tendermint/spec/light-client/verification/verification_001_published.md

Light Client Verification

The light client implements a read operation of a header from the blockchain, by communicating with full nodes. As some full nodes may be faulty, this functionality must be implemented in a fault-tolerant way.

In the Tendermint blockchain, the validator set may change with every new block. The staking and unbonding mechanism induces a security model: starting at time Time of the header, more than two-thirds of the next validators of a new block are correct for the duration of TrustedPeriod. The fault-tolerant read operation is designed for this security model.

The challenge addressed here is that the light client might have a block of height h1 and needs to read the block of height h2 greater than h1. Checking all headers of heights from h1 to h2 might be too costly (e.g., in terms of energy for mobile devices). This specification tries to reduce the number of intermediate blocks that need to be checked, by exploiting the guarantees provided by the security model.

Status

This document is thoroughly reviewed, and the protocol has been formalized in TLA+ and model checked.

Issues that need to be addressed

As it is part of the larger light node, its data structures and functions interact with the fork dectection functionality of the light client. As a result of the work on Pull Request 479 we established the need for an update in the data structures in Issue 499. This will not change the verification logic, but it will record information about verification that can be used in fork detection (in particular in computing more efficiently the proof of fork).

Outline

• Part I: Introduction of relevant terms of the Tendermint blockchain.

• Part II: Introduction of the problem addressed by the Lightclient Verification protocol.

  • Verification Informal Problem statement: For the general audience, that is, engineers who want to get an overview over what the component is doing from a bird's eye view.
  • Sequential Problem statement: Provides a mathematical definition of the problem statement in its sequential form, that is, ignoring the distributed aspect of the implementation of the blockchain.

• Part III: Distributed aspects of the light client, system assumptions and temporal logic specifications.

  • Incentives: how faulty full nodes may benefit from misbehaving and how correct full nodes benefit from cooperating.

  • Computational Model: timing and correctness assumptions.

  • Distributed Problem Statement: temporal properties that formalize safety and liveness properties in the distributed setting.

• Part IV: Specification of the protocols.

  • Definitions: Describes inputs, outputs, variables used by the protocol, auxiliary functions

  • Core Verification: gives an outline of the solution, and details of the functions used (with preconditions, postconditions, error conditions).

  • Liveness Scenarios: when the light client makes progress depends heavily on the changes in the validator sets of the blockchain. We discuss some typical scenarios.

• Part V: The above parts focus on a common case where the last verified block has height h1 and the requested height h2 satisfies h2 > h1. For IBC, there are scenarios where this might not be the case. In this part, we provide some preliminaries for supporting this. As not all details of the IBC requirements are clear by now, we do not provide a complete specification at this point. We mark with "Open Question" points that need to be addressed in order to finalize this specification. It should be noted that the technically most challenging case is the one specified in Part IV.

In this document we quite extensively use tags in order to be able to reference assumptions, invariants, etc. in future communication. In these tags we frequently use the following short forms:

• TMBC: Tendermint blockchain
• SEQ: for sequential specifications
• LCV: Lightclient Verification
• LIVE: liveness
• SAFE: safety
• FUNC: function
• INV: invariant
• A: assumption

Part I - Tendermint Blockchain

Header Fields necessary for the Light Client

[TMBC-HEADER.1]

A set of blockchain transactions is stored in a data structure called block, which contains a field called header. (The data structure block is defined here). As the header contains hashes to the relevant fields of the block, for the purpose of this specification, we will assume that the blockchain is a list of headers, rather than a list of blocks.

[TMBC-HASH-UNIQUENESS.1]

We assume that every hash in the header identifies the data it hashes. Therefore, in this specification, we do not distinguish between hashes and the data they represent.

[TMBC-HEADER-FIELDS.1]

A header contains the following fields:

• Height: non-negative integer
• Time: time (integer)
• LastBlockID: Hashvalue
• LastCommit DomainCommit
• Validators: DomainVal
• NextValidators: DomainVal
• Data: DomainTX
• AppState: DomainApp
• LastResults: DomainRes

[TMBC-SEQ.1]

The Tendermint blockchain is a list chain of headers.

