pkt on Nostr: The new Tor Onion service PoW scheme is worth reading. Since this is nostr, let's try ...

The new Tor Onion service PoW scheme is worth reading. Since this is nostr, let's try including the whole thing:

Filename: 327-pow-over-intro.txt
Title: A First Take at PoW Over Introduction Circuits
Author: George Kadianakis, Mike Perry, David Goulet, tevador
Created: 2 April 2020
Status: Draft

0. Abstract

This proposal aims to thwart introduction flooding DoS attacks by introducing
a dynamic Proof-Of-Work protocol that occurs over introduction circuits.

1. Motivation

So far our attempts at limiting the impact of introduction flooding DoS
attacks on onion services has been focused on horizontal scaling with
Onionbalance, optimizing the CPU usage of Tor and applying congestion control
using rate limiting. While these measures move the goalpost forward, a core
problem with onion service DoS is that building rendezvous circuits is a
costly procedure both for the service and for the network. For more
information on the limitations of rate-limiting when defending against DDoS,
see [REF_TLS_1].

If we ever hope to have truly reachable global onion services, we need to
make it harder for attackers to overload the service with introduction
requests. This proposal achieves this by allowing onion services to specify
an optional dynamic proof-of-work scheme that its clients need to participate
in if they want to get served.

With the right parameters, this proof-of-work scheme acts as a gatekeeper to
block amplification attacks by attackers while letting legitimate clients
through.

1.1. Related work

For a similar concept, see the three internet drafts that have been proposed
for defending against TLS-based DDoS attacks using client puzzles [REF_TLS].

1.2. Threat model [THREAT_MODEL]

1.2.1. Attacker profiles [ATTACKER_MODEL]

This proposal is written to thwart specific attackers. A simple PoW proposal
cannot defend against all and every DoS attack on the Internet, but there are
adverary models we can defend against.

Let's start with some adversary profiles:

"The script-kiddie"

The script-kiddie has a single computer and pushes it to its
limits. Perhaps it also has a VPS and a pwned server. We are talking about
an attacker with total access to 10 Ghz of CPU and 10 GBs of RAM. We
consider the total cost for this attacker to be zero $.

"The small botnet"

The small botnet is a bunch of computers lined up to do an introduction
flooding attack. Assuming 500 medium-range computers, we are talking about
an attacker with total access to 10 Thz of CPU and 10 TB of RAM. We
consider the upfront cost for this attacker to be about $400.

"The large botnet"

The large botnet is a serious operation with many thousands of computers
organized to do this attack. Assuming 100k medium-range computers, we are
talking about an attacker with total access to 200 Thz of CPU and 200 TB of
RAM. The upfront cost for this attacker is about $36k.

We hope that this proposal can help us defend against the script-kiddie
attacker and small botnets. To defend against a large botnet we would need
more tools at our disposal (see [FUTURE_DESIGNS]).

1.2.2. User profiles [USER_MODEL]

We have attackers and we have users. Here are a few user profiles:

"The standard web user"

This is a standard laptop/desktop user who is trying to browse the
web. They don't know how these defences work and they don't care to
configure or tweak them. They are gonna use the default values and if the
site doesn't load, they are gonna close their browser and be sad at Tor.
They run a 2Ghz computer with 4GB of RAM.

"The motivated user"

This is a user that really wants to reach their destination. They don't
care about the journey; they just want to get there. They know what's going
on; they are willing to tweak the default values and make their computer do
expensive multi-minute PoW computations to get where they want to be.

"The mobile user"

This is a motivated user on a mobile phone. Even tho they want to read the
news article, they don't have much leeway on stressing their machine to do
more computation.

We hope that this proposal will allow the motivated user to always connect
where they want to connect to, and also give more chances to the other user
groups to reach the destination.

1.2.3. The DoS Catch-22 [CATCH22]

This proposal is not perfect and it does not cover all the use cases. Still,
we think that by covering some use cases and giving reachability to the
people who really need it, we will severely demotivate the attackers from
continuing the DoS attacks and hence stop the DoS threat all together.
Furthermore, by increasing the cost to launch a DoS attack, a big
class of DoS attackers will disappear from the map, since the expected ROI
will decrease.

2. System Overview

2.1. Tor protocol overview

+----------------------------------+
| Onion Service |
+-------+ INTRO1 +-----------+ INTRO2 +--------+ |
|Client |-------->|Intro Point|------->| PoW |-----------+ |
+-------+ +-----------+ |Verifier| | |
+--------+ | |
| | |
| | |
| +----------v---------+ |
| |Intro Priority Queue| |
+---------+--------------------+---+
| | |
Rendezvous | | |
circuits | | |
v v v



The proof-of-work scheme specified in this proposal takes place during the
introduction phase of the onion service protocol.

The system described in this proposal is not meant to be on all the time, and
it can be entirely disabled for services that do not experience DoS attacks.

When the subsystem is enabled, suggested effort is continuously adjusted and
the computational puzzle can be bypassed entirely when the effort reaches
zero. In these cases, the proof-of-work subsystem can be dormant but still
provide the necessary parameters for clients to voluntarily provide effort
in order to get better placement in the priority queue.

The protocol involves the following major steps:

1) Service encodes PoW parameters in descriptor [DESC_POW]
2) Client fetches descriptor and computes PoW [CLIENT_POW]
3) Client completes PoW and sends results in INTRO1 cell [INTRO1_POW]
4) Service verifies PoW and queues introduction based on PoW effort
[SERVICE_VERIFY]
5) Requests are continuously drained from the queue, highest effort first,
subject to multiple constraints on speed [HANDLE_QUEUE]

2.2. Proof-of-work overview

2.2.1. Algorithm overview

For our proof-of-work function we will use the Equi-X scheme by tevador
[REF_EQUIX]. Equi-X is an assymetric PoW function based on Equihash<60,3>,
using HashX as the underlying layer. It features lightning fast verification
speed, and also aims to minimize the assymetry between CPU and GPU.
Furthermore, it's designed for this particular use-case and hence
cryptocurrency miners are not incentivized to make optimized ASICs for it.

