> Hello list,
> hope everyone is safe and doing well!
> I present you an initial draft of a proposal on PoW-based defences for
> onion services under DoS.

Hello again,

many thanks for all the thoughtful feedback!

In the end of this email I inline a new version of the proposal
addressing various issues discussed over IRC and on this thread.
Here is a rough changelog:

- Specifying some features we might want from "v1.5".
- Adding suggested-effort to the descriptor.
- Specifying the effort() function.
- Specifying the format of the expiration time.
- Adding a protocol-specific label to the PoW computation.
- Removing the seed and output values from the INTRODUCE1 cell.
- Specifying what happens when a client does not send a PoW token when PoW is 
- Revamping the UX section.
- Added Mike and David in the authors list.

I'm also pushing the spec to my git repo so that you can see a diff:

Now before going in to the proposal here are the three big topics currently
under discussion in the thread:

== How the scheduler should work ==

   I'm not gonna touch on this, since David is writing an initial draft of a
   scheduler design soon, so let's wait for that email before we discuss this

== Should there be a target difficulty on the descriptor? ==

   I have made changes in the proposal to this effect. See sections
   [EFFORT_ESTIMATION] and [CLIENT_TIMEOUT] for more information.

   While there is no hard-target difficulty, the descriptor now contains
   a suggested difficulty that clients should aim at. The service will
   still add requests with lower effort than the suggested one in the
   priority queue. That's to make the system more resilient to attacks
   in cases where the client cannot get the latest descriptor (and hence
   latest suggested effort) due to the descriptor upload/fetch
   rate-limiting restrictions in place.

== Which PoW function should we use? ==

   The proposal suggests argon2, and Mike has been looking at Randomx. However,
   after further consideration and speaking with some people (props to Alex
   Biryukov), it seems like those two functions are not well fitted for this
   purpose, since they are memory-hard both for the client and the service. And
   since we are trying to minimize the verification overhead, so that the
   service can do hundreds of verifications per second, they don't seem like
   good fits.

   In particular, slimming down argon2 to the point that services can do
   hundreds of those verifications per second, results in an argon2 without any
   memory-hardness. And Randomx is even heavier, since it uses argon2 under the
   hood and also does extra stuff. In particular, from some preliminary
   computations, it seems like the top-half of the cell processing takes about
   2ms, whereas Randomx takes at least 17ms in my computer, which means that it
   puts an almost 1000% overhead to the top-half processing of a single

   This means that assymetric PoW schemes like Equihash and family is what we
   should be looking at next. These schemes aim to have small proof sizes, and
   be memory-hard for the prover, but lightweight for the verifier. They are
   currently used by Zcash so there is quite some literature and improvements.

   In particular, Equihash has two important parameters (n,k). These parameters
   together control the proof size (so for example, Equihash<144,5> has a 100B
   proof, and Equihash<200,9> has a 1344B proof), and the 'k' parameter
   controls the verification speed (the verifier has to do 2^k hash invocations
   to do the verification). Also see this for more details:

   The good thing here is that these parameters look good and offer good
   security. Furthermore, Equihash is used by big and friendly projects like

   The negative thing is that because Equihash is widely used there is already
   ASIC hardware for it, so we would need to look at the parameters we pick and
   how ASIC-friendly they are. Furthermore, an attacker who buys Equihash ASIC
   can also use it for coin mining which makes it an easier investment.

   IMO, we should look more into Equihash and other assymetric types of PoW, as
   well as speak with people who know Equihash well.

   Finally, our proposal has a big benefit over the blockchain use cases: it's
   much more agile. We can deploy changes to the PoW algorithm without having
   to hard-fork, and we can do this even through the consensus for maximum
   agility. This means that we should try to use this agility to our advantage.

Looking forward to more feedback!


And here comes the updated proposal:

Filename: xxx-pow-over-intro-v1
Title: A First Take at PoW Over Introduction Circuits
Author: George Kadianakis, Mike Perry, David Goulet
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

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 in our disposal (see [FUTURE_DESIGNS]).

