[tor-dev] Brainstorming about steganographic transports

David Fifield david at bamsoftware.com
Thu Jul 26 04:18:37 UTC 2012

This is a summary of some discussion among developers of pluggable
transports about steganographic channels and deriving them from protocol
grammars. Two things prompted the discussion:

* A program called appid, http://code.google.com/p/appid/ , which
  compiles simple protocol specifications into big regular expressions
  and uses them to classify network streams. Supported protocols are
  https://code.google.com/p/appid/source/browse/trunk/apps ; a sample is
  https://code.google.com/p/appid/source/browse/trunk/apps/afs . Roger
  suggested to make a program that takes one of these specifications and
  embeds data within a stream that appid will classify as the chosen

* This paper:
    "Provably Secure Steganography"
  The authors define a "channel" as a probability distribution on
  sequences. You can think of a channel as something that answers "given
  this prior history of packets, what are the possible next packets and
  their probabilities?" or even as an oracle that merely allows sampling
  this distribution. They show a method of steganographically encoding a
  bit within a channel such that that a passive adversary cannot
  distinguish it from "normal" traffic (Sec. 4.1 and Fig. 1). For the
  topics we were talking about, the most important sections to read are
  2 and 4.1.

You can embed data in a string that will match a given regular
expression by constructing a DFA (http://swtch.com/~rsc/regexp/regexp1.html)
and walking it state by state, choosing state transition edges so as to
encode something. For example, if there are two outgoing edges from a
state, which one you choose can encode a bit. Many of the appid
signatures contain any* blocks that can straightforwardly encode bytes.
An example of this idea is the regular expression /^(ab*[cd])+/. The b*
lets us encode one bit (say "" = 0 and "b" = 1), and the choice of c or
d allows another bit ("c" = 0 and "d = 1). We could send the message
00110001 as "acabdacad".

This idea can really be thought of an application of the paper. A
regular expression defines a probabilistic channel if we assign
probabilties to edge transitions, which we may do uniformly. So, for
example, with the regular expression given above, the first byte is 'a'
with probability 1. The second byte is 'b' with probability 0.5, 'c'
with probability 0.25, and 'c' with probability 0.25. But we see how a
channel is sensitive to history: if the string so far is "ab", then the
next byte may be 'c' or 'd'; but if the string so far is "ac", then the
next byte must be 'a' (or EOF).

We can use appid-like signatures to make steganographic channels, if we
assume that the signatures are a realistic reflection of actual use of
the protocols. But: this relies critically on the accuracy of the model.
(Specifically, does it match the censor's model? If he uses simple
regular expressions for blocking, then we win; if not, then we probably
lose.) Robert Ransom gave the example of a model of HTTP using just the
syntax; i.e. using RFC 2616 as the definition of a channel. Such a thing
would not only not look like real-world HTTP, but would be broken easily
by proxies that rearrange headers, for example.

rransom also suggested a way to use arithmetic encoding to obfuscate a
stream using a probabilistic model of a protocol; I'll quote him in
* send it through an arithmetic-code encoder, using a model which
  contains a (low-probability) 'pad' symbol;
* encrypt it with a stream cipher;
* send it through an arithmetic-code decoder, using a model which
  matches the 'cover protocol' (the protocol you are trying to mimic).

David (yours truly) wants to write or help write a simple pluggable
transport derived from regular-expression signatures, even with the
limitations shown above. Client and relay would need matching signature
models. For the same of simplicity, it will only seek to match the given
signature, and not be indistinguishable in the strong sense mentioned
above. It won't do symmetric encryption of the underlying TLS (or if it
does, will use a fixed key). It won't use the constructions from the
Provably Secure Steganography paper, rather it will just encode its
stream directly in DFA edge transitions. I think it will be interesting
to see 1) how far a simple system can get us, and 2) what additional
changes we would have to make to be provably secure against censors
using more sophisticated computational models than regex.

David Fifield

More information about the tor-dev mailing list