Subject: Re: [bitcoin-dev] BIP proposal - Dandelion: Privacy Preserving Transaction Propagation

From: Giulia Fanti <[email-masked]>
Date: Wed, 20 Sep 2017 22:10:29 -0400

Greetings bitcoin-dev,

  We’re returning to this thread to give an update on the Dandelion project
after several months of additional work. (Dandelion is a new
privacy-preserving transaction propagation method, which we are proposing
as a BIP. See the original post in this thread
https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2017-June/014571.html
for more background) The feedback on our initial BIP from Greg Maxwell in
this thread touched on several important issues affecting the protocol
design, which it has taken us until now to adequately address.

The focus of this update is a new variant of the Dandelion++ mechanism
presented earlier. The new variant is called “Per-Incoming-Edge” routing.
In a nutshell, while the earlier Dandelion++ variant calls for routing
*each* stem transaction through a randomly chosen path, Per-Incoming Edge
routing causes each transaction from the same source to traverse the same
pseudorandom path. The most important benefit of Per-Incoming-Edge is that
it prevents “intersection attacks” that result if a client broadcasts
multiple transactions over a short period of time. We validate this new
variant with new analysis and simulation as explained below.

Today’s update also includes an outline of our next development plans. We
have not yet completed a reference implementation, so this update does not
include a new BIP. Instead we’re just outlining the steps we plan to take
before an updated BIP. The new approach also  impacts our implementation
approach. Since Per-Incoming Edge routing simplifies the handling of orphan
transactions, we’re now planning on adopting Greg Maxwell’s suggestion to
bypass the txMempool for dandelion stem transactions.

======

The feedback on Dandelion from Greg Maxwell touched on a few important
issues: (1) robustness to observations over time, aka “intersection
attacks”, (2) protocol- or implementation-level data leaks, and (3) graph
learning.

(1) With time, the adversary may be able to observe many message
trajectories, thereby eventually learning the underlying graph structure
and/or improving its deanonymization estimate for a given estimate of the
graph structure. In our original Dandelion BIP, we addressed this by
changing the anonymity graph topology from a directed line to a directed
4-regular graph. (In short, instead of a single outgoing edge for Dandelion
transactions, each node selects from  *two* such edges). This topology
provides robustness to adversaries who are able to learn the graph, but
those results still assume that each node generates only one transaction in
each “epoch” (time between reshuffling the anonymity graph). Hence a big
remaining question is to understand the effect of intersection attacks--an
adversary observing multiple dependent transactions--on deanonymization
precision and recall.

(2) The second issue is protocol- or implementation-level behavior that
would allow an adversary to actively probe Dandelion to learn more
information than before. As you correctly note, we want to avoid the
adversary using conflicting transactions to infer which nodes are in the
stem. This issue is related to issue (1), in that our mechanism for
addressing intersection attacks will determine what data structures we need
in the implementation.

(3) The third issue is that an adversary may be able to infer the structure
of the graph by observing network traffic. We want to prevent this.

----------

Intersection Attacks

----------

An adversary’s ability to launch intersection attacks depends on the
internal Dandelion routing policy. Two natural ways to approach routing are
the following:

 1. Per-Hop: For each incoming stem transaction, make an independent random
decision of (a) whether to transition to “fluff” phase, and (b) if “stem”,
then which node should we relay to. This means that two transactions, even
starting from the same source, take independent random walks through the
anonymity graph. This is what our current implementation does.

 2. Per-Inbound-Edge: For each inbound edge e, randomly select one outbound
edge g, and relay all transactions arriving on edge e to edge g (assuming
the transaction remains in stem phase). Each node uses this relay mapping
for an entire epoch, which lasts about 10 min. Each source also randomly
chooses one outbound edge g’ for its own transactions; so if a node
generates 5 transactions, they will all get propagated over edge g’. This
approach has the property that during an epoch, all transactions from a
single source will take the same path through the stem graph.