[TMBC-VALIDATOR-PAIR.1]

Given a full node, a validator pair is a pair (peerID, voting_power), where

• peerID is the PeerID (public key) of a full node,
• voting_power is an integer (representing the full node's voting power in a certain consensus instance).

In the Golang implementation the data type for validator pair is called Validator

[TMBC-VALIDATOR-SET.1]

A validator set is a set of validator pairs. For a validator set vs, we write TotalVotingPower(vs) for the sum of the voting powers of its validator pairs.

[TMBC-VOTE.1]

A vote contains a prevote or precommit message sent and signed by a validator node during the execution of consensus. Each message contains the following fields

• Type: prevote or precommit
• Height: positive integer
• Round a positive integer
• BlockID a Hashvalue of a block (not necessarily a block of the chain)

[TMBC-COMMIT.1]

A commit is a set of precommit message.

Tendermint Failure Model

[TMBC-AUTH-BYZ.1]

We assume the authenticated Byzantine fault model in which no node (faulty or correct) may break digital signatures, but otherwise, no additional assumption is made about the internal behavior of faulty nodes. That is, faulty nodes are only limited in that they cannot forge messages.

[TMBC-TIME-PARAMS.1]

A Tendermint blockchain has the following configuration parameters:

• unbondingPeriod: a time duration.
• trustingPeriod: a time duration smaller than unbondingPeriod.

[TMBC-CORRECT.1]

We define a predicate correctUntil(n, t), where n is a node and t is a time point. The predicate correctUntil(n, t) is true if and only if the node n follows all the protocols (at least) until time t.

[TMBC-FM-2THIRDS.1]

If a block h is in the chain, then there exists a subset CorrV of h.NextValidators, such that:

• TotalVotingPower(CorrV) > 2/3 TotalVotingPower(h.NextValidators); cf. [TMBC-VALIDATOR-SET.1]
• For every validator pair (n,p) in CorrV, it holds correctUntil(n, h.Time + trustingPeriod); cf. [TMBC-CORRECT.1]

The definition of correct [[TMBC-CORRECT.1]][TMBC-CORRECT-link] refers to realtime, while it is used here with Time and trustingPeriod, which are "hardware times". We do not make a distinction here.

[TMBC-CORR-FULL.1]

Every correct full node locally stores a prefix of the current list of headers from **[TMBC-SEQ.1]**.

What the Light Client Checks

From [TMBC-FM-2THIRDS.1] we directly derive the following observation:

[TMBC-VAL-CONTAINS-CORR.1]

Given a (trusted) block tb of the blockchain, a given set of full nodes N contains a correct node at a real-time t, if

• t - trustingPeriod < tb.Time < t
• the voting power in tb.NextValidators of nodes in N is more than 1/3 of TotalVotingPower(tb.NextValidators)

The following describes how a commit for a given block b must look like.

[TMBC-SOUND-DISTR-POSS-COMMIT.1]

For a block b, each element pc of PossibleCommit(b) satisfies:

• pc contains only votes (cf. [TMBC-VOTE.1]) by validators from b.Validators
• the sum of the voting powers in pc is greater than 2/3 TotalVotingPower(b.Validators)
• and there is an r such that each vote v in pc satisfies
  • v.Type = precommit
  • v.Height = b.Height
  • v.Round = r
  • v.blockID = hash(b)

The following property comes from the validity of the consensus: A correct validator node only sends prevote or precommit, if BlockID of the new (to-be-decided) block is equal to the hash of the last block.

[TMBC-VAL-COMMIT.1]

If for a block b, a commit c

• contains at least one validator pair (v,p) such that v is a correct validator node, and
• is contained in PossibleCommit(b)

then the block b is on the blockchain.

Context of this document

In this document we specify the light client verification component, called Core Verification. The Core Verification communicates with a full node. As full nodes may be faulty, it cannot trust the received information, but the light client has to check whether the header it receives coincides with the one generated by Tendermint consensus.