The overall scheme consists of several layers that provide different pieces
of this functionality:

1) At the lowest layers, blake2b and siphash are used as hashing and PRNG
algorithms that are well suited to common 64-bit CPUs.
2) A custom hash function, HashX, uses dynamically generated functions that
are tuned to be a good match for pipelined integer and floating point
performance on current 64-bit CPUs. This layer provides the strongest ASIC
resistance, since a reimplementation in hardware would need to implement
much of a CPU to compute these functions efficiently.
3) The Equi-X layer itself builds on HashX and adds an algorithmic puzzle
that's designed to be strongly asymmetric and to require RAM to solve
efficiently.
4) The PoW protocol itself builds on this Equi-X function with a particular
construction of the challenge input and particular constraints on the
allowed blake2b hash of the solution. This layer provides a linearly
adjustible effort that we can verify.
5) Above the level of individual PoW handshakes, the client and service
form a closed-loop system that adjusts the effort of future handshakes.

The Equi-X scheme provides two functions that will be used in this proposal:
- equix_solve(challenge) which solves a puzzle instance, returning
a variable number of solutions per invocation depending on the specific
challenge value.
- equix_verify(challenge, solution) which verifies a puzzle solution
quickly. Verification still depends on executing the HashX function,
but far fewer times than when searching for a solution.

For the purposes of this proposal, all cryptographic algorithms are assumed
to produce and consume byte strings, even if internally they operate on
some other data type like 64-bit words. This is conventionally little endian
order for blake2b, which contrasts with Tor's typical use of big endian.
HashX itself is configured with an 8-byte output but its input is a single
64-bit word of undefined byte order, of which only the low 16 bits are used
by Equi-X in its solution output. We treat Equi-X solution arrays as byte
arrays using their packed little endian 16-bit representation.

We tune Equi-X in section [EQUIX_TUNING].

2.2.2. Dynamic PoW

DoS is a dynamic problem where the attacker's capabilities constantly change,
and hence we want our proof-of-work system to be dynamic and not stuck with a
static difficulty setting. Hence, instead of forcing clients to go below a
static target like in Bitcoin to be successful, we ask clients to "bid" using
their PoW effort. Effectively, a client gets higher priority the higher
effort they put into their proof-of-work. This is similar to how
proof-of-stake works but instead of staking coins, you stake work.

The benefit here is that legitimate clients who really care about getting
access can spend a big amount of effort into their PoW computation, which
should guarantee access to the service given reasonable adversary models. See
[PARAM_TUNING] for more details about these guarantees and tradeoffs.

As a way to improve reachability and UX, the service tries to estimate the
effort needed for clients to get access at any given time and places it in
the descriptor. See [EFFORT_ESTIMATION] for more details.

2.2.3. PoW effort

It's common for proof-of-work systems to define an exponential effort
function based on a particular number of leading zero bits or equivalent.
For the benefit of our effort estimation system, it's quite useful if we
instead have a linear scale. We use the first 32 bits of a hashed version
of the Equi-X solution as compared to the full 32-bit range.

Conceptually we could define a function:
unsigned effort(uint8_t *token)
which takes as its argument a hashed solution, interprets it as a
bitstring, and returns the quotient of dividing a bitstring of 1s by it.

So for example:
effort(00000001100010101101) = 11111111111111111111
/ 00000001100010101101
or the same in decimal:
effort(6317) = 1048575 / 6317 = 165.

In practice we can avoid even having to perform this division, performing
just one multiply instead to see if a request's claimed effort is supported
by the smallness of the resulting 32-bit hash prefix. This assumes we send
the desired effort explicitly as part of each PoW solution. We do want to
force clients to pick a specific effort before looking for a solution,
otherwise a client could opportunistically claim a very large effort any
time a lucky hash prefix comes up. Thus the effort is communicated explicitly
in our protocol, and it forms part of the concatenated Equi-X challenge.

3. Protocol specification

3.1. Service encodes PoW parameters in descriptor [DESC_POW]

This whole protocol starts with the service encoding the PoW parameters in
the 'encrypted' (inner) part of the v3 descriptor. As follows:

"pow-params" SP type SP seed-b64 SP suggested-effort
SP expiration-time NL

[At most once]

type: The type of PoW system used. We call the one specified here "v1"

seed-b64: A random seed that should be used as the input to the PoW
hash function. Should be 32 random bytes encoded in base64
without trailing padding.

suggested-effort: An unsigned integer specifying an effort value that
clients should aim for when contacting the service. Can be
zero to mean that PoW is available but not currently
suggested for a first connection attempt. See
[EFFORT_ESTIMATION] for more details here.

expiration-time: A timestamp in "YYYY-MM-DDTHH:MM:SS" format (iso time
with no space) after which the above seed expires and
is no longer valid as the input for PoW. It's needed
so that our replay cache does not grow infinitely. It
should be set to RAND_TIME(now+7200, 900) seconds.

The service should refresh its seed when expiration-time passes. The service
SHOULD keep its previous seed in memory and accept PoWs using it to avoid
race-conditions with clients that have an old seed. The service SHOULD avoid
generating two consequent seeds that have a common 4 bytes prefix. See
[INTRO1_POW] for more info.

By RAND_TIME(ts, interval) we mean a time between ts-interval and ts, chosen
uniformly at random.

3.2. Client fetches descriptor and computes PoW [CLIENT_POW]

If a client receives a descriptor with "pow-params", it should assume that
the service is prepared to receive PoW solutions as part of the introduction
protocol.

The client parses the descriptor and extracts the PoW parameters. It makes
sure that the <expiration-time> has not expired and if it has, it needs to
fetch a new descriptor.

The client should then extract the <suggested-effort> field to configure its
PoW 'target' (see [REF_TARGET]). The client SHOULD NOT accept 'target' values
that will cause unacceptably long PoW computation.

The client uses a "personalization string" P equal to the following
nul-terminated ascii string: "Tor hs intro v1\0".

The client looks up `ID`, the current 32-byte blinded public ID
(KP_hs_blind_id) for the onion service.

To complete the PoW the client follows the following logic:

a) Client selects a target effort E, based on <suggested-effort> and past
connection attempt history.
b) Client generates a secure random 16-byte nonce N, as the starting
point for the solution search.
c) Client derives seed C by decoding 'seed-b64'.
d) Client calculates S = equix_solve(P || ID || C || N || E)
e) Client calculates R = ntohl(blake2b_32(P || ID || C || N || E || S))
f) Client checks if R * E <= UINT32_MAX.
f1) If yes, success! The client can submit N, E, the first 4 bytes of
C, and S.
f2) If no, fail! The client interprets N as a 16-byte little-endian
integer, increments it by 1 and goes back to step d).

