tendermint/spec/consensus/light-client.md

Lite client

A lite client is a process that connects to Tendermint full nodes and then tries to verify application data using the Merkle proofs.

Context of this document

In order to make sure that full nodes have the incentive to follow the protocol, we have to address the following three Issues

1. The lite client needs a method to verify headers it obtains from full nodes according to trust assumptions -- this document.

2. The lite client must be able to connect to one correct full node to detect and report on failures in the trust assumptions (i.e., conflicting headers) -- a future document.

3. In the event the trust assumption fails (i.e., a lite client is fooled by a conflicting header), the Tendermint fork accountability protocol must account for the evidence -- see #3840

Problem statement

We assume that the lite client knows a (base) header inithead it trusts (by social consensus or because the lite client has decided to trust the header before). The goal is to check whether another header newhead can be trusted based on the data in inithead.

The correctness of the protocol is based on the assumption that inithead was generated by an instance of Tendermint consensus. The term "trusting" above indicates that the correctness on the protocol depends on this assumption. It is in the responsibility of the user that runs the lite client to make sure that the risk of trusting a corrupted/forged inithead is negligible.

Definitions

Data structures

In the following, only the details of the data structures needed for this specification are given.

• header fields

  • height
  • bfttime: the chain time when the header (block) was generated
  • V: validator set containing validators for this block.
  • NextV: validator set for next block.
  • commit: evidence that block with height height - 1 was committed by a set of validators (canonical commit). We will use signers(commit) to refer to the set of validators that committed the block.

• signed header fields: contains a header and a commit for the current header; a "seen commit". In the Tendermint consensus the "canonical commit" is stored in header height + 1.

• For each header h it has locally stored, the lite client stores whether it trusts h. We write trust(h) = true, if this is the case.

• Validator fields. We will write a validator as a tuple (v,p) such that

  • v is the identifier (we assume identifiers are unique in each validator set)
  • p is its voting power

Functions

For the purpose of this lite client specification, we assume that the Tendermint Full Node exposes the following function over Tendermint RPC:

    func Commit(height int64) (SignedHeader, error)
      // returns signed header: header (with the fields from
      // above) with Commit that include signatures of
      // validators that signed the header


    type SignedHeader struct {
      Header        Header
      Commit        Commit
    }

Definitions

• tp: trusting period
• for realtime t, the predicate correct(v,t) is true if the validator v follows the protocol until time t (we will see about recovery later).

Tendermint Failure Model

If a block h is generated at time bfttime (and this time is stored in the block), then a set of validators that hold more than 2/3 of the voting power in h.Header.NextV is correct until time h.Header.bfttime + tp.

Formally, [ \sum_{(v,p) \in h.Header.NextV \wedge correct(v,h.Header.bfttime + tp)} p > 2/3 \sum_{(v,p) \in h.Header.NextV} p ]

Assumption: "correct" is defined w.r.t. realtime (some Newtonian global notion of time, i.e., wall time), while bfttime corresponds to the reading of the local clock of a validator (how this time is computed may change when the Tendermint consensus is modified). In this note, we assume that all clocks are synchronized to realtime. We can make this more precise eventually (incorporating clock drift, accuracy, precision, etc.). Right now, we consider this assumption sufficient, as clock synchronization (under NTP) is in the order of milliseconds and tp is in the order of weeks.

Remark: This failure model might change to a hybrid version that takes heights into account in the future.

The specification in this document considers an implementation of the lite client under this assumption. Issues like counter-factual signing and fork accountability and evidence submission are mechanisms that justify this assumption by incentivizing validators to follow the protocol. If they don't, and we have more that 1/3 faults, safety may be violated. Our approach then is to detect these cases (after the fact), and take suitable repair actions (automatic and social). This is discussed in an upcoming document on "Fork accountability". (These safety violations include the lite client wrongly trusting a header, a fork in the blockchain, etc.)

Lite Client Trusting Spec

The lite client communicates with a full node and learns new headers. The goal is to locally decide whether to trust a header. Our implementation needs to ensure the following two properties:

• Lite Client Completeness: If header h was correctly generated by an instance of Tendermint consensus (and its age is less than the trusting period), then the lite client should eventually set trust(h) to true.