We have simulated and analyzed these two routing protocols, and find that
per-inbound-edge routing seems to be more robust to intersection attacks.
For our simulations we consider the “first-spy” estimator --- this means
the rule where the attacker simply guesses that the first peer to relay a
transaction to a spy node is the real source. Figure 1 (link below)
illustrates the first-spy precision for per-incoming-edge routing and
per-transaction routing when each node has *one* transaction. Higher
precision means worse anonymity. For comparison, this figure includes
diffusion, which is the spreading mechanism currently used. Here ‘p’
denotes the fraction of nodes in the network that are spies. (Recall that
in our model, we treat the attacker has having control over some fraction
of random nodes). The turquoise curve (labelled ‘p’) is shown for
reference---it does not represent any routing protocol.

https://github.com/gfanti/bips/blob/master/per-edge-vs-per-tx.jpg

First, note that the first-spy estimator is thought to be significantly
suboptimal for diffusion (red line). Prior literature has shown that on
certain classes of graphs, there exist estimators that can detect diffusion
sources with much higher probability than the first-spy estimator. While
it’s unclear how to apply those algorithms to Bitcoin’s graph, it is likely
that strong algorithms exist. Hence the first-spy estimator serves as a
lower bound on precision for diffusion. On the other hand, we can show
theoretically that the first-spy precision for per-tx and per-incoming-edge
routing is within a small constant factor of the optimal precision for
per-incoming-edge routing. Thus, we expect that the green (per-edge) and
blue (per-tx) lines reflect the near-optimal attack, whereas the red line
(diffusion) could be much higher in practice.

The second issue to note is that the blue line (per-tx forwarding) has the
lowest precision of the three protocols for one tx per node. The green line
(per-edge forwarding) has higher precision than per-tx forwarding when
there are very few spies, but approaches per-tx forwarding as p increases.
Moreover, it has lower precision than diffusion for p>=0.05.

However, the real benefits of per-edge forwarding emerge as nodes start to
transmit multiple transactions. Under per-edge forwarding, even if nodes
transmit multiple transactions each, those transactions will traverse the
same path in the anonymity graph, thereby preventing the adversary from
learning any new information from later transactions. Meanwhile, under
per-tx routing, we find empirically that as nodes generate an increasing
number of transactions, each source generates a unique signature of
spy-node-observations (we are currently working on a more detailed
exploration of this question). We expect that such signatures can be used
to exactly deanonymize users in cases where the adversary learns the
graph. Hence
per-tx forwarding is actually quite fragile to adversaries learning the
graph, whereas per-incoming-edge is robust to intersection attacks. This is
one key reason for adopting per-incoming-edge forwarding.

Adopting per-incoming-edge forwarding has another important implication: it
becomes easy to enforce the condition that child transactions never enter
fluff mode before parent transactions. This significantly simplifies orphan
handling, and means that adversaries cannot infer that a preceding
transaction is still in stem mode just by passively listening to network
traffic. We revisit this issue in the next section.

----------

Implementation-Level Metadata Leaks

----------

tl;dr: concept ACK for gmaxwell’s suggestion on a new per-peer data
structure instead of mempool

Regardless of which routing policy we choose, it is important that
implementations do not leak more information about transactions than they
do in our model. It’s especially important that spies do not get an
“off-path” view of the nodes involved in the stem of a transaction. This
practically means that implementations must be careful not to expose
whether or not a stem transaction was received, to any node except the two
randomly chosen ones. (i.e., not to supernodes that may make inbound
connections to thousands of nodes).

We are currently developing a reference implementation for Dandelion++, as
a patch against Bitcoin Core. It requires thoughtful integration to make
this patch, and the choice of routing policy informs our approach. We have
so far considered two main integration approaches, whose main difference is
whether or not they reuse the existing *txMempool* data structure to store
stem mode transactions.

A. Mempool embargo:

This how is our current implementation works. Stem transactions are only
relayed if they are accepted to mempool. Stem transactions are “embargoed”
by suppressing them from MEMPOOL and INV messages sent from the node. This
was the easiest to implement while preserving all of Bitcoin’s existing DoS
prevention. In particular, it simplifies the handling of orphan
transactions, because the AcceptToMempool routine already handles orphan
transactions. However, this approach comes with a risk of indirect leakage,
especially if some edge case is missed in implementation.

B. Avoid modifying mempool (or any global structure) for stem transactions:

This is the approach preferred by Greg Maxwell. The main benefit is that it
is much more clear that there is no indirect leakage, although it makes it
harder to argue there is no additional DoS concern. We have already taken a
couple of steps towards implementing this here:
https://github.com/gfanti/bitcoin/commits/dandelion-nomempool The main idea
is to avoid duplicating the rules for whether a transaction would be
accepted into mempool or not, by adding a “dry run” option to the
AcceptToMempool function. Our implementation of this approach is not yet
finished; it still remains to develop the per-peer data structure.

Orphan transactions are important for per-tx routing, because with per-tx
routing, the child and the parent might travel along different stems. A
burst of transactions from a single sender would have to be queued so they
enter fluff mode sequentially. A lot of our testing (with the included test
framework) involved ensuring such transactions were handled effectively.
This was also the deciding factor for our choice of using Option B “Mempool
Embargo” above. With Per-incoming Edge routing, however, orphan transaction
handling can be simplified, since out-of-order transactions would not be
sent along stems.