Note that the blake2b hash includes the output length parameter in its
initial state vector, so a blake2b_32 is not equivalent to the prefix of a
blake2b_512. We calculate the 32-bit blake2b specifically, and interpret it
in network byte order as an unsigned integer.

At the end of the above procedure, the client should have S as the solution
of the Equix-X puzzle with N as the nonce, C as the seed. How quickly this
happens depends solely on the target effort E parameter.

The algorithm as described is suitable for single-threaded computation.
Optionally, a client may choose multiple nonces and attempt several solutions
in parallel on separate CPU cores. The specific choice of nonce is entirely
up to the client, so parallelization choices like this do not impact the
network protocol's interoperability at all.

3.3. Client sends PoW in INTRO1 cell [INTRO1_POW]

Now that the client has an answer to the puzzle it's time to encode it into
an INTRODUCE1 cell. To do so the client adds an extension to the encrypted
portion of the INTRODUCE1 cell by using the EXTENSIONS field (see
[PROCESS_INTRO2] section in rend-spec-v3.txt). The encrypted portion of the
INTRODUCE1 cell only gets read by the onion service and is ignored by the
introduction point.

We propose a new EXT_FIELD_TYPE value:

[02] -- PROOF_OF_WORK

The EXT_FIELD content format is:

POW_VERSION [1 byte]
POW_NONCE [16 bytes]
POW_EFFORT [4 bytes]
POW_SEED [4 bytes]
POW_SOLUTION [16 bytes]

where:

POW_VERSION is 1 for the protocol specified in this proposal
POW_NONCE is the nonce 'N' from the section above
POW_EFFORT is the 32-bit integer effort value, in network byte order
POW_SEED is the first 4 bytes of the seed used

This will increase the INTRODUCE1 payload size by 43 bytes since the
extension type and length is 2 extra bytes, the N_EXTENSIONS field is always
present and currently set to 0 and the EXT_FIELD is 41 bytes. According to
ticket #33650, INTRODUCE1 cells currently have more than 200 bytes
available.

3.4. Service verifies PoW and handles the introduction [SERVICE_VERIFY]

When a service receives an INTRODUCE1 with the PROOF_OF_WORK extension, it
should check its configuration on whether proof-of-work is enabled on the
service. If it's not enabled, the extension SHOULD BE ignored. If enabled,
even if the suggested effort is currently zero, the service follows the
procedure detailed in this section.

If the service requires the PROOF_OF_WORK extension but received an
INTRODUCE1 cell without any embedded proof-of-work, the service SHOULD
consider this cell as a zero-effort introduction for the purposes of the
priority queue (see section [INTRO_QUEUE]).

3.4.1. PoW verification [POW_VERIFY]

To verify the client's proof-of-work the service MUST do the following steps:

a) Find a valid seed C that starts with POW_SEED. Fail if no such seed
exists.
b) Fail if N = POW_NONCE is present in the replay cache
(see [REPLAY_PROTECTION])
c) Calculate R = ntohl(blake2b_32(P || ID || C || N || E || S))
d) Fail if R * E > UINT32_MAX
e) Fail if equix_verify(P || ID || C || N || E, S) != EQUIX_OK
f) Put the request in the queue with a priority of E

If any of these steps fail the service MUST ignore this introduction request
and abort the protocol.

In this proposal we call the above steps the "top half" of introduction
handling. If all the steps of the "top half" have passed, then the circuit
is added to the introduction queue as detailed in section [INTRO_QUEUE].

3.4.1.1. Replay protection [REPLAY_PROTECTION]

The service MUST NOT accept introduction requests with the same (seed, nonce)
tuple. For this reason a replay protection mechanism must be employed.

The simplest way is to use a simple hash table to check whether a (seed,
nonce) tuple has been used before for the active duration of a
seed. Depending on how long a seed stays active this might be a viable
solution with reasonable memory/time overhead.

If there is a worry that we might get too many introductions during the
lifetime of a seed, we can use a Bloom filter as our replay cache
mechanism. The probabilistic nature of Bloom filters means that sometimes we
will flag some connections as replays even if they are not; with this false
positive probability increasing as the number of entries increase. However,
with the right parameter tuning this probability should be negligible and
well handled by clients.

{TODO: Design and specify a suitable bloom filter for this purpose.}

3.4.2. The Introduction Queue [INTRO_QUEUE]

3.4.2.1. Adding introductions to the introduction queue [ADD_QUEUE]

When PoW is enabled and a verified introduction comes through, the service
instead of jumping straight into rendezvous, queues it and prioritizes it
based on how much effort was devoted by the client to PoW. This means that
introduction requests with high effort should be prioritized over those with
low effort.

To do so, the service maintains an "introduction priority queue" data
structure. Each element in that priority queue is an introduction request,
and its priority is the effort put into its PoW:

When a verified introduction comes through, the service uses its included
effort commitment value to place each request into the right position of the
priority_queue: The bigger the effort, the more priority it gets in the
queue. If two elements have the same effort, the older one has priority over
the newer one.

3.4.2.2. Handling introductions from the introduction queue [HANDLE_QUEUE]

The service should handle introductions by pulling from the introduction
queue. We call this part of introduction handling the "bottom half" because
most of the computation happens in this stage. For a description of how we
expect such a system to work in Tor, see [TOR_SCHEDULER] section.

3.4.3. PoW effort estimation [EFFORT_ESTIMATION]

3.4.3.1. High-level description of the effort estimation process

The service starts with a default suggested-effort value of 0, which keeps
the PoW defenses dormant until we notice signs of overload.

The overall process of determining effort can be thought of as a set of
multiple coupled feedback loops. Clients perform their own effort
adjustments via [CLIENT_TIMEOUT] atop a base effort suggested by the service.
That suggestion incorporates the service's control adjustments atop a base
effort calculated using a sum of currently-queued client effort.

Each feedback loop has an opportunity to cover different time scales. Clients
can make adjustments at every single circuit creation request, whereas
services are limited by the extra load that frequent updates would place on
HSDir nodes.

