Timing Channels, Anonymity, Mixes, and Spikes

1. Timing Channels, Anonymity, Mixes, and Spikes Ira Moskowitz Naval Research Lab moskowitz@nrl.itd.navy.mil Richard Newman Univ. of Florida nemo@cise.ufl.edu

2. Focus • Review timing channels from high assurance computing and anonymity • Analyze timing channels • Review neuronal communications • Compare neuron’s spikes with timing channels • Synergy between these areas of study

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

9. 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

10. 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

11. 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)

12. 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))

13. 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

14. 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

15. Timing Channels & Spikes

16. 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]

17. 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

18. 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

19. 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)

20. 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