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Covert Channels and Anonymizing Networks. Ira S. Moskowitz --- NRL Richard E. Newman --- UF Daniel P. Crepeau --- NRL Allen R. Miller --- just hanging out. Motivation. Anonymity --- What do you think/say? optional desire or mandated necessity

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Covert channels and anonymizing networks

Covert Channels and Anonymizing Networks

Ira S. Moskowitz --- NRL

Richard E. Newman --- UF

Daniel P. Crepeau --- NRL

Allen R. Miller --- just hanging out


Motivation
Motivation

Anonymity --- What do you think/say?

optional desire or mandated necessity

Our interest is in hiding who is sending what to whom. Yet, even if we have this type of “anonymity” one might still be able to leak info.

Is this from a failure to truly obtain anonymity, or is it an inherent flaw in the model/design?


Covert channels
Covert Channels

The information is leaked via a covert channel (which is …)

Paranoid threat? Yes, but ....

This paper is a first step (for us) in tying anonymity and covert channels together.


Mixes
MIXes

A MIX is a device intended to hide source/message/destination associations.

A MIX can use crypto, delay, shuffling, padding, etc. to accomplish this.

Others have studied ways to “beat the MIX”

--active attacks to flush the MIX.

--passive attacks may study probabilities.

You all know this better than I :-)


Our scenario

covert channel

Our Scenario

MIX Firewalls separating 2 enclaves.

Eve

Enclave 2

Enclave 1

Alice

& Cluelessi

overt channel --- anonymous

Timed MIX, total flush per tick

Eve: counts # message per tick – perfect sync, knows # Cluelessi

Cluelessi are IID, p = probability that Cluelessi does not send a message

Alice is clueless w.r.t to Cluelessi


Toy scenario only clueless 1
Toy Scenario – only Clueless1

Alice can: not send a message (0), or send (0c)

Only two input symbols to the (covert) channel

What does Eve see? {0,1,2}

0

p

0

q

Eve

1

Alice

p

0c

q

2


Discrete memoryless channel

anonymizing

network

X

Y

Discrete Memoryless Channel

Y

A is the random variable representing

Alice, the transmitter to the cc

X has a prob dist

P(X=0) = x

P(X=0c) = 1-x

Y represents Eve

prob dist derived from A and channel matrix

X


In general P(X = xi) = p(xi), similarly p(yk)

H(X) = -∑i p(xi)log[p(xi)] Entropy of X

H(X|Y) = -∑kp(yk) ∑ip(xi|yk)log[p(xi|yk)]

Mutual information

I(X,Y) = H(X) – H(Y|X) = H(Y)-H(Y|X) (we use the latter)

Capacity is the maximum over dist X of I

For toy scenario

C = max x{ -( pxlogpx +[qx+p(1-x)]log[qx+p(1-x)]

+q(1-x)logq(1-x) ) –h(p) }

where h(p) = -{ p logp + (1-p) log(1-p) }


General scenario n clueless i
General Scenario N Cluelessi

0

pN

NpN-1q

0

1

.

.

.

pN

qN

NqN-1p

N

0c

qN

N+1


Conclusions
Conclusions

  • Highest capacity when very low or very high clueless traffic

  • Capacity (of p) bounded below by C(0.5)

  • Capacity monotonically decreases to 0 with N

  • C(p) is a continuous function of p

  • Alice’s optimal bias is function of p, and is always near 0.5


Future work
Future Work

  • One MIX firewall –distinguishable receivers

  • Relax IID assumption on Cluelessi

  • If Alice has knowledge of Cluelessi behavior…


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