  {XXX: Do the above make sense? What other attackers do we care about? What
        other metrics do we care about? Network speed? I got the botnet costs
        from here [REF_BOTNET] Back up our claims of defence.}

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

                                          |                                  |
   +-------+ 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
  should only be enabled by services when under duress. The percentage of
  clients receiving puzzles can also be configured based on the load of the

  In summary, the following steps are taken for the protocol to complete:

  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 

2.2. Proof-of-work overview

2.2.1. Primitives

  For our proof-of-work scheme we want to minimize the spread of resources
  between a motivated attacker and legitimate clients. This means that we are
  looking to minimize any benefits that GPUs or ACICs can offer to an attacker.

  For this reason we chose argon2 [REF_ARGON2] as the hash function for our
  proof-of-work scheme since it's well audited and GPU-resistant and to some
  extend ASIC-resistant as well.

  As a password hash function, argon2 by default outputs 32 bytes of hash, and
  takes as primary input a message and a nonce/salt. For the purposes of this
  specification we will define an argon2() function as:
     uint8_t hash_output[32] = argon2(uint8_t *message, uint8_t *nonce)'.

  See section [ARGON_PARAMS] for more information on the secondary inputs of

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

  For our dynamic PoW system to work, we will need to be able to compare PoW
  tokens with each other. To do so we define a function:
         unsigned effort(uint8_t *token)
  which takes as its argument a hash output token, and returns the number of
  leading zero bits on it.

  So for example effort(0000000110001010110100101) == 7.

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 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. See
                  [EFFORT_ESTIMATION] for more details here.

        expiration-time: A timestamp in "YYYY-MM-DD SP HH:MM:SS" format after
                         which the above seed expires and is no longer valid as
                         the input for PoW. It's needed so that the size of our
                         replay cache does not grow infinitely. It should be
                         set to three hours in the future (+- some randomness).
                         {TODO: PARAM_TUNING}

       {XXX: Expiration time makes us even more susceptible to clock skews, but
             it's needed so that our replay cache refreshes. How to fix this?
             See [CLIENT_BEHAVIOR] for more details.}

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 expecting a PoW input 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 an infinite PoW computation. {XXX: How to enforce this?}

  To complete the PoW the client follows the following logic:

      a) Client generates 'nonce' as 32 random bytes.
      b) Client derives 'seed' by decoding 'seed-b64'.
      c) Client derives 'labeled_seed = seed + "TorV1PoW"'
      d) Client computes hash_output = argon2(labeled_seed, nonce)
      e) Client checks if effort(hash_output) >= target.
        e1) If yes, success! The client uses 'hash_output' as the puzzle
            solution and 'nonce' and 'seed' as its inputs.
        e2) If no, fail! The client interprets 'nonce' as a big-endian integer,
            increments it by one, and goes back to step (d).

  At the end of the above procedure, the client should have a triplet
  (hash_output, seed, nonce) that can be used as the answer to the PoW
  puzzle. How quickly this happens depends solely on the 'target' parameter.

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:

     [01] -- PROOF_OF_WORK

   The EXT_FIELD content format is:

      POW_VERSION    [1 byte]
      POW_NONCE      [32 bytes]


    POW_VERSION is 1 for the protocol specified in this proposal
    POW_NONCE is 'nonce' from the section above

   This will increase the INTRODUCE1 payload size by 33 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 32 bytes. According to
   ticket #33650, INTRODUCE1 cells currently have more than 200 bytes

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 required to
   complete the introduction. If it's not required, the extension SHOULD BE
   ignored. If it is required, 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 extracts (hash_output,
   seed, nonce) from the INTRODUCE1 cell and MUST do the following steps:

   1) Make sure that the client's seed is identical to the active seed.
   2) Check the client's nonce for replays (see [REPLAY_PROTECTION] section).
   3) Verify that 'hash_output =?= argon2(seed, nonce)

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

   If all the steps passed, then the circuit is added to the introduction queue
   as detailed in section [INTRO_QUEUE]. 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 actiev 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: PARAM_TUNING}

3.4.2. The Introduction Queue  [INTRO_QUEUE] 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 the effort()
  function with hash_output as its input, and uses the output to place requests
  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.