The two properties [TMBC-VAL-CONTAINS-CORR.1] and [TMBC-VAL-COMMIT] formalize the checks done by this specification: Given a trusted block tb and an untrusted block ub with a commit cub, one has to check that cub is in PossibleCommit(ub), and that cub contains a correct node using tb.

Part II - Sequential Definition of the Verification Problem

Verification Informal Problem statement

Given a height targetHeight as an input, the Verifier eventually stores a header h of height targetHeight locally. This header h is generated by the Tendermint blockchain. In particular, a header that was not generated by the blockchain should never be stored.

Sequential Problem statement

[LCV-SEQ-LIVE.1]

The Verifier gets as input a height targetHeight, and eventually stores the header of height targetHeight of the blockchain.

[LCV-SEQ-SAFE.1]

The Verifier never stores a header which is not in the blockchain.

Part III - Light Client as Distributed System

Incentives

Faulty full nodes may benefit from lying to the light client, by making the light client accept a block that deviates (e.g., contains additional transactions) from the one generated by Tendermint consensus. Users using the light client might be harmed by accepting a forged header.

The fork detector of the light client may help the correct full nodes to understand whether their header is a good one. Hence, in combination with the light client detector, the correct full nodes have the incentive to respond. We can thus base liveness arguments on the assumption that correct full nodes reliably talk to the light client.

Computational Model

[LCV-A-PEER.1]

The verifier communicates with a full node called primary. No assumption is made about the full node (it may be correct or faulty).

[LCV-A-COMM.1]

Communication between the light client and a correct full node is reliable and bounded in time. Reliable communication means that messages are not lost, not duplicated, and eventually delivered. There is a (known) end-to-end delay Delta, such that if a message is sent at time t then it is received and processes by time t + Delta. This implies that we need a timeout of at least 2 Delta for remote procedure calls to ensure that the response of a correct peer arrives before the timeout expires.

[LCV-A-TFM.1]

The Tendermint blockchain satisfies the Tendermint failure model **[TMBC-FM-2THIRDS.1]**.

[LCV-A-VAL.1]

The system satisfies [TMBC-AUTH-BYZ.1]** and [TMBC-FM-2THIRDS.1]**. Thus, there is a blockchain that satisfies the soundness requirements (that is, the validation rules in [block]).

Distributed Problem Statement

Two Kinds of Termination

We do not assume that primary is correct. Under this assumption no protocol can guarantee the combination of the sequential properties. Thus, in the (unreliable) distributed setting, we consider two kinds of termination (successful and failure) and we will specify below under what (favorable) conditions Core Verification ensures to terminate successfully, and satisfy the requirements of the sequential problem statement:

[LCV-DIST-TERM.1]

Core Verification either terminates successfully or it terminates with failure.

Design choices

[LCV-DIST-STORE.1]

Core Verification has a local data structure called LightStore that contains light blocks (that contain a header). For each light block we record whether it is verified.

[LCV-DIST-PRIMARY.1]

Core Verification has a local variable primary that contains the PeerID of a full node.

[LCV-DIST-INIT.1]

LightStore is initialized with a header trustedHeader that was correctly generated by the Tendermint consensus. We say trustedHeader is verified.

Temporal Properties

[LCV-DIST-SAFE.1]

It is always the case that every verified header in LightStore was generated by an instance of Tendermint consensus.

[LCV-DIST-LIVE.1]

From time to time, a new instance of Core Verification is called with a height targetHeight greater than the height of any header in LightStore. Each instance must eventually terminate.

• If
  • the primary is correct (and locally has the block of targetHeight), and
  • LightStore always contains a verified header whose age is less than the trusting period,
    then Core Verification adds a verified header hd with height targetHeight to LightStore and it terminates successfully

These definitions imply that if the primary is faulty, a header may or may not be added to LightStore. In any case, [LCV-DIST-SAFE.1]** must hold. The invariant [LCV-DIST-SAFE.1]** and the liveness requirement **[LCV-DIST-LIVE.1]** allow that verified headers are added to LightStore whose height was not passed to the verifier (e.g., intermediate headers used in bisection; see below). Note that for liveness, initially having a trustedHeader within the trustinPeriod is not sufficient. However, as this specification will leave some freedom with respect to the strategy in which order to download intermediate headers, we do not give a more precise liveness specification here. After giving the specification of the protocol, we will discuss some liveness scenarios below.