• Lite Client Accuracy: If header h was not generated by an instance of Tendermint consensus, then the lite client should never set trust(h) to true.

Remark: If in the course of the computation, the lite client obtains certainty that some headers were forged by adversaries (that is were not generated by an instance of Tendermint consensus), it may submit (a subset of) the headers it has seen as evidence of misbehavior.

Remark: In Completeness we use "eventually", while in practice trust(h) should be set to true before h.Header.bfttime + tp. If not, the block cannot be trusted because it is too old.

Remark: If a header h is marked with trust(h), but it is too old (its bfttime is more than tp ago), then the lite client should set trust(h) to false again.

Assumption: Initially, the lite client has a header inithead that it trusts correctly, that is, inithead was correctly generated by the Tendermint consensus.

To reason about the correctness, we may prove the following invariant.

Verification Condition: Lite Client Invariant. For each lite client l and each header h: if l has set trust(h) = true, then validators that are correct until time h.Header.bfttime + tp have more than two thirds of the voting power in h.Header.NextV.

Formally, [ \sum_{(v,p) \in h.Header.NextV \wedge correct(v,h.Header.bfttime + tp)} p > 2/3 \sum_{(v,p) \in h.Header.NextV} p ]

Remark. To prove the invariant, we will have to prove that the lite client only trusts headers that were correctly generated by Tendermint consensus, then the formula above follows from the Tendermint failure model.

High Level Solution

Upon initialization, the lite client is given a header inithead it trusts (by social consensus). It is assumed that inithead satisfies the lite client invariant. (If inithead has been correctly generated by Tendermint consensus, the invariant follows from the Tendermint Failure Model.)

When a lite clients sees a signed new header snh, it has to decide whether to trust the new header. Trust can be obtained by (possibly) the combination of three methods.

1. Uninterrupted sequence of proof. If a block is appended to the chain, where the last block is trusted (and properly committed by the old validator set in the next block), and the new block contains a new validator set, the new block is trusted if the lite client knows all headers in the prefix. Intuitively, a trusted validator set is assumed to only chose a new validator set that will obey the Tendermint Failure Model.

2. Trusting period. Based on a trusted block h, and the lite client invariant, which ensures the fault assumption during the trusting period, we can check whether at least one validator, that has been continuously correct from h.Header.bfttime until now, has signed snh. If this is the case, similarly to above, the chosen validator set in snh does not violate the Tendermint Failure Model.

3. Bisection. If a check according to the trusting period fails, the lite client can try to obtain a header hp whose height lies between h and snh in order to check whether h can be used to get trust for hp, and hp can be used to get trust for snh. If this is the case we can trust snh; if not, we may continue recursively.

How to use it

We consider the following use case: the lite client wants to verify a header for some given height k. Thus:

• it requests the signed header for height k from a full node
• it tries to verify this header with the methods described here.

This can be used in several settings:

• someone tells the lite client that application data that is relevant for it can be read in the block of height k.
• the lite clients wants the latest state. It asks a full nude for the current height, and uses the response for k.

Details

Assumptions

1. tp < unbonding period.
2. snh.Header.bfttime < now
3. snh.Header.bfttime < h.Header.bfttime+tp
4. trust(h)=true

Observation 1. If h.Header.bfttime + tp > now, we trust the old validator set h.Header.NextV.

When we say we trust h.Header.NextV we do not trust that each individual validator in h.Header.NextV is correct, but we only trust the fact that at most 1/3 of them are faulty (more precisely, the faulty ones have at most 1/3 of the total voting power).

Functions

The function Bisection checks whether to trust header h2 based on the trusted header h1. It does so by calling the function CheckSupport in the process of bisection/recursion. CheckSupport implements the trusted period method and, for two adjacent headers (in term of heights), it checks uninterrupted sequence of proof.

Assumption: In the following, we assume that h2.Header.height > h1.Header.height. We will quickly discuss the other case in the next section.

We consider the following set-up:

• the lite client communicates with one full node

• the lite client locally stores all the signed headers it obtained (trusted or not). In the pseudo code below we write Store(header) for this.

• If Bisection returns false, then the lite client has seen a forged header.

