1. Non Interference, Open Systems, Information flows quantification Loïc HélouëtINRIA Rennes

2. 2 Non Interference [Goguen&Messeguer82] A system S, with n users U 1, …U n U 1 intereferes with U 2 through S iff what U 1 does affects what U 2 can do or observe

3. 3 U 1 (high) U 2(low) Low high S S Inheritance from 70’s Information systems Several levels of security (high,low) Users granted up to certain level. Can U 2 infer something about U 1 ’s actions or high values from his enabled actions and observation of all low values ?

4. 4 More formally ( U1 || S ) || U2  S || U2 q1q2 U1:o1 U2:o2 U2:o3 q3 q4 q5 U2:o2

5. 5 More formally ( U1 || S ) || U2  S || U2 q1q2 U1:o1 U2:o2q3 q4 U2:o2

6. 6 h1, h2 l1, l2 h1,  h2 l1, l2 h1, h2 l1, l2 h1, h2 l1, l2 h1,  h2 l1, l2 h1,  h2 l1,  l2 U1:o1 U2:o2 U1:o1U2:o2

7. 7 Non Interference, variations n Models for U 1,U 2, S (Automata, CSP, …) n Semantics of || n Notion of equivalence  –(Bisimulation,trace equivalence + Input/output) [Lowe][Ryan] [Focardi&Gorrieri 00] …

8. 8 Non interference with typing [Volpano & Smith] Typing programs of the form: p::= e | c e ::= x | l | n | e+e’ | e – e’ | e=e’ | e<e’ C::= e:= e’ | c; c’ | if e then c else c’ | while e do c | letvar x:=e in c | try x= e op e’ in c

9. 9 Some typing rules e :  c: , c’ :  If e then c else c’ If h then l := false else l=true A well-typed program Is non-interferent Reject programs such as :

10. 10 Idem for a Pseudo language with threads [Volpano98] Idem for probabilistic non-interference [Volpano98] [Boudol &Catellani] Concurrent language Non-interference problems: coarse grain semantics, Interference depends on reachability of some statements While e>e’ do e’:= f(e,e’) If e’ mod y = 0 then e’’:=0 Done If e’’ = 0 then l:=h else l:= l’

11. 11 Games & covert Channels Confinement Zone User Spy Security (Monitoring, firewall,…)

12. Message Sequence Charts 12 HMSC M1 M2 M3 M4M5 n n0n0 n1n1 n2n2 n3n3 Chose two processes p,q Build an arena : choices of p vs Rest of the system Observations of q : w i w1w1 w2w2 w3w3 w4w4 w5w5 w6w6

13. Message Sequence Charts 13 AB m(v) C p bMSC M1 bMSC M2 Choices AB n C q M1 M2 Events observed on instance C events executed on instance A ?p=>!m(v) ?q=>!n 01

14. 14 n0n0 n1n1 w1w1 w2w2 w3w3 w4w4 w5w5 w6w6 n2n2 n3n3 w7w7 Identify positions where p can pass information to q

15. 15 n0n0 n1n1 w1w1 w2w2 w3w3 w4w4 w5w5 w6w6 n2n2 n3n3 w7w7 Pass infinitely often through Covert channel = Winning strategy in a game (Muller or Buchi winning condition)

16. 16 Master Aldric Diamond Automata + ATL

17. 17 ATL A set of players  n Propositions p, labeling states ,  1   2 ATL formulas >   >   >  1 U  2, 

18. 18 ATL (Semantics) q ╞ >   iff –players in A have strategies such that in any computation staring from q,  holds at next stage [1] ╞  q ╞ >   iff –players in A have strategies such that in any computation statring from q, f holds along  i, l[i] ╞  >  1 U  2,  iff –players in A have strategies such that in any computation starting from q,  i, [i] ╞   and  0  j <i, [j] ╞  

19. 19 Covert flows in ATL  interf : A |=  interf iff  An interference in the system  covert : A |=  covert iff  A covert channel in the system  covert = « always eventually »  interf

20. 20 Concurrent Secrets [Darondeau06] A set of observers/users 1,..n A finite sate system A, with language L A  (  1,…,  n )* Some secret trajectories in the system S i  L A, shall never be known from user i Can users deduce that a trajectory belong to a secret ? The system must be opaque, i.e  w  S i,  w’  L A \ S i,  i (w)=  i (w’)

21. 21 Quantification [Lowe] n Classical Interference in timed CSP n + quantification of number of bits leaked per second a o1 o2 b o1 P: Q: o2

22. 22 Information Theory [Moskowitz 94] Relation between random variables of the system X, Y n Discrete Memoryless channels

23. 23 [Palamidessi] n Voting Systems, Loss of anonymity i1i1 i2i2 i3i3 o1o1 o2o2 VOTE

24. 24 Quantified Interference n [Denning] : Information Leak if –H(h s |l s’ ) < H(h s |l s ) – moving from s to s’ provides information on high values. –No analysis technique n [McLean] : Safe system if at time t –p(L t |L s ) =p(L t |(H s,L s )) n L s= L 1.L 2 … L t-1, n H s = H 1.H 2 … H t-1, sequences of values taken by H, L before t. n [Gray] :idem but I(H s ;L t |L s ) =0

25. 25 n [Clark] –Simple programming language –Quantify the information learned from the observation of inputs/outputs of a program. –Deterministic language : while,if, x:=f(y) –Leakage into a set of variables X L(X) = I(H i ;X  | L i ) n H i initial high (hidden)values n L i initial low (known) values X  Final values of X

26. 26 Aline, Eric, Loic HMSC M1 M2 M3 M4M5 n n0n0 n1n1 n2n2 n3n3 w1w1 w2w2 w3w3 w4w4 w5w5 w6w6 w7w7 w8w8

27. 27 Aline, Eric, Loic n0n0 n1n1 n2n2 n3n3 w1w1 w2w2 w3w3 w4w4 w5w5 w6w6 w7w7 w8w8 X1X1 X2X2 Y1Y1 Y2Y2 Y3Y3 I(X 1 …X n | Y 1 …Y q )

28. 28 Problems n Some information lost during concatenation: –abba.a = ab.baa=ab.ba.a n Y 1 =w 1 & Y 2 =w 2 n or Y 1 =w 3 & Y 2 = w 3 n or Y 1 =w 3 & Y 2 = w 4 & Y 3 = w 5 –Solution: w 1, …,w k form a code (unique decomposition). n No « nice form » for

29. 29 n The amount of information sent at n th use of the channel depends on the n-1 previous ones. n Special channel model –With memory –Stuttering n0n0 n1n1 n3n3 w1w1 w2w2 w3w3 w3w3 w5w5 w4w4

30. 30 Around AXML n Secret, interference –Where are the opponents –What should be kept secret n Coarse grain typing ? n Information theory ?