Solving the sequential specification

This specification provides a partial solution to the sequential specification. The Verifier solves the invariant of the sequential part

[LCV-DIST-SAFE.1]** => [LCV-SEQ-SAFE.1]**

In the case the primary is correct, and there is a recent header in LightStore, the verifier satisfies the liveness requirements.

⋀ primary is correct
⋀ always ∃ verified header in LightStore. header.Time > now - trustingPeriod
⋀ [LCV-A-Comm.1]** ⋀ ( ( [TMBC-CorrFull.1]** ⋀ [LCV-DIST-LIVE.1]** ) ⟹ [LCV-SEQ-LIVE.1]** )

Part IV - Light Client Verification Protocol

We provide a specification for Light Client Verification. The local code for verification is presented by a sequential function VerifyToTarget to highlight the control flow of this functionality. We note that if a different concurrency model is considered for an implementation, the sequential flow of the function may be implemented with mutexes, etc. However, the light client verification is partitioned into three blocks that can be implemented and tested independently:

• FetchLightBlock is called to download a light block (header) of a given height from a peer.
• ValidAndVerified is a local code that checks the header.
• Schedule decides which height to try to verify next. We keep this underspecified as different implementations (currently in Goland and Rust) may implement different optimizations here. We just provide necessary conditions on how the height may evolve.

Definitions

Data Types

The core data structure of the protocol is the LightBlock.

[LCV-DATA-LIGHTBLOCK.1]

type LightBlock struct {
  Header          Header
  Commit          Commit
  Validators      ValidatorSet
  NextValidators  ValidatorSet
  Provider        PeerID
}

[LCV-DATA-LIGHTSTORE.1]

LightBlocks are stored in a structure which stores all LightBlock from initialization or received from peers.

type LightStore struct {
 ...
}

Each LightBlock is in one of the following states:

type VerifiedState int

const (
 StateUnverified = iota + 1
 StateVerified
 StateFailed
 StateTrusted
)

Only the detector module sets a lightBlock state to StateTrusted and only if it was StateVerified before.

The LightStore exposes the following functions to query stored LightBlocks.

[LCV-FUNC-GET.1]

func (ls LightStore) Get(height Height) (LightBlock, bool)

• Expected postcondition
  • returns a LightBlock at a given height or false in the second argument if the LightStore does not contain the specified LightBlock.

[LCV-FUNC-LATEST-VERIF.1]

func (ls LightStore) LatestVerified() LightBlock

• Expected postcondition
  • returns the highest light block whose state is StateVerified or StateTrusted

[LCV-FUNC-UPDATE.2]

func (ls LightStore) Update(lightBlock LightBlock, 
                            verfiedState VerifiedState
       verifiedBy Height)

• Expected postcondition
  • The state of the LightBlock is set to verifiedState.
  • verifiedBy of the Lightblock is set to Height

The following function is used only in the detector specification listed here for completeness.

[LCV-FUNC-LATEST-TRUSTED.1]

func (ls LightStore) LatestTrusted() LightBlock

• Expected postcondition
  • returns the highest light block that has been verified and checked by the detector.

[LCV-FUNC-FILTER.1]

func (ls LightStore) FilterVerified() LightSTore

• Expected postcondition
  • returns only the LightBlocks with state verified.

Inputs

• lightStore: stores light blocks that have been downloaded and that passed verification. Initially it contains a light block with trustedHeader.
• primary: peerID
• targetHeight: the height of the needed header

Configuration Parameters

• trustThreshold: a float. Can be used if correctness should not be based on more voting power and 1/3.
• *trustingPeriod*: a time duration [TMBC-TIME_PARAMS.1].
• clockDrift: a time duration. Correction parameter dealing with only approximately synchronized clocks.