  {TODO: PARAM_TUNING: If the priority queue is only ordered based on the
   effort what attacks can happen in various scenarios? Do we want to order on
   time+effort?  Which scenarios and attackers should we examine here?} Handling introductions from the introduction queue [HANDLE_QUEUE]

  The service should handle introductions by pulling from the introduction

  Similar to how our cell scheduler works, the onion service subsystem will
  poll the priority queue every 100ms tick and process the first 20 cells from
  the priority queue (if they exist). The service will perform the rendezvous
  and the rest of the onion service protocol as normal.

  With this tempo, we can process 200 introduction cells per second.
  {XXX: Is this good?}

  After the introduction request is handled from the queue, the service trims
  the priority queue if the queue is too big.
  {TODO: PARAM_TUNING: What's the max size of the queue? How do we trim it? Can
  we use WRED usefully?}

  {TODO: PARAM_TUNING: STRAWMAN: This needs hella tuning. Processing 20 cells
  per 100ms is probably unmaintainable, since each cell is quite expensive:
  doing so involving path selection, crypto and making circuits. We will need
  to profile this procedure and see how we can do this scheduling better.}

3.4.3. PoW effort estimation [EFFORT_ESTIMATION]

  During its operation the service continuously keeps track of the received PoW
  cell efforts to inform its clients of the effort they should put in their
  introduction to get service. The service informs the clients by using the
  <suggested-effort> field in the descriptor.

  In particular, the service starts with a default suggested-effort value of 15.

  Everytime the service handles an introduction request from the priority queue
  in [HANDLE_QUEUE], the service compares the request's effort to the current
  suggested-effort value. If the new request's effort is lower than the
  suggested-effort, set the suggested-effort equal to the effort of the new

  Everytime the service trims the priority queue in [HANDLE_QUEUE], the service
  compares the request at the trim point against the current suggested-effort
  value. If the trimmed request's effort is higher than the suggested-effort,
  set the suggested-effort equal to the effort of the new request.

  The above two operations are meant to balance the suggested effort based on
  the requests currently waiting in the priority queue. If the priority queue
  is filled with high-effort requests, make the suggested effort higher. And
  when all the high-effort requests get handled and the priority queue is back
  to normal operation, relax the suggested effort to lower levels.

  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].

  {XXX: What attacks are possible here?} Updating descriptor with new suggested effort

  When a service changes its suggested-effort value, it SHOULD upload a new
  descriptor with the new value.

  The service should avoid uploading descriptors too often to avoid overwheming
  the HSDirs. The service SHOULD NOT upload descriptors more often than
  'hs-pow-desc-upload-rate-limit' seconds (which is controlled through a
  consensus parameter and has a default value of 300 seconds).

  {XXX: Is this too often? Or too rare? Perhaps we can set different limits
  for when the difficulty goes up and different for when it goes down. It's
  more important to update the descriptor when the difficulty goes up.}

  {XXX: What attacks are possible here? Can the attacker intentionally hit this
  rate-limit and then influence the suggested effort so that clients do not
  learn about the new effort? The service will still accept efforts lower than
  the suggested effort so the attack is not so serious, but it still can be a

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

  For this reason we need to define some client behaviors to work around these

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.

  {XXX: How should timeout values change here since the priority queue will
  cause bigger delays than usual to rendezvous?}

  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. The client SHOULD NOT fetch service
  descriptors more often than every 'hs-pow-desc-fetch-rate-limit' seconds
  (which is controlled through a consensus parameter and has a default value of
  600 seconds).

  {XXX: Is this too rare? Too often?}

  When the client fetches a new descriptor, it should try connecting to the
  service with the new suggested-effort and PoW seed. If that doesn't work, it
  should double the effort and retry. The client should keep on
  doubling-and-retrying until it manages to get service, or its able to fetch a
  new descriptor again.