We therefore plan to re-engineer a much of our reference implementation to:

1) use per-incoming edge routing,

2) simplify handling of orphan transactions,

3) adopt the proposed approach of avoiding the mempool data structure for
stem transactions.

We’ll give an update soon on our development progress before updating the
BIP.

----------

Graph Learning

----------

Greg Maxwell also asked:

```

Has any work been given to the fact that dandelion propagation
potentially making to measure properties of the inter-node connection
graph?  e.g.  Say I wish to partition node X by disconnecting all of
its outbound connections, to do that it would be useful to learn whom
is connected to X.  I forward a transaction to X, observe the first
node to fluff it,  then DOS attack that node to take it offline.  Will
I need to DOS attack fewer or more nodes  to get all of X's outbounds
if X supports rapid stem forwarding?

```

In terms of graph learning, there are two graphs to consider: the anonymity
graph (i.e., the stem set of each node), and the main P2P graph. Dandelion
has at least as good graph-hiding properties as diffusion for a natural
class of attacks (which include the attack described in the comment above).

Consider the task of learning the main P2P graph in today’s network (under
diffusion spreading). Suppose a supernode is connected to all nodes, and
wants to learn the 1-hop neighbors of a given target node. The eavesdropper
passes a transaction to the target, and waits to hear which nodes relay the
transaction first. If the target has 8 outbound neighbors, then in each
experiment, the supernode will receive 8 independent relay timestamps from
the target’s 1-hop neighbors. By repeating this many times, the adversary
can infer the 1-hop neighbors as the nodes who relay the transaction with
the appropriate mean delay (taking into account the appropriate exponential
parameters). Eventually, this set will be learned with high certainty.

Now consider the same task if the target is a Dandelion node. Note that the
supernode’s probe tx must be relayed as a Dandelion message to observe any
difference with the prior experiment. First of all, the target will only
pass the tx to one node in its stem set. Hence, in each experiment, the
supernode can learn at most one timestamp from a relevant node, whereas
previously it learned eight per experiment. This inherently reduces the
adversary’s learning rate. Second, if the target’s relay is a Dandelion
node and chooses to extend the stem, then the supernode will not receive any
relevant timestamp (i.e. a timestamp from a 1-hop neighbor) unless the
supernode lies in the relay’s stem set. This happens with a probability
that depends on the level of deployment and the number of (seemingly)
distinct nodes being run by the supernode, but is strictly smaller than 1.

   _ Hence, the rate at which an attacker can learn the main P2P graph is
strictly higher under diffusion (as in Bitcoin Core today) compared to
using Dandelion. _

A similar argument can be made for the anonymity graph, which we currently
implement as an overlay to the main P2P graph.

=====

Responses to Other Miscellaneous Comments

====

```

An alternative construction would be that when a stem transaction goes
out there is a random chance that the stem flag is not set (with
suitable adjustment to keep the same expected path length)

For some reason I believe this would be a superior construction, but I
am only able to articulate one clear benefit:  It allows non-dandelion
capable nodes to take on the role of the last stem hop, which I
believe would improve the anonymity set during the transition phase.

```

Agreed, this is actually what we have implemented.

---------

Thanks!

Giulia Fanti <[email-masked]>
Andrew Miller <[email-masked]>
Surya Bakshi <[email-masked]>
Shaileshh Bojja Venkatakrishnan <[email-masked]>
Pramod Viswanath <[email-masked]>