In the combined client/service system these client-side increases are
expected to provide the most effective quick response to an emerging DoS
attack. After early clients increase the effort using [CLIENT_TIMEOUT],
later clients will benefit from the service detecting this increased queued
effort and offering a larger suggested_effort.

Effort increases and decreases both have an intrinsic cost. Increasing effort
will make the service more expensive to contact, and decreasing effort makes
new requests likely to become backlogged behind older requests. The steady
state condition is preferable to either of these side-effects, but ultimately
it's expected that the control loop always oscillates to some degree.

3.4.3.2. Service-side effort estimation

Services keep an internal effort estimation which updates on a regular
periodic timer in response to measurements made on the queueing behavior
in the previous period. These internal effort changes can optionally trigger
client-visible suggested_effort changes when the difference is great enough
to warrant republishing to the HSDir.

This evaluation and update period is referred to as HS_UPDATE_PERIOD.
The service side effort estimation takes inspiration from TCP congestion
control's additive increase / multiplicative decrease approach, but unlike
a typical AIMD this algorithm is fixed-rate and doesn't update immediately
in response to events.

{TODO: HS_UPDATE_PERIOD is hardcoded to 300 (5 minutes) currently, but it
should be configurable in some way. Is it more appropriate to use the
service's torrc here or a consensus parameter?}

3.4.3.3. Per-period service state

During each update period, the service maintains some state:

1. TOTAL_EFFORT, a sum of all effort values for rendezvous requests that
were successfully validated and enqueued.

2. REND_HANDLED, a count of rendezvous requests that were actually
launched. Requests that made it to dequeueing but were too old to launch
by then are not included.

3. HAD_QUEUE, a flag which is set if at any time in the update period we
saw the priority queue filled with more than a minimum amount of work,
greater than we would expect to process in approximately 1/4 second
using the configured dequeue rate.

4. MAX_TRIMMED_EFFORT, the largest observed single request effort that we
discarded during the period. Requests are discarded either due to age
(timeout) or during culling events that discard the bottom half of the
entire queue when it's too full.

3.4.3.4. Service AIMD conditions

At the end of each period, the service may decide to increase effort,
decrease effort, or make no changes, based on these accumulated state values:

1. If MAX_TRIMMED_EFFORT > our previous internal suggested_effort,
always INCREASE. Requests that follow our latest advice are being
dropped.

2. If the HAD_QUEUE flag was set and the queue still contains at least
one item with effort >= our previous internal suggested_effort,
INCREASE. Even if we haven't yet reached the point of dropping requests,
this signal indicates that the our latest suggestion isn't high enough
and requests will build up in the queue.

3. If neither condition (1) or (2) are taking place and the queue is below
a level we would expect to process in approximately 1/4 second, choose
to DECREASE.

4. If none of these conditions match, the suggested effort is unchanged.

When we INCREASE, the internal suggested_effort is increased to either its
previous value + 1, or (TOTAL_EFFORT / REND_HANDLED), whichever is larger.

When we DECREASE, the internal suggested_effort is scaled by 2/3rds.

Over time, this will continue to decrease our effort suggestion any time the
service is fully processing its request queue. If the queue stays empty, the
effort suggestion decreases to zero and clients should no longer submit a
proof-of-work solution with their first connection attempt.

It's worth noting that the suggested-effort is not a hard limit to the
efforts that are accepted by the service, and it's only meant to serve as a
guideline for clients to reduce the number of unsuccessful requests that get
to the service. The service still adds requests with lower effort than
suggested-effort to the priority queue in [ADD_QUEUE].

3.4.3.5. Updating descriptor with new suggested effort

The service descriptors may be updated for multiple reasons including
introduction point rotation common to all v3 onion services, the scheduled
seed rotations described in [DESC_POW], and updates to the effort suggestion.
Even though the internal effort estimate updates on a regular timer, we avoid
propagating those changes into the descriptor and the HSDir hosts unless
there is a significant change.

If the PoW params otherwise match but the seed has changed by less than 15
percent, services SHOULD NOT upload a new descriptor.

4. Client behavior [CLIENT_BEHAVIOR]

This proposal introduces a bunch of new ways where a legitimate client can
fail to reach the onion service.

Furthermore, there is currently no end-to-end way for the onion service to
inform the client that the introduction failed. The INTRO_ACK cell is not
end-to-end (it's from the introduction point to the client) and hence it does
not allow the service to inform the client that the rendezvous is never gonna
occur.

From the client's perspective there's no way to attribute this failure to
the service itself rather than the introduction point, so error accounting
is performed separately for each introduction-point. Existing mechanisms
will discard an introduction point that's required too many retries.

4.1. Clients handling timeouts [CLIENT_TIMEOUT]

Alice can fail to reach the onion service if her introduction request gets
trimmed off the priority queue in [HANDLE_QUEUE], or if the service does not
get through its priority queue in time and the connection times out.

This section presents a heuristic method for the client getting service even
in such scenarios.

If the rendezvous request times out, the client SHOULD fetch a new descriptor
for the service to make sure that it's using the right suggested-effort for
the PoW and the right PoW seed. If the fetched descriptor includes a new
suggested effort or seed, it should first retry the request with these
parameters.

{TODO: This is not actually implemented yet, but we should do it. How often
should clients at most try to fetch new descriptors? Determined by a
consensus parameter? This change will also allow clients to retry
effectively in cases where the service has just been reconfigured to
enable PoW defenses.}

Every time the client retries the connection, it will count these failures
per-introduction-point. These counts of previous retries are combined with
the service's suggested_effort when calculating the actual effort to spend
on any individual request to a service that advertises PoW support, even
when the currently advertised suggested_effort is zero.

On each retry, the client modifies its solver effort:

1. If the effort is below (CLIENT_POW_EFFORT_DOUBLE_UNTIL = 1000)
it will be doubled.

2. Otherwise, multiply the effort by (CLIENT_POW_RETRY_MULTIPLIER = 1.5).

3. Constrain the new effort to be at least
(CLIENT_MIN_RETRY_POW_EFFORT = 8) and no greater than
(CLIENT_MAX_POW_EFFORT = 10000)

{TODO: These hardcoded limits should be replaced by timed limits and/or
an unlimited solver with robust cancellation. This is issue tor#40787}

5. Attacker strategies [ATTACK_META]

Now that we defined our protocol we need to start tweaking the various
knobs. But before we can do that, we first need to understand a few
high-level attacker strategies to see what we are fighting against.

