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 arising in anonymity systems

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 figure Enclave, Eve, Alice, Clueless

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

Threshold Mix – No Clueless Noiseless timing channel Minimum delay of q Other delays of q +1, q +2, … Capacity of this simple timing channel: C = lim n!1 sup (log |Sn|)/n

Simple Timing Channel Capacity Delays of q +1, q +2, … Capacity of this simple timing channel: C = log w[q,1] , where w[q,1] is the unique positive root of 1 – (x –q + x –1) For theta=1, C=1, for 2, C = .6942, for 10, C=.26, for 50, 0.0832

Bounded Timing Channel Capacity Delays of q, q +1, q +2, …, q +N Capacity of bounded timing channel: C = log w[q,N] , where w[q,N] is the unique positive root of 1 – (x–q + x–(q +1) + … + x–(q +N)) For theta=1, C=1, for 2, C = .6942, for 10, C=.26, for 50, 0.0832

Neurons Basis for nervous system Soma receives information from dendrites Soma sends information via electrical impulse (spike) down axon Spike releases neurotransmitters across synaptic cleft at end of axon to dendrite Give picture of neuron

Spikes Spike, or action potential, changes potential from –70 mV to 50 mV Information passed by timing, not by magnitude of spike voltage Action potential propagation speed from 1 to 100’s of km/hr, F(size, sheath) Spike duration is 1-2 ms. Minimum refractory period between spikes Give picture spike voltage change – action potential

Timing Channels & Spikes Minimum delay Refractory period Information in timing Constant # messages Constant D voltage

MacKay-McCulloch Considered neuronal data rates Refractory time TR = 1 msec Increments of DT = 0.05 msec Maximum time TM = TR + nDT = 2 msec Capacity estimated (incorrectly) as: C = log n / [(TM + TR )/2] Incorrect numerator, should be n+1, denominator assumes uniform distribution of symbols.

MacKay-McCulloch Estimated 2.9 bps (3.1 bps is right) Can rewrite estimated capacity as: C = log n / [TR + nDT/2] But lim n!1log n / [TR + nDT/2] = 0 , when in fact, limiting rate is 3.24 bps Graph of capacities of correct and M&M vs. log(n)

Majani & Rumsey For constant symbol time, 2-input DMC, with noise, showed optimal distribution for inputs had pr(0) in [1/e , 1-1/e] Liang proved conjecture for n-input DMC These results do not apply when the symbol times vary Graph of capacities of correct and M&M vs. log(n)

Noise What about when there is noise? Can no longer use algebraic approach Rather than using simple mutual info, It = H(X)/E(T) must use conditional entropy, It = H(X)-H(X|Y)/E(T) Graph of capacities of correct and M&M vs. log(n)

Conclusions Introduced problem of covert channels through threshold Mix-firewalls Analyzed simple (noiseless) channel Compared to biological information model Corrected earlier estimates of M & M Showed that MRL results do not apply First shot at analysis in presence of noise Graph of capacities of correct and M&M vs. log(n)