... Y n ) and X ≤ w Y i for some i: 1≤i≤n

13. 1st PKI Research Workshop, NIST, Gaithersburg 200213 Basic Properties Results:  w is a preorder  w is sound, i.e. X  w Y implies X  Y  w is incomplete Example: (a (* set b c))  (* set (a b) (a c)) but neither (a (* set b c))  (a b) nor (a (* set b c))  (a c)

14. 1st PKI Research Workshop, NIST, Gaithersburg 200214 (9) Is Problem Case Replace 9.X not b nor (* set...) form, Y = (* set Y 1... Y n ) and X ≤ w Y i for some i: 1≤i≤n By ix.X not b nor (* set...) form, Y = (* set Y 1... Y n ) and || X ||  || Y || Theorem: Preorder with ix. in place of 9. is sound and complete w.r.t. 

15. 1st PKI Research Workshop, NIST, Gaithersburg 200215 Restricted S-Expressions Non-atomic members of *-set expressions should have unique ”tag” r ::= (*) | a | b | (a r 1... r n ) | (* set r a1... r am ) r a ::= a’ | b | (a r 1... r n ) All a i must be distinct Idea: Push ”conflicts” to the leaves: (a (* set (b c) (b d) b)) -> (a (* set (b (* set c d)) b))

16. 1st PKI Research Workshop, NIST, Gaithersburg 200216 Restricted S-Expressions, 2 Result: For the restricted syntax  w is sound and complete: r 1  r 2 iff r 1  w r 2 Result: Any S-expression can be rewritten into equivalent restricted S-expression By: Eliminating ”tag conflicts” and nested *-sets

17. 1st PKI Research Workshop, NIST, Gaithersburg 200217 AIntersect Assume the Val(b) closed under intersections Exploit ”tags” when computing AIntersect (details in paper) Possible n log n algorithm: Sort *-set expressions according to tag, then use binary search Obtain: || AIntersect(r,r’) || = || r || iff r ≤ r’

18. 1st PKI Research Workshop, NIST, Gaithersburg 200218 Summary Characterisation of SPKI authorisation relation as partial order ≤ Weak version ≤ w of ≤ –Sound, incomplete, x ≤ w y computable in time O(|x||y|) Restricted S-expression syntax –≤ w complete –Appears to reflect SPKI practice AIntersect is glb with respect to ≤ –Running time n log n

19. 1st PKI Research Workshop, NIST, Gaithersburg 200219 The Objections 1.Certificates are small 2.Requests do not involve *-set expressions Does this hold water?

20. 1st PKI Research Workshop, NIST, Gaithersburg 200220 The Objections, 2 1.What is SPKI practice? 2.SPKI cert-cert reductions can involve *-sets in both arg’s – are they sometimes time critical? 3.Cannot application program-generated certs become quite complex/large? –Ex: Request precomputation –Ex: Use *-set’s as macros, e.g. MidWestLocs = (* set... (loc Nebraska Lincoln) (loc Kansas Topeka Centre) (loc Kansas Topeka North)... )

21. 1st PKI Research Workshop, NIST, Gaithersburg 200221 Related Work: Delegation AB A to delegate authority to B to administer A’s security policies

22. 1st PKI Research Workshop, NIST, Gaithersburg 200222 Delegation, 2 Richer models of delegation Constrained delegation: Explicit issuance of new privileges Delegation tree constraints (a b* c) Stepwise refinement of constraints (requests) Forthcoming: SPKI + Kleene star Papers: Sadighi, Sergot, Bandmann - Security protocols 01 Bandmann, Dam, Sadighi - S&P 02