5.1.1. Overwhelm PoW verification (aka "Overwhelm top half") [ATTACK_TOP_HALF]

A basic attack here is the adversary spamming with bogus INTRO cells so that
the service does not have computing capacity to even verify the
proof-of-work. This adversary tries to overwhelm the procedure in the
[POW_VERIFY] section.

That's why we need the PoW algorithm to have a cheap verification time so
that this attack is not possible: we tune this PoW parameter in section
[POW_TUNING_VERIFICATION].

5.1.2. Overwhelm rendezvous capacity (aka "Overwhelm bottom half")
[ATTACK_BOTTOM_HALF]

Given the way the introduction queue works (see [HANDLE_QUEUE]), a very
effective strategy for the attacker is to totally overwhelm the queue
processing by sending more high-effort introductions than the onion service
can handle at any given tick. This adversary tries to overwhelm the procedure
in the [HANDLE_QUEUE] section.

To do so, the attacker would have to send at least 20 high-effort
introduction cells every 100ms, where high-effort is a PoW which is above the
estimated level of "the motivated user" (see [USER_MODEL]).

An easier attack for the adversary, is the same strategy but with
introduction cells that are all above the comfortable level of "the standard
user" (see [USER_MODEL]). This would block out all standard users and only
allow motivated users to pass.

5.1.3. Hybrid overwhelm strategy [ATTACK_HYBRID]

If both the top- and bottom- halves are processed by the same thread, this
opens up the possibility for a "hybrid" attack. Given the performance figures
for the bottom half (0.31 ms/req.) and the top half (5.5 ms/req.), the
attacker can optimally deny service by submitting 91 high-effort requests and
1520 invalid requests per second. This will completely saturate the main loop
because:

0.31*(1520+91) ~ 0.5 sec.
5.5*91 ~ 0.5 sec.

This attack only has half the bandwidth requirement of [ATTACK_TOP_HALF] and
half the compute requirement of [ATTACK_BOTTOM_HALF].

Alternatively, the attacker can adjust the ratio between invalid and
high-effort requests depending on their bandwidth and compute capabilities.

5.1.4. Gaming the effort estimation logic [ATTACK_EFFORT]

Another way to beat this system is for the attacker to game the effort
estimation logic (see [EFFORT_ESTIMATION]). Essentialy, there are two attacks
that we are trying to avoid:

- Attacker sets descriptor suggested-effort to a very high value effectively
making it impossible for most clients to produce a PoW token in a
reasonable timeframe.
- Attacker sets descriptor suggested-effort to a very small value so that
most clients aim for a small value while the attacker comfortably launches
an [ATTACK_BOTTOM_HALF] using medium effort PoW (see [REF_TEVADOR_1])

5.1.4. Precomputed PoW attack

The attacker may precompute many valid PoW nonces and submit them all at once
before the current seed expires, overwhelming the service temporarily even
using a single computer. The current scheme gives the attackers 4 hours to
launch this attack since each seed lasts 2 hours and the service caches two
seeds.

An attacker with this attack might be aiming to DoS the service for a limited
amount of time, or to cause an [ATTACK_EFFORT] attack.

6. Parameter tuning [POW_TUNING]

There are various parameters in this PoW system that need to be tuned:

We first start by tuning the time it takes to verify a PoW token. We do this
first because it's fundamental to the performance of onion services and can
turn into a DoS vector of its own. We will do this tuning in a way that's
agnostic to the chosen PoW function.

We will then move towards analyzing the default difficulty setting for our
PoW system. That defines the expected time for clients to succeed in our
system, and the expected time for attackers to overwhelm our system. Same as
above we will do this in a way that's agnostic to the chosen PoW function.

Finally, using those two pieces we will tune our PoW function and pick the
right default difficulty setting. At the end of this section we will know the
resources that an attacker needs to overwhelm the onion service, the
resources that the service needs to verify introduction requests, and the
resources that legitimate clients need to get to the onion service.

6.1. PoW verification [POW_TUNING_VERIFICATION]

Verifying a PoW token is the first thing that a service does when it receives
an INTRODUCE2 cell and it's detailed in section [POW_VERIFY]. This
verification happens during the "top half" part of the process. Every
milisecond spent verifying PoW adds overhead to the already existing "top
half" part of handling an introduction cell. Hence we should be careful to
add minimal overhead here so that we don't enable attacks like [ATTACK_TOP_HALF].

During our performance measurements in [TOR_MEASUREMENTS] we learned that the
"top half" takes about 0.26 msecs in average, without doing any sort of PoW
verification. Using that value we compute the following table, that describes
the number of cells we can queue per second (aka times we can perform the
"top half" process) for different values of PoW verification time:

+---------------------+-----------------------+--------------+
|PoW Verification Time| Total "top half" time | Cells Queued |
| | | per second |
|---------------------|-----------------------|--------------|
| 0 msec | 0.26 msec | 3846 |
| 1 msec | 1.26 msec | 793 |
| 2 msec | 2.26 msec | 442 |
| 3 msec | 3.26 msec | 306 |
| 4 msec | 4.26 msec | 234 |
| 5 msec | 5.26 msec | 190 |
| 6 msec | 6.26 msec | 159 |
| 7 msec | 7.26 msec | 137 |
| 8 msec | 8.26 msec | 121 |
| 9 msec | 9.26 msec | 107 |
| 10 msec | 10.26 msec | 97 |
+---------------------+-----------------------+--------------+

Here is how you can read the table above:

- For a PoW function with a 1ms verification time, an attacker needs to send
793 dummy introduction cells per second to succeed in a [ATTACK_TOP_HALF] attack.

- For a PoW function with a 2ms verification time, an attacker needs to send
442 dummy introduction cells per second to succeed in a [ATTACK_TOP_HALF] attack.

- For a PoW function with a 10ms verification time, an attacker needs to send
97 dummy introduction cells per second to succeed in a [ATTACK_TOP_HALF] attack.

Whether an attacker can succeed at that depends on the attacker's resources,
but also on the network's capacity.

Our purpose here is to have the smallest PoW verification overhead possible
that also allows us to achieve all our other goals.

[Note that the table above is simply the result of a naive multiplication and
does not take into account all the auxiliary overheads that happen every
second like the time to invoke the mainloop, the bottom-half processes, or
pretty much anything other than the "top-half" processing.

