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Cyphernomicon 8.10

Anonymity, Digital Mixes, and Remailers:
Cryptanalysis of Remailer Networks

   8.10.1. The Need for More Detailed Analysis of Mixes and Remailers
           + "Have remailer systems been adequately cryptanalyzed?"
             - Not in my opinion, no. Few calculations have been done,
                just mostly some estimates about how much "confusion" has
                been created by the remailer nodes.
             - But thinking that a lot of complication and messiness
                makes a strong crypto system is a basic mistake...sort of
                like thinking an Enigma rotor machine makes a good cipher
                system, by today's standards, just because millions of
                combinations of pathways through the rotor system are
                possible. Not so.
           + Deducing Patterns in Traffic and Deducing Nyms
             - The main lesson of mathematical cryptology has been that
                seemingly random things can actually be shown to have
                structure. This is what cryptanalysis is all about.
             - The same situation applies to "seemingly random" message
                traffic, in digital mixes, telephone networks, etc.
                "Cryptanalysis of remailers" is of course possible,
                depending on the underlying model. (Actually, it's always
                possible, it just may not yield anything, as with
                cryptanalysis of ciphers.)
             + on the time correlation in remailer cryptanalysis
               - imagine Alice and Bob communicating through
         observer, unable to follow specific
                  messages through the remailers, could still notice
                  pairwise correlations between messages sent and
                  received by these two
               + like time correlations between events, even if the
                  intervening path or events are jumbled
                 - e.g., if within a few hours of every submarine's
                    departure from Holy Loch a call is placed to Moscow,
                    one may make draw certain conclusions about who is a
                    Russian spy, regardless of not knowing the
                    intermediate paths
                 - or, closer to home, correlating withdrawals from one
                    bank to deposits in another, even if the intervening
                    transfers are jumbled
               + just because it seems "random" does not mean it is
                 - Scott Collins speculates that a "dynamic Markov
                    compressor" could discern or uncover the non-
                    randomness in remailer uses
           - Cryptanalysis of remailers has been woefully lacking. A
              huge fraction of posts about remailer improvements make
              hand-waving arguments about the need for more traffic,
              longer delays, etc. (I'm not pointing fingers, as I make
              the same informal, qualitative comments, too. What is
              needed is a rigorous analysis of remailer security.)
           - We really don't have any good estimates of overall security
              as a function of number of messages circulating, the
              latency ( number of stored messages before resending), the
              number of remailer hops, etc. This is not cryptographically
              "exciting" work, but it's still needed. There has not been
              much focus in the academic community on digital mixes or
              remailers, probably because David Chaum's 1981 paper on
              "Untraceable E-Mail" covered most of the theoretically
              interesting material. That, and the lack of commercial
              products or wide usage.
           + Time correlations may reveal patterns that individual
              messages lack. That is, repeated communicatin between Alice
              and Bob, even if done through remailers and even if time
              delays/dwell times are built-in, may reveal nonrandom
              correlations in sent/received messages.
             - Scott Collins speculates that a dynamic Markov compressor
                applied to the traffic would have reveal such
                correlations. (The application of such tests to digital
                cash and other such systems would be useful to look at.)
             - Another often overlooked weakness is that many people
                send test messages to themselves, a point noted by Phil
                Karn: "Another way that people often let themselves be
                caught is that they inevitably send a test message to
                themselves right before the forged message in question.
                This shows up clearly in the sending system's sendmail
                logs. It's a point to consider with remailer chains too,
                if you don't trust the last machine on the chain." [P.K.,
           + What's needed:
             - aggreement on some terminology (this doesn't require
                consensus, just a clearly written paper to de facto
                establish the terminology)
             - a formula relating degree of untraceability to the major
                factors that go into remailers: packet size and
                quantization, latency (# of messages), remailer policies,
                timing, etc.
             - Also, analysis of how deliberate probes or attacks might
                be mounted to deduce remailer patterns (e.g., Fred always
                remails to Josh and Suzy and rarely to Zeke).
           - I think this combinatorial analysis would be a nice little
              monograph for someone to write.
   8.10.2. A much-needed thing. Hal Finney has posted some calculations
            (circa 1994-08-08), but more work is sorely needed.
   8.10.3. In particular, we should be skeptical of hand-waving analyses
            of the "it sure looks complicated to follow the traffic"
            sort. People think that by adding "messy" tricks, such as
            MIRVing messages, that security is increased. Maybe it is,
            maybe it isn't. But it needs formal analysis before claims
            can be confidantly believed.
   8.10.4. Remailers and entropy
           - What's the measure of "mixing" that goes on in a mix, or
           - Hand=waving about entropy and reordering may not be too
           + Going back to Shannon's concept of entropy as measuring the
              degree of uncertainty...
             + trying to "guess" or "predict' where a message leaving
                one node will exit the system
               - not having clear entrance and exit points adds to the
                  difficulty, somewhat analogously to having a password
                  of unknown length (an attacker can't just try all 10-
                  character passwords, as he has no idea of the length)
               - the advantages of every node being a remailer, of
                  having no clearly identified sources and sinks
           + This predictability may depend on a _series_ of messages
              sent between Alice and
             - it seems there may be links to Persi Diaconis' work on
                "perfect shuffles" (a problem which seemed easy, but
                which eluded solving until recently...should give us
                comfort that our inability to tackle the real meat of
                this issue is not too surprising
   8.10.5. Scott Collins believes that remailer networks can be
            cryptanalyzed roughly the same way as pseudorandom number
            generators are analyzed, e.g., with dynamic Markov
            compressors (DNCs). (I'm more skeptical: if each remailer is
            using an information-theoretically secure RNG to reorder the
            messages, and if all messages are the same size and (of
            course) are encypted with information-theoretically secure
            (OTP) ciphers, then it seems to me that the remailing would
            itself be information-theoretically secure.)

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