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

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

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

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 Picture here would be nice

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 Picture of Hi and Lo timing…

Anonymity Systems Started with Chaum Mixes Mix receives encrypted, padded msg Decrypts/re-encrypts padded msg Delays forwarding msg Scrambles order of msg forwarding Picture of mix taking messages and scrambling them

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

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 Show CC from Alice to Eve

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)

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 For theta=1, C=1, for 2, C = .6942, for 10, C=.26, for 50, 0.0832

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 For theta=1, C=1, for 2, C = .6942, for 10, C=.26, for 50, 0.0832

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 Give picture of neuron

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) Give picture spike voltage change – action potential

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] Incorrect numerator, should be n+1, denominator assumes uniform distribution of symbols.

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) Incorrect numerator, should be n+1, denominator assumes uniform distribution of symbols.

Channel Transitions 0,0 ! 0 0,1 & 1 1,0 % 1,1 ! 2 0,0 ! 0 0,1 & 1 1,0 % 1,1 ! 2 Graph of capacities of correct and M&M vs. log(n)

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) Graph of capacities of correct and M&M vs. log(n)

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! Graph of capacities of correct and M&M vs. log(n)