During our measurements the time to handle INTRODUCE2 cells dominates any
other action time: There might be events that require a long processing time,
but these are pretty infrequent (like uploading a new HS descriptor) and
hence over a long time they smooth out. Hence extrapolating the total cells
queued per second based on a single "top half" time seems like good enough to
get some initial intuition. That said, the values of "Cells queued per
second" from the table above, are likely much smaller than displayed above
because of all the auxiliary overheads.]

6.2. PoW difficulty analysis [POW_DIFFICULTY_ANALYSIS]

The difficulty setting of our PoW basically dictates how difficult it should
be to get a success in our PoW system. An attacker who can get many successes
per second can pull a successfull [ATTACK_BOTTOM_HALF] attack against our
system.

In classic PoW systems, "success" is defined as getting a hash output below
the "target". However, since our system is dynamic, we define "success" as an
abstract high-effort computation.

Our system is dynamic but we still need a default difficulty settings that
will define the metagame and be used for bootstrapping the system. The client
and attacker can still aim higher or lower but for UX purposes and for
analysis purposes we do need to define a default difficulty.

6.2.1. Analysis based on adversary power

In this section we will try to do an analysis of PoW difficulty without using
any sort of Tor-related or PoW-related benchmark numbers.

We created the table (see [REF_TABLE]) below which shows how much time a
legitimate client with a single machine should expect to burn before they get
a single success. The x-axis is how many successes we want the attacker to be
able to do per second: the more successes we allow the adversary, the more
they can overwhelm our introduction queue. The y-axis is how many machines
the adversary has in her disposal, ranging from just 5 to 1000.

===============================================================
| Expected Time (in seconds) Per Success For One Machine |
===========================================================================
| |
| Attacker Succeses 1 5 10 20 30 50 |
| per second |
| |
| 5 5 1 0 0 0 0 |
| 50 50 10 5 2 1 1 |
| 100 100 20 10 5 3 2 |
| Attacker 200 200 40 20 10 6 4 |
| Boxes 300 300 60 30 15 10 6 |
| 400 400 80 40 20 13 8 |
| 500 500 100 50 25 16 10 |
| 1000 1000 200 100 50 33 20 |
| |
============================================================================

Here is how you can read the table above:

- If an adversary has a botnet with 1000 boxes, and we want to limit her to 1
success per second, then a legitimate client with a single box should be
expected to spend 1000 seconds getting a single success.

- If an adversary has a botnet with 1000 boxes, and we want to limit her to 5
successes per second, then a legitimate client with a single box should be
expected to spend 200 seconds getting a single success.

- If an adversary has a botnet with 500 boxes, and we want to limit her to 5
successes per second, then a legitimate client with a single box should be
expected to spend 100 seconds getting a single success.

- If an adversary has access to 50 boxes, and we want to limit her to 5
successes per second, then a legitimate client with a single box should be
expected to spend 10 seconds getting a single success.

- If an adversary has access to 5 boxes, and we want to limit her to 5
successes per second, then a legitimate client with a single box should be
expected to spend 1 seconds getting a single success.

With the above table we can create some profiles for default values of our
PoW difficulty. So for example, we can use the last case as the default
parameter for Tor Browser, and then create three more profiles for more
expensive cases, scaling up to the first case which could be hardest since
the client is expected to spend 15 minutes for a single introduction.

6.2.2. Analysis based on Tor's performance [POW_DIFFICULTY_TOR]

To go deeper here, we can use the performance measurements from
[TOR_MEASUREMENTS] to get a more specific intuition on the default
difficulty. In particular, we learned that completely handling an
introduction cell takes 5.55 msecs in average. Using that value, we can
compute the following table, that describes the number of introduction cells
we can handle per second for different values of PoW verification:

+---------------------+-----------------------+--------------+
|PoW Verification Time| Total time to handle | Cells handled|
| | introduction cell | per second |
|---------------------|-----------------------|--------------|
| 0 msec | 5.55 msec | 180.18 |
| 1 msec | 6.55 msec | 152.67 |
| 2 msec | 7.55 msec | 132.45 |
| 3 msec | 8.55 msec | 116.96 |
| 4 msec | 9.55 mesc | 104.71 |
| 5 msec | 10.55 msec | 94.79 |
| 6 msec | 11.55 msec | 86.58 |
| 7 msec | 12.55 msec | 79.68 |
| 8 msec | 13.55 msec | 73.80 |
| 9 msec | 14.55 msec | 68.73 |
| 10 msec | 15.55 msec | 64.31 |
+---------------------+-----------------------+--------------+

Here is how you can read the table above:

- For a PoW function with a 1ms verification time, an attacker needs to send
152 high-effort introduction cells per second to succeed in a
[ATTACK_BOTTOM_HALF] attack.

- For a PoW function with a 10ms verification time, an attacker needs to send
64 high-effort introduction cells per second to succeed in a
[ATTACK_BOTTOM_HALF] attack.

We can use this table to specify a default difficulty that won't allow our
target adversary to succeed in an [ATTACK_BOTTOM_HALF] attack.

Of course, when it comes to this table, the same disclaimer as in section
[POW_TUNING_VERIFICATION] is valid. That is, the above table is just a
theoretical extrapolation and we expect the real values to be much lower
since they depend on auxiliary processing overheads, and on the network's
capacity.

6.3. Tuning equix difficulty [EQUIX_DIFFICULTY]

The above two sections were not depending on a particular PoW scheme. They
gave us an intuition on the values we are aiming for in terms of verification
speed and PoW difficulty. Now we need to make things concrete:

As described in section [EFFORT_ESTIMATION] we start the service with a
default suggested-effort value of 5000. Given the benchmarks of EquiX
[REF_EQUIX] this should take about 2 to 3 seconds on a modern CPU.

With this default difficulty setting and given the table in
[POW_DIFFICULTY_ANALYSIS] this means that an attacker with 50 boxes will be
able to get about 20 successful PoWs per second, and an attacker with 100
boxes about 40 successful PoWs per second.

Then using the table in [POW_DIFFICULTY_TOR] we can see that the number of
attacker's successes is not enough to overwhelm the service through an
[ATTACK_BOTTOM_HALF] attack. That is, an attacker would need to do about 152
introductions per second to overwhelm the service, whereas they can only do
40 with 100 boxes.

