Multiple Access Covert Channels

1. Multiple Access Covert Channels Ira Moskowitz Naval Research Lab moskowitz@nrl.itd.navy.mil Richard Newman Univ. of Florida nemo@cise.ufl.edu

2. Focus • Review covert channels from high assurance computing and anonymity • Define quasi-anonymous channel • Review analysis of single sender DMC • Analyze 2-sender DMC

3. Covert Channels • CC = communication contrary to design • Storage channels and timing channels • Storage channel capacity given by mutual information, in bits per symbol • Timing channel capacity analysis requires optimizing ratio of mutual information to expected time cost

4. Storage Channel Example • File system full/not full • High fills/leaves space in FS to signal 1 or 0 • Low tries to obtain space and fails or succeeds to “read” 1 or 0 • Low returns system to previous state

5. Timing Channel Example • High uses full time quantum in time sharing host to send 1, gives up CPU early to send 0 • Low measures time gaps between accesses to “read” 1 or 0

6. Anonymity Systems • Started with Chaum Mixes • Mix receives encrypted, padded msg • Decrypts/re-encrypts padded msg • Delays forwarding msg • Scrambles order of msg forwarding

7. Mixes • Mix may be timed (count number of msgs forwarded each time it fires) • Mix may fire when threshold reached (count time between firings) • Mixes may be chained • Studied timed Mix-firewalls and covert channels – now for threshold Mix-firewalls

8. Mix-firewall CC Model • Alice behind M-F • Eve listening to output of M-F • Clueless senders behind M-F • Each sender (Alice or Clueless) may either send or not send a msg each tick • Alice modulates her behavior to try to communicate with Eve

9. Channel Model • Discrete storage channel • Each clueless sends 0 or 1 msg per tick • Clueless are i.i.d. Bernouli random vars • Alice sends 0 or 1 msg per tick • Eve counts msgs per Mix firing • Clueless act as noise, rate decreases to zero as N increases (for fixed p)

10. Two Transmitter Model • Now two Alices, Alice1 and Alice2 • Each Alice has a quasi-anomymous channel to Eve • Alices act as noise with respect to each other

11. NRL Pump • NRL Network Pump considered multiple senders before • Lows send to Highs, with the timing of ACKs forming a CC from Highs to Lows • Pump modulates ACK timing to reduce the CC rate (but not eliminate it) • Highs interfere with each other’s timing • Pump uses timing channels – can’t apply

12. Degree of Collusion • If Alices work perfectly together, then can achieve C=log 3 bits/tick data rate (assuming no clueless) • “Existence assumption” - assume Alices know of each other (stationary), and pre-arrange coding, but do not collude once transmission begins

13. Shannon Channel • Distributions X, Y • Mutual Information I(X;Y) = I(Y;X) I(X;Y) = H(X) – H(X|Y) • Entropy H(X) and H(X|Y) conditional H • Capacity C = maxX I(X,Y)

14. Multiple Access Channels • Now have two inputs, X1 and X2 • Existence assumption, with a priori knowledge • Achievable error-free rates are joint • Rate pair (R1,R2) • Capacity estimated (incorrectly) as: C = log n / [(TM + TR )/2]

15. Multiple Access Channels • Mutual Information for A, B, C I(A;B|C) = H(A|C) – H(A|B,C) I(A,B;C) = H(A,B) – H(A,B|C) • Rate pair (R1,R2) must satisfy: 0 <= R1 <= I(X1;Y|X2), and 0 <= R2 <= I(X2;Y|X1), and 0 <= R1 + R2 <= I(X1 ,X2;Y)

16. Channel Transitions 0,0 ! 0 0,1 & 1 1,0 % 1,1 ! 2

17. Collaborating Alices • Can conspire to send data at rate 3/2 • Max possible is log2 3 = 1.58 • With feedback, can do better than 3/2: each at rate .76! (Gaarder & Wolf)

18. Conclusions • Introduced multiple access channels into analysis of covert channels • Analyzed simple (noiseless) channel with two Alices • Noted effects of varying levels of collusion • Noted difficulties with timing channels • Can’t study CCs in isolation!