Date: Tue, 13 Jun 2017 01:00:50 +0000
> From: Gregory Maxwell <[email-masked]>
> To: Andrew Miller <[email-masked]>
> Cc: Bitcoin Dev <[email-masked]>
> Subject: Re: [bitcoin-dev] BIP proposal - Dandelion: Privacy
>         Preserving Transaction Propagation
> Message-ID:
>         <CAAS2fgRAnGMMxKPCaj1SL=z3O2wuGS8nyPrgtGhSpuGgAoVtKg@mail.
> gmail.com>
> Content-Type: text/plain; charset="UTF-8"
>
> On Mon, Jun 12, 2017 at 2:46 PM, Andrew Miller via bitcoin-dev
> <[email-masked]> wrote:
> > Dear bitcoin-dev,
> >    We've put together a preliminary implementation and BIP for
> > Dandelion, and would love to get your feedback on it. Dandelion is a
> > privacy-enhancing modification to Bitcoin's transaction propagation
> > mechanism. Its goal is to obscure the original source IP of each
> > transaction.
>
> I'm glad to see this out now, so I'm not longer invading the git repo
> uninvited. :)
>
> >  - Stronger attacker model: we defend against an attacker that
> > actively tries to learn which nodes were involved in the stem phase.
> > Our approach is called "Mempool Embargo", meaning a node that receives
> > a "stem phase" transaction behaves as though it never heard of it,
> > until it receives it again from someone else (or until a random timer
> > elapsess).
>
>
> The description in the BIP appears inadequate:
>
>
> > That is, Alice will not include the embargoed transaction when
> responding to MEMPOOL requests, and will not respond to GETDATA requests
> from another node (Bob) unless Alice previously sent an INV to Bob. The
> embargo period ends as soon as Alice receives an INV advertising the
> transaction as being in fluff mode.
>
> For example, it's not clear if I can query for the existence of a
> transaction by sending a conflict.  If this doesn't seem problematic,
> consider the case where I, communicating with you over some private
> channel, send you a payment inside a payment protocol message. You
> announce it to the network and I concurrently send a double spend.
> Only nodes that were part of the stem will reject my double spend, so
> I just learned a lot about your network location.
>
> It's also appears clear that I can query by sending an inv and
> noticing that no getdata arrives.  An example attack in the latter is
> that when I get a stem transaction I rapidly INV interrogate the
> entire network and by observing who does and doesn't getdata I will
> likely learn the entire stem path upto permutation.
>
> The extra network capacity used by getdata-ing a transaction you
> already saw via dandelion would be pretty insignificant.
>
> I believe the text should be simplified and clarified so just say:
>
> "With the exception of her behavior towards the peer sending in the
> stem transaction and the peer sending out the transaction Alice's
> behavior should be indistinguishable from a node which has not seen
> the transaction at all until she receives it via ordinary forwarding
> or until after the timeout." -- then its up to the implementation to
> achieve indistinguishably regardless of what other protocol features
> it uses.
>
> > Are there other ways we haven't thought of? We think the alternative
> > approach (bypassing mempool entirely) seems even harder to get right,
> > and foregoes existing DoS protection.
>
> I think avoiding the is the most sensible way; and from a software
> maintenance perspective I expect that anything less will end up
> continually suffering from serious information leaks which are hard to
> avoid accidentally introducing via other changes.
>
> The primary functionality should be straightforward to implement,
> needing just a flag to determine if a transaction would be accepted to
> the mempool but for the flag, but which skips actually adding it.
>
> Handling chains of unconfirmed stem transactions is made more
> complicated by this and this deserves careful consideration. I'm not
> sure if its possible to forward stem children of stem transactions
> except via the same stem path as the parent without leaking
> information, it seems unlikely.
>
> This approach would mostly take additional complexity from the need to
> limit the amplification of double spends. I believe this can be
> resolved by maintaining a per-peer map of the not yet expired vin's
> consumed by stem fowards sent out via that peer. E.g. vin->{timeout,
> feerate}.  Then any new forward via that stem-peer is tested against
> that map and suppressed if it it spends a non-timed-out input and
> doesn't meet the feerate epsilon for replacement.
>
> Use of the orphan map is not indistinguishable as it is used for block
> propagation, and itself also a maintenance burden to make sure
> unrelated code is not inadvertently leaking the stem transactions.
>
> > After a random number of hops along the stem, the transaction enters the
> fluff phase,
>
> The BIP is a bit under-specified on this transition, I think-- but I
> know how it works from reading the prior implementation (I have not
> yet read the new implementation).
>
> The way it works (assuming I'm not confused and it hasn't changed) is
> that when a new stem transaction comes in there is a chance that it is
> treated as coming in as a normal transaction.
>
> An alternative construction would be that when a stem transaction goes
> out there is a random chance that the stem flag is not set (with
> suitable adjustment to keep the same expected path length)
>
> For some reason I believe this would be a superior construction, but I
> am only able to articulate one clear benefit:  It allows non-dandelion
> capable nodes to take on the role of the last stem hop, which I
> believe would improve the anonymity set during the transition phase.
>
> Unrelated:
>
> Has any work been given to the fact that dandelion propagation
> potentially making to measure properties of the inter-node connection
> graph?  e.g.  Say I wish to partition node X by disconnecting all of
> its outbound connections, to do that it would be useful to learn whom
> is connected to X.  I forward a transaction to X, observe the first
> node to fluff it,  then DOS attack that node to take it offline.  Will
> I need to DOS attack fewer or more nodes  to get all of X's outbounds
> if X supports rapid stem forwarding?
>
>
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