7. Discussion

7.1. UX

This proposal has user facing UX consequences.

Here is some UX improvements that don't need user-input:

- Primarily, there should be a way for Tor Browser to display to users that
additional time (and resources) will be needed to access a service that is
under attack. Depending on the design of the system, it might even be
possible to estimate how much time it will take.

And here are a few UX approaches that will need user-input and have an
increasing engineering difficulty. Ideally this proposal will not need
user-input and the default behavior should work for almost all cases.

a) Tor Browser needs a "range field" which the user can use to specify how
much effort they want to spend in PoW if this ever occurs while they are
browsing. The ranges could be from "Easy" to "Difficult", or we could try
to estimate time using an average computer. This setting is in the Tor
Browser settings and users need to find it.

b) We start with a default effort setting, and then we use the new onion
errors (see #19251) to estimate when an onion service connection has
failed because of DoS, and only then we present the user a "range field"
which they can set dynamically. Detecting when an onion service connection
has failed because of DoS can be hard because of the lack of feedback (see
[CLIENT_BEHAVIOR])

c) We start with a default effort setting, and if things fail we
automatically try to figure out an effort setting that will work for the
user by doing some trial-and-error connections with different effort
values. Until the connection succeeds we present a "Service is
overwhelmed, please wait" message to the user.

7.2. Future work [FUTURE_WORK]

7.2.1. Incremental improvements to this proposal

There are various improvements that can be done in this proposal, and while
we are trying to keep this v1 version simple, we need to keep the design
extensible so that we build more features into it. In particular:

- End-to-end introduction ACKs

This proposal suffers from various UX issues because there is no end-to-end
mechanism for an onion service to inform the client about its introduction
request. If we had end-to-end introduction ACKs many of the problems from
[CLIENT_BEHAVIOR] would be aleviated. The problem here is that end-to-end
ACKs require modifications on the introduction point code and a network
update which is a lengthy process.

- Multithreading scheduler

Our scheduler is pretty limited by the fact that Tor has a single-threaded
design. If we improve our multithreading support we could handle a much
greater amount of introduction requests per second.

7.2.2. Future designs [FUTURE_DESIGNS]

This is just the beginning in DoS defences for Tor and there are various
futured designs and schemes that we can investigate. Here is a brief summary
of these:

"More advanced PoW schemes" -- We could use more advanced memory-hard PoW
schemes like MTP-argon2 or Itsuku to make it even harder for
adversaries to create successful PoWs. Unfortunately these schemes
have much bigger proof sizes, and they won't fit in INTRODUCE1 cells.
See #31223 for more details.

"Third-party anonymous credentials" -- We can use anonymous credentials and a
third-party token issuance server on the clearnet to issue tokens
based on PoW or CAPTCHA and then use those tokens to get access to the
service. See [REF_CREDS] for more details.

"PoW + Anonymous Credentials" -- We can make a hybrid of the above ideas
where we present a hard puzzle to the user when connecting to the
onion service, and if they solve it we then give the user a bunch of
anonymous tokens that can be used in the future. This can all happen
between the client and the service without a need for a third party.

All of the above approaches are much more complicated than this proposal, and
hence we want to start easy before we get into more serious projects.

7.3. Environment

We love the environment! We are concerned of how PoW schemes can waste energy
by doing useless hash iterations. Here is a few reasons we still decided to
pursue a PoW approach here:

"We are not making things worse" -- DoS attacks are already happening and
attackers are already burning energy to carry them out both on the
attacker side, on the service side and on the network side. We think that
asking legitimate clients to carry out PoW computations is not gonna
affect the equation too much, since an attacker right now can very
quickly cause the same damage that hundreds of legitimate clients do a
whole day.

"We hope to make things better" -- The hope is that proposals like this will
make the DoS actors go away and hence the PoW system will not be used. As
long as DoS is happening there will be a waste of energy, but if we
manage to demotivate them with technical means, the network as a whole
will less wasteful. Also see [CATCH22] for a similar argument.

8. Acknowledgements

Thanks a lot to tevador for the various improvements to the proposal and for
helping us understand and tweak the RandomX scheme.

Thanks to Solar Designer for the help in understanding the current PoW
landscape, the various approaches we could take, and teaching us a few neat
tricks.

Appendix A. Little-t tor introduction scheduler

This section describes how we will implement this proposal in the "tor"
software (little-t tor).

The following should be read as if tor is an onion service and thus the end
point of all inbound data.

A.1. The Main Loop [MAIN_LOOP]

Tor uses libevent for its mainloop. For network I/O operations, a mainloop
event is used to inform tor if it can read on a certain socket, or a
connection object in tor.

From there, this event will empty the connection input buffer (inbuf) by
extracting and processing a cell at a time. The mainloop is single threaded
and thus each cell is handled sequentially.

Processing an INTRODUCE2 cell at the onion service means a series of
operations (in order):

1) Unpack cell from inbuf to local buffer.

2) Decrypt cell (AES operations).

3) Parse cell header and process it depending on its RELAY_COMMAND.

4) INTRODUCE2 cell handling which means building a rendezvous circuit:
i) Path selection
ii) Launch circuit to first hop.

5) Return to mainloop event which essentially means back to step (1).

Tor will read at most 32 cells out of the inbuf per mainloop round.

A.2. Requirements for PoW

With this proposal, in order to prioritize cells by the amount of PoW work
it has done, cells can _not_ be processed sequentially as described above.

Thus, we need a way to queue a certain number of cells, prioritize them and
then process some cell(s) from the top of the queue (that is, the cells that
have done the most PoW effort).

We thus require a new cell processing flow that is _not_ compatible with
current tor design. The elements are:

- Validate PoW and place cells in a priority queue of INTRODUCE2 cells (as
described in section [INTRO_QUEUE]).

- Defer "bottom half" INTRO2 cell processing for after cells have been
queued into the priority queue.

A.3. Proposed scheduler [TOR_SCHEDULER]

The intuitive way to address the A.2 requirements would be to do this
simple and naive approach:

1) Mainloop: Empty inbuf INTRODUCE2 cells into priority queue

2) Process all cells in pqueue

3) Goto (1)

However, we are worried that handling all those cells before returning to the
mainloop opens possibilities of attack by an adversary since the priority
queue is not gonna be kept up to date while we process all those cells. This
means that we might spend lots of time dealing with introductions that don't
deserve it. See [BOTTOM_HALF_SCHEDULER] for more details.