  • However, it does not know which header(s) is/are the problematic one(s).
  • In this case, the lite client can submit (some of) the headers it has seen as evidence. As the lite client communicates with one full node only when executing Bisection, there are two cases
    • the full node is faulty
    • the full node is correct and there was a fork in Tendermint consensus. Header h1 is from a different branch than the one taken by the full node. This case is not focus of this document, but will be treated in the document on fork accountability.

• the lite client must retry to retrieve correct headers from another full node

  • it picks a new full node
  • it restarts Bisection
  • there might be optimizations; a lite client may not need to call Commit(k), for a height k for which it already has a signed header it trusts.
  • how to make sure that a lite client can communicate with a correct full node will be the focus of a separate document (recall Issue 3 from "Context of this document").

Auxiliary Functions. We will use the function votingpower_in(V1,V2) to compute the voting power the validators in set V1 have according to their voting power in set V2; we will write totalVotingPower(V) for votingpower_in(V,V), which returns the total voting power in V. We further use the function signers(Commit) that returns the set of validators that signed the Commit.

CheckSupport. The following function checks whether we can trust the header h2 based on header h1 following the trusting period method. Time constraint is captured by the hasExpired function that depends on trusted period (tp) and a parameter Delta that denotes minimum duration of header so it is not considered expired.

  // return true if header has expired, i.e., it is outside its trusted period; otherwise it returns false
  func hasExpired(h) bool {
    if h.Header.bfttime + tp - Delta < now { // Observation 1
      return true
  }

  // return true if header is correctly signed by 2/3+ voting power in the corresponding validator set; otherwise false. Additional checks should be done in the implementation
  // to ensure header is well formed.
  func verify(h) bool {
    vp_all := totalVotingPower(h.Header.V) // total sum of voting power of validators in h
    return votingpower_in(signers(h.Commit),h.Header.V) > 2/3 * vp_all
  }

  // Captures skipping condition. h1 and h2 has already passed basic validation (function `verify`).
  // returns (true, nil) in case h2 can be trusted based on h1, (false, nil) in case it cannot be trusted but no errors are observed during check and (false, error) in case
  // an error is detected (for example adjacent headers are not consistent).
  func CheckSupport(h1,h2,trustlevel) (bool, error) {
      assume h1.Header.Height < h2.header.Height

      if hasExpired(h1) return (false, ErrHeaderExpired(h1))

      // total sum of voting power of validators in h1.NextV
      vp_all := totalVotingPower(h1.Header.NextV)

      // check for adjacent headers
      if (h2.Header.height == h1.Header.height + 1) {
            if h1.Header.NextV == h2.Header.V return (true, nil)
            else return (false, ErrInvalidAdjacentHeaders)
      } else {
      // check for non-adjacent headers
            return (votingpower_in(signers(h2.Commit),h1.Header.NextV) > max(1/3,trustlevel) * vp_all, nil)
      }
  }

Remark: Basic header verification must be done for h2. Similar checks are done in:
https://github.com/tendermint/tendermint/blob/master/types/validator_set.go#L591-L633

Remark: There are some sanity checks which are not in the code: h2.Header.height > h1.Header.height and h2.Header.bfttime > h1.Header.bfttime and h2.Header.bfttime < now.

Remark: return (votingpower_in(signers(h2.Commit),h1.Header.NextV) > max(1/3,trustlevel) * vp_all) may return false even if h2 was properly generated by Tendermint consensus in the case of big changes in the validator sets. However, the check return (votingpower_in(signers(h2.Commit),h1.Header.NextV) > 2/3 * vp_all) must return true if h1 and h2 were generated by Tendermint consensus.

Remark: The 1/3 check differs from a previously proposed method that was based on intersecting validator sets and checking that the new validator set contains "enough" correct validators. We found that the old check is not suited for realistic changes in the validator sets. The new method is not only based on cardinalities, but also exploits that we can trust what is signed by a correct validator (i.e., signed by more than 1/3 of the voting power).

Correctness arguments

Towards Lite Client Accuracy:

• Assume by contradiction that h2 was not generated correctly and the lite client sets trust to true because CheckSupport returns true.
• h1 is trusted and sufficiently new
• by Tendermint Fault Model, less than 1/3 of voting power held by faulty validators => at least one correct validator v has signed h2.
• as v is correct up to now, it followed the Tendermint consensus protocol at least up to signing h2 => h2 was correctly generated, we arrive at the required contradiction.