Variables

• nextHeight: initially targetHeight

  nextHeight should be thought of the "height of the next header we need to download and verify"

Assumptions

[LCV-A-INIT.1]

• trustedHeader is from the blockchain

• targetHeight > LightStore.LatestVerified.Header.Height

Invariants

[LCV-INV-TP.1]

It is always the case that LightStore.LatestTrusted.Header.Time > now - trustingPeriod.

If the invariant is violated, the light client does not have a header it can trust. A trusted header must be obtained externally, its trust can only be based on social consensus.

Used Remote Functions

We use the functions commit and validators that are provided by the RPC client for Tendermint.

func Commit(height int64) (SignedHeader, error)

• Implementation remark
  • RPC to full node n
  • JSON sent:

// POST /commit
{
 "jsonrpc": "2.0",
 "id": "ccc84631-dfdb-4adc-b88c-5291ea3c2cfb", // UUID v4, unique per request
 "method": "commit",
 "params": {
  "height": 1234
 }
}

• Expected precondition
  • header of height exists on blockchain
• Expected postcondition
  • if n is correct: Returns the signed header of height height from the blockchain if communication is timely (no timeout)
  • if n is faulty: Returns a signed header with arbitrary content
• Error condition
  • if n is correct: precondition violated or timeout
  • if n is faulty: arbitrary error

---

func Validators(height int64) (ValidatorSet, error)

• Implementation remark
  • RPC to full node n
  • JSON sent:

// POST /validators
{
 "jsonrpc": "2.0",
 "id": "ccc84631-dfdb-4adc-b88c-5291ea3c2cfb", // UUID v4, unique per request
 "method": "validators",
 "params": {
  "height": 1234
 }
}

• Expected precondition
  • header of height exists on blockchain
• Expected postcondition
  • if n is correct: Returns the validator set of height height from the blockchain if communication is timely (no timeout)
  • if n is faulty: Returns arbitrary validator set
• Error condition
  • if n is correct: precondition violated or timeout
  • if n is faulty: arbitrary error

---

Communicating Function

[LCV-FUNC-FETCH.1]

func FetchLightBlock(peer PeerID, height Height) LightBlock

• Implementation remark
  • RPC to peer at PeerID
  • calls Commit for height and Validators for height and height+1
• Expected precondition
  • height is less than or equal to height of the peer [LCV-IO-PRE-HEIGHT.1]
• Expected postcondition:
  • if node is correct:
    • Returns the LightBlock lb of height height that is consistent with the blockchain
    • lb.provider = peer [LCV-IO-POST-PROVIDER.1]
    • lb.Header is a header consistent with the blockchain
    • lb.Validators is the validator set of the blockchain at height nextHeight
    • lb.NextValidators is the validator set of the blockchain at height nextHeight + 1
  • if node is faulty: Returns a LightBlock with arbitrary content **[TMBC-AUTH-BYZ.1]**
• Error condition
  • if n is correct: precondition violated
  • if n is faulty: arbitrary error
  • if lb.provider != peer
  • times out after 2 Delta (by assumption n is faulty)

---

Core Verification

Outline

The VerifyToTarget is the main function and uses the following functions.

• FetchLightBlock is called to download the next light block. It is the only function that communicates with other nodes
• ValidAndVerified checks whether header is valid and checks if a new lightBlock should be trusted based on a previously verified lightBlock.
• Schedule decides which height to try to verify next

In the following description of VerifyToTarget we do not deal with error handling. If any of the above function returns an error, VerifyToTarget just passes the error on.