We thus propose to split the INTRODUCE2 handling into two different steps:
"top half" and "bottom half" process, as also mentioned in [POW_VERIFY]
section above.

A.3.1. Top half and bottom half scheduler

The top half process is responsible for queuing introductions into the
priority queue as follows:

a) Unpack cell from inbuf to local buffer.

b) Decrypt cell (AES operations).

c) Parse INTRODUCE2 cell header and validate PoW.

d) Return to mainloop event which essentially means step (1).

The top-half basically does all operations of section [MAIN_LOOP] except from (4).

An then, the bottom-half process is responsible for handling introductions
and doing rendezvous. To achieve this we introduce a new mainloop event to
process the priority queue _after_ the top-half event has completed. This new
event would do these operations sequentially:

a) Pop INTRODUCE2 cell from priority queue.

b) Parse and process INTRODUCE2 cell.

c) End event and yield back to mainloop.

A.3.2. Scheduling the bottom half process [BOTTOM_HALF_SCHEDULER]

The question now becomes: when should the "bottom half" event get triggered
from the mainloop?

We propose that this event is scheduled in when the network I/O event
queues at least 1 cell into the priority queue. Then, as long as it has a
cell in the queue, it would re-schedule itself for immediate execution
meaning at the next mainloop round, it would execute again.

The idea is to try to empty the queue as fast as it can in order to provide a
fast response time to an introduction request but always leave a chance for
more cells to appear between cell processing by yielding back to the
mainloop. With this we are aiming to always have the most up-to-date version
of the priority queue when we are completing introductions: this way we are
prioritizing clients that spent a lot of time and effort completing their PoW.

If the size of the queue drops to 0, it stops scheduling itself in order to
not create a busy loop. The network I/O event will re-schedule it in time.

Notice that the proposed solution will make the service handle 1 single
introduction request at every main loop event. However, when we do
performance measurements we might learn that it's preferable to bump the
number of cells in the future from 1 to N where N <= 32.

A.4 Performance measurements

This section will detail the performance measurements we've done on tor.git
for handling an INTRODUCE2 cell and then a discussion on how much more CPU
time we can add (for PoW validation) before it badly degrades our
performance.

A.4.1 Tor measurements [TOR_MEASUREMENTS]

In this section we will derive measurement numbers for the "top half" and
"bottom half" parts of handling an introduction cell.

These measurements have been done on tor.git at commit
80031db32abebaf4d0a91c01db258fcdbd54a471.

We've measured several set of actions of the INTRODUCE2 cell handling process
on Intel(R) Xeon(R) CPU E5-2650 v4. Our service was accessed by an array of
clients that sent introduction requests for a period of 60 seconds.

1. Full Mainloop Event

We start by measuring the full time it takes for a mainloop event to
process an inbuf containing INTRODUCE2 cells. The mainloop event processed
2.42 cells per invocation on average during our measurements.

Total measurements: 3279

Min: 0.30 msec - 1st Q.: 5.47 msec - Median: 5.91 msec
Mean: 13.43 msec - 3rd Q.: 16.20 msec - Max: 257.95 msec

2. INTRODUCE2 cell processing (bottom-half)

We also measured how much time the "bottom half" part of the process
takes. That's the heavy part of processing an introduction request as seen
in step (4) of the [MAIN_LOOP] section:

Total measurements: 7931

Min: 0.28 msec - 1st Q.: 5.06 msec - Median: 5.33 msec
Mean: 5.29 msec - 3rd Q.: 5.57 msec - Max: 14.64 msec

3. Connection data read (top half)

Now that we have the above pieces, we can use them to measure just the
"top half" part of the procedure. That's when bytes are taken from the
connection inbound buffer and parsed into an INTRODUCE2 cell where basic
validation is done.

There is an average of 2.42 INTRODUCE2 cells per mainloop event and so we
divide that by the full mainloop event mean time to get the time for one
cell. From that we substract the "bottom half" mean time to get how much
the "top half" takes:

=> 13.43 / (7931 / 3279) = 5.55
=> 5.55 - 5.29 = 0.26

Mean: 0.26 msec

To summarize, during our measurements the average number of INTRODUCE2 cells
a mainloop event processed is ~2.42 cells (7931 cells for 3279 mainloop
invocations).

This means that, taking the mean of mainloop event times, it takes ~5.55msec
(13.43/2.42) to completely process an INTRODUCE2 cell. Then if we look deeper
we see that the "top half" of INTRODUCE2 cell processing takes 0.26 msec in
average, whereas the "bottom half" takes around 5.33 msec.

The heavyness of the "bottom half" is to be expected since that's where 95%
of the total work takes place: in particular the rendezvous path selection
and circuit launch.

A.2. References

[REF_EQUIX]: https://github.com/tevador/equix
https://github.com/tevador/equix/blob/master/devlog.md
[REF_TABLE]: The table is based on the script below plus some manual editing for readability:
https://gist.github.com/asn-d6/99a936b0467b0cef88a677baaf0bbd04
[REF_BOTNET]: https://media.kasperskycontenthub.com/wp-content/uploads/sites/43/2009/07/01121538/ynam_botnets_0907_en.pdf
[REF_CREDS]: https://lists.torproject.org/pipermail/tor-dev/2020-March/014198.html
[REF_TARGET]: https://en.bitcoin.it/wiki/Target
[REF_TLS]: https://www.ietf.org/archive/id/draft-nygren-tls-client-puzzles-02.txt
https://tools.ietf.org/id/draft-nir-tls-puzzles-00.html
https://tools.ietf.org/html/draft-ietf-ipsecme-ddos-protection-10
[REF_TLS_1]: https://www.ietf.org/archive/id/draft-nygren-tls-client-puzzles-02.txt
[REF_TEVADOR_1]: https://lists.torproject.org/pipermail/tor-dev/2020-May/014268.html
[REF_TEVADOR_2]: https://lists.torproject.org/pipermail/tor-dev/2020-June/014358.html
[REF_TEVADOR_SIM]: https://github.com/tevador/scratchpad/blob/master/tor-pow/effort_sim.md