  {XXX: This means that the client will keep on spinning and
  doubling-and-retrying for a service under this situation. There will never be
  a "Client connection timed out" page for the user. Is this good? Is this bad?
  Should we stop doubling-and-retrying after some iterations? Or should we
  throw a custom error page to the user, and ask the user to stop spinning
  whenever they want?}

4.2. Seed expiration issues

  As mentioned in [DESC_POW], the expiration timestamp on the PoW seed can
  cause issues with clock skewed clients. Furthermore, even not clock skewed
  clients can encounter TOCTOU-style race conditions here.

  The client descriptor refetch logic of [CLIENT_TIMEOUT] should take care of
  such seed-expiration issues, since the client will refetch the descriptor.

  {XXX: Is this sufficient? Should we have multiple active seeds at the same
  time similar to how we have overlapping descriptors and time periods in v3?
  This would solve the problem but it grows the complexity of the system

4.3. Other descriptor issues

  Another race condition here is if the service enables PoW, while a client has
  a cached descriptor. How will the client notice that PoW is needed? Does it
  need to fetch a new descriptor? Should there be another feedback mechanism?

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. Total overwhelm strat

  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.

  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.

  {XXX: What other attack strategies we should care about?}

6. Parameter tuning [PARAM_TUNING]

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

  We will first start by tuning the default difficulty of our PoW
  system. That's gonna define an expected time for attackers and clients to

  We are then gonna tune the parameters of the argon2 hash function. That will
  define the resources that an attacker needs to spend to overwhelm the onion
  service, the resources that the service needs to spend to verify introduction
  requests, and the resources that legitimate clients need to spend to get to
  the onon service.

6.1. PoW Difficulty settings

  The difficulty setting of our PoW basically dictates how difficult it should
  be to get a success in our PoW 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.

  Even tho our system is dynamic, we still need default difficulty settings
  that will define the metagame. The client and attacker can still aim higher
  or lower, but for UX purposes and for analysis purposes we do need to define
  some difficulties.

  We hence 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.

  {TODO: PARAM_TUNING You can see that this section is completely CPU/memory
  agnostic, and it does not take into account potential optimizations that can
  come from GPU/ASICs. This is intentional so that we don't put more variables
  into this equation right now, but as this proposal moves forward we will need
  to put more concrete values here.}

6.2. Argon2 parameters [ARGON_PARAMS]

  We now need to define the secondary argon2 parameters as defined in
  [REF_ARGON2]. This includes the number of lanes 'h', the memory size 'm', the
  number of iterations 't'. Section 9 of [REF_ARGON2] recommends an approach of
  how to tune these parameters.

  To tune these parameters we are looking to *minimize* the verification speed
  of an onion service, while *maximizing* the sparse resources spent by an
  adversary trying to overwhelm the service using [ATTACK_META].

  When it comes to verification speed, to verify a single introduction cell the
  service needs to do a single argon2 call: so the service will need to do
  hundreds of those per second as INTRODUCE2 cells arrive. The service will
  have to do this verification step even for very cheap zero-effort PoW
  received, so this has to be a cheap procedure so that it doesn't become a DoS
  vector of each own. Hence each individual argon2 call must be cheap enough to
  be able to be done comfortably and plentifuly by an onion service with a
  single host (or horizontally scaled with Onionbalance).

  At the same time, the adversary will have to do thousands of these calls if
  she wants to make high-effort PoW, so it's this assymetry that we are looking
  to exploit here. Right now, the most expensive resource for adversaries is
  the RAM size, and that's why we chose argon2 which is memory-hard.

  To minmax this game we will need

  {TODO: PARAM_TUNING: I've had a hard time minmaxing this game for
  argon2. Even argon2 invocations with a small memory parameter will take
  multiple milliseconds to run on my machine, and the parameters recommended in
  section 8 of the paper all take many hundreds of milliseconds. This is just
  not practical for our use case, since we want to process hundreds of such PoW
  per second... I also did not manage to find a benchmark of argon2 calls for
  different CPU/GPU/FPGA configurations.}

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

  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. References

  [REF_TABLE]: The table is based on the script below plus some manual editing 
for readability:
  [REF_TARGET]: https://en.bitcoin.it/wiki/Target

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