[LCV-FUNC-MAIN.1]

func VerifyToTarget(primary PeerID, lightStore LightStore,
                    targetHeight Height) (LightStore, Result) {

    nextHeight := targetHeight

    for lightStore.LatestVerified.height < targetHeight {

        // Get next LightBlock for verification
        current, found := lightStore.Get(nextHeight)
        if !found {
            current = FetchLightBlock(primary, nextHeight)
            lightStore.Update(current, StateUnverified)
        }

        // Verify
        verdict = ValidAndVerified(lightStore.LatestVerified, current)

        // Decide whether/how to continue
        if verdict == SUCCESS {
            lightStore.Update(current, StateVerified)
        }
        else if verdict == NOT_ENOUGH_TRUST {
            // do nothing
   // the light block current passed validation, but the validator
            // set is too different to verify it. We keep the state of
   // current at StateUnverified. For a later iteration, Schedule
   // might decide to try verification of that light block again.
        }
        else {
            // verdict is some error code
            lightStore.Update(current, StateFailed)
            // possibly remove all LightBlocks from primary
            return (lightStore, ResultFailure)
        }
        nextHeight = Schedule(lightStore, nextHeight, targetHeight)
    }
    return (lightStore, ResultSuccess)
}

• Expected precondition
  • lightStore contains a LightBlock within the trustingPeriod [LCV-PRE-TP.1]
  • targetHeight is greater than the height of all the LightBlocks in lightStore
• Expected postcondition:
  • returns lightStore that contains a LightBlock that corresponds to a block of the blockchain of height targetHeight (that is, the LightBlock has been added to lightStore) [LCV-POST-LS.1]
• Error conditions
  • if the precondition is violated
  • if ValidAndVerified or FetchLightBlock report an error
  • if **[LCV-INV-TP.1]** is violated

Details of the Functions

[LCV-FUNC-VALID.1]

func ValidAndVerified(trusted LightBlock, untrusted LightBlock) Result

• Expected precondition:
  • untrusted is valid, that is, satisfies the soundness checks
  • untrusted is well-formed, that is,
    • untrusted.Header.Time < now + clockDrift
    • untrusted.Validators = hash(untrusted.Header.Validators)
    • untrusted.NextValidators = hash(untrusted.Header.NextValidators)
  • trusted.Header.Time > now - trustingPeriod
  • trusted.Commit is a commit for the header trusted.Header, i.e., it contains the correct hash of the header, and +2/3 of signatures
  • the Height and Time of trusted are smaller than the Height and Time of untrusted, respectively
  • the untrusted.Header is well-formed (passes the tests from [block]), and in particular
    • if the untrusted header unstrusted.Header is the immediate successor of trusted.Header, then it holds that
      • trusted.Header.NextValidators = untrusted.Header.Validators, and moreover,
      • untrusted.Header.Commit
        • contains signatures by more than two-thirds of the validators
        • contains no signature from nodes that are not in trusted.Header.NextValidators
• Expected postcondition:
  • Returns SUCCESS:
    • if untrusted is the immediate successor of trusted, or otherwise,
    • if the signatures of a set of validators that have more than max(1/3,trustThreshold) of voting power in trusted.Nextvalidators is contained in untrusted.Commit (that is, header passes the tests [TMBC-VAL-CONTAINS-CORR.1]** and [TMBC-VAL-COMMIT.1]**)
  • Returns NOT_ENOUGH_TRUST if:
    • untrusted is not the immediate successor of trusted and the max(1/3,trustThreshold) threshold is not reached (that is, if **[TMBC-VAL-CONTAINS-CORR.1]** fails and header is does not violate the soundness checks [block]).
• Error condition:
  • if precondition violated

---

[LCV-FUNC-SCHEDULE.1]

func Schedule(lightStore, nextHeight, targetHeight) Height

• Implementation remark: If picks the next height to be verified. We keep the precise choice of the next header under-specified. It is subject to performance optimizations that do not influence the correctness
• Expected postcondition: [LCV-SCHEDULE-POST.1] Return H s.t.
  1. if lightStore.LatestVerified.Height = nextHeight and lightStore.LatestVerified < targetHeight then
     nextHeight < H <= targetHeight
  2. if lightStore.LatestVerified.Height < nextHeight and lightStore.LatestVerified.Height < targetHeight then
     lightStore.LatestVerified.Height < H < nextHeight
  3. if lightStore.LatestVerified