[freehaven-cvs] more touch-ups

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Update of /home/freehaven/cvsroot/doc/alpha-mixing
In directory moria:/home/arma/work/freehaven/doc/alpha-mixing

Modified Files:
	alpha-mixing.tex 
Log Message:
more touch-ups


Index: alpha-mixing.tex
===================================================================
RCS file: /home/freehaven/cvsroot/doc/alpha-mixing/alpha-mixing.tex,v
retrieving revision 1.27
retrieving revision 1.28
diff -u -d -r1.27 -r1.28
--- alpha-mixing.tex	11 Mar 2006 02:41:00 -0000	1.27
+++ alpha-mixing.tex	11 Mar 2006 03:08:23 -0000	1.28
@@ -267,7 +267,7 @@
 whether the adversary knows one's strategy or not.  And, if the
 adversary knows nothing about the strategies of choosing alphas or
 knows simply the distribution of strategies, then increasing the
-$alpha$-range for any message improves anonymity for all messages.
+$\alpha$-range for any message improves anonymity for all messages.
 
 \subsection{Attacker knowledge}
 \label{sec:attacker-knowledge}
@@ -560,20 +560,19 @@
 over one's own security and utility. Indeed, if an adversary can make
 reasonable guesses about a choice of alpha range for a message, then
 increased alpha for other messages in a mix might actually decrease
-anonymity for a target message. For example, assume a mix containing a
-target message with low alpha and an ancillary message that is from
+anonymity for a target message. For example, consider a mix containing a
+target message with low alpha and an ancillary message that is either from
 about the same alpha range or from a much larger alpha range than the
-target message.  If the adversary can guess which is the case, then
-his uncertainty about the target message decreases when the ancillary
-message is assigned alpha from a larger range.
+target message.  If the adversary learns that the second message has a
+larger range, then his uncertainty about the target message decreases.
 
 Even more significantly, however, security is hard to get right when it
 doesn't depend on the strategic behavior of others. Users of the
-system are not likely to have such fine tuned knowledge of the system,
+system are not likely to have such fine-tuned knowledge of the system,
 the behavior of others, and their own needs. Thus if we can prescribe
 recommendations for choice of alpha, e.g., based on analysis and
 observed patterns within the network, we can expect most people to
-heed them. (Although they may not follow them. We can expect
+heed them. (Although they may not follow them --- we can expect
 hyperbolic discounting of risk, disregard of risk for expedience,
 etc.~\cite{acquisti04}.)
 
@@ -626,40 +625,42 @@
 necessarily including $0$). This would (1) prevent such an attack if
 the adversary cannot predict her distribution, (2) still have as much
 predictability on delivery time as stop-and-go mixes, and (3) unlike
-stop-and-go, still allow eventual delivery of all messages not
-completely blocked. We are not primarily focused in this paper
+stop-and-go, still allow eventual delivery of all messages (unless
+they're dropped by the attacker).
+We are not primarily focused in this paper
 on end-to-end timing attacks, and we will say no more about them.
 
 
 \subsection{Variations on deterministic-alpha mixing}
 
 In the basic threshold deterministic-alpha mix, if there are
-$\mbox{\emph{threshold}} = t$ messages in alpha levels $0$ through
-$n$, all of the messages in levels $0$ through $n$ will be sent at
+$\mbox{\emph{threshold}} = n$ messages in each of alpha levels $0$ through
+$\ell$, all of the messages in levels $0$ through $\ell$ will be sent at
 once; however, they will not be mixed. The mix will send all messages
 with $\alpha = 0$, lower the stack, send the next batch of messages
 that now have $\alpha = 0$, etc. An adversary may not know exactly
 where level $i$ ends and level $i+1$ begins because there may be more
-than $t$ messages in a given level, but if more than $t$ messages
+than $n$ messages in a given level, but if more than $n$ messages
 emerge he can know that the last messages to emerge were considered
-more sensitive by there senders than the first, in a stepped linear
+more sensitive by their senders than the first, in a stepped linear
 order of sensitivity. And by sending in messages of his own at known
 alpha levels above $0$ the adversary can learn the exact levels of the
 messages that emerge between his messages at that alpha level. Then,
-by flooding first $\alpha = n$, then $\alpha = n-1$, \ldots, then
+by flooding first $\alpha = \ell$, then $\alpha = \ell-1$, \ldots, then
 $\alpha = 0$, the adversary can guarantee a flush of the mix all the
-way up to $\alpha = n$ with a knowledge of the alpha level of most of
+way up to $\alpha = \ell$ while also learning the alpha level of most of
 the messages.
 
 The simplest solution is to simply mix all messages that emerge at
-once. This will prevent an adversary from learning the sensitivity of
-messages by observing their alpha levels from their positions in the
-batch. This together with the minimal dummy scheme presented in
+once. This will prevent an adversary from observing when the messages
+exit during a flush and thus learning about their sensitivity.
+This together with the minimal dummy scheme presented in
 Section~\ref{sec:dummies} would substantially reduce the effect of
 blending: an adversary emptying the mix of all messages up to the
-highest reasonably expected level, trickling in a message then
+highest reasonably expected level, trickling in a message, then
 flooding with $\alpha_0 = 0$ messages repeatedly to learn the
 sensitivity of that message and its next destination.
+%XXX not a sentence
 
 We could also require that the firing of the mix be
 threshold-and-timed, which would prevent the adversary from triggering
@@ -683,8 +684,8 @@
 
 In this design, alphas are assigned to messages as they have been
 all along, except instead
-of them deterministically decreasing by one after each mix firing, there is
-a probabilistic function $f$.\\
+of deterministically decreasing by one after each mix firing, there is
+a probabilistic function $f$ that dictates how they decrement:\\
 $\alpha_{M,i+1} = f(\alpha_{M,i}, \mathit{Pool}(\alpha_{M,i}))$
 
 $\mathit{Pool}(\alpha_{M,i}) = | \{M' : 1 \leq \alpha_{M',i-1} \leq

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