Towards Lite Client Completeness:

• The check is successful if sufficiently many validators of h1 are still validators in h2 and signed h2.
• If h2.Header.height = h1.Header.height + 1, and both headers were generated correctly, the test passes

Verification Condition: We may need a Tendermint invariant stating that if h2.Header.height = h1.Header.height + 1 then signers(h2.Commit) \subseteq h1.Header.NextV.

Remark: The variable trustlevel can be used if the user believes that relying on one correct validator is not sufficient. However, in case of (frequent) changes in the validator set, the higher the trustlevel is chosen, the more unlikely it becomes that CheckSupport returns true for non-adjacent headers.

Bisection. The following function uses CheckSupport in a recursion to find intermediate headers that allow to establish a sequence of trust.

// return (true, nil) in case we can trust header h2 based on header h1; otherwise return (false, error) where error captures the nature of the error.
func Bisection(h1,h2,trustlevel) (bool, error) {
  assume h1.Header.Height < h2.header.Height

  ok, err = CheckSupport(h1,h2,trustlevel)
  if (ok or err != nil) return (ok, err)

  // we cannot verify h2 based on h1, so we try to move trusted header closer to h2 so we can verify h2
  th := h1 // th is trusted header
  while th.Header.Height <= h2.Header.height - 1 do {
       // try to move trusted header forward with stored headers
       ih := th
       for all stored headers h s.t ih.Header.Height < h.Header.height < h2.Header.height do {  // try to move trusted header forward
            // we assume here that iteration is done in the order of header heights
            ok, err = CheckSupport(th,h,trustlevel)
            if err != nil { return (ok, err) }
            if ok {
                th = h
            }
        }

        // at this point we have potentially updated th based on stored headers so we try to verify h2 based on new trusted header
        ok, err = CheckSupport(th,h2,trustlevel)
        if (ok or err != nil) return (ok, err)

        // we cannot verify h2 based on th, so we try to move trusted header closer to h2 by downloading header(s) between th and h2
        endHeight = h2.Header.height
        foundPivot = false
        while(!foundPivot) {
            pivot := (th.Header.height + endHeight) / 2
            hp := Commit(pivot)
            if !verify(hp) return (false, ErrInvalidHeader(hp))
            Store(hp)

            // try to move trusted header forward to hp
            ok, err = CheckSupport(th,hp,trustlevel)
            if err != nil { return (ok, err) }
            if ok {
                th = hp
                foundPivot = true
            }
            endHeight = pivot
        }
  }
}

Correctness arguments (sketch)

Lite Client Accuracy:

• Assume by contradiction that h2 was not generated correctly and the lite client sets trust to true because Bisection returns true.
• Bisection returns true only if all calls to CheckSupport in the recursion return true.
• Thus we have a sequence of headers that all satisfied the CheckSupport
• again a contradiction

Lite Client Completeness:

This is only ensured if upon Commit(pivot) the lite client is always provided with a correctly generated header.

Stalling

With Bisection, a faulty full node could stall a lite client by creating a long sequence of headers that are queried one-by-one by the lite client and look OK, before the lite client eventually detects a problem. There are several ways to address this:

• Each call to Commit could be issued to a different full node
• Instead of querying header by header, the lite client tells a full node which header it trusts, and the height of the header it needs. The full node responds with the header along with a proof consisting of intermediate headers that the light client can use to verify. Roughly, Bisection would then be executed at the full node.
• We may set a timeout how long bisection may take.

The case h2.Header.height < h1.Header.height

In the use case where someone tells the lite client that application data that is relevant for it can be read in the block of height k and the lite client trusts a more recent header, we can use the hashes to verify headers "down the chain." That is, we iterate down the heights and check the hashes in each step.

Remark. For the case were the lite client trusts two headers i and j with i < k < j, we should discuss/experiment whether the forward or the backward method is more effective.

func Backwards(h1,h2) bool {
  assert (h2.Header.height < h1.Header.height)
  old := h1
  for i := h1.Header.height - 1; i > h2.Header.height; i-- {
    new := Commit(i)
    Store(new)
    if (hash(new) != old.Header.hash) {
      return false
    }
    old := new
  }
  return (hash(h2) == old.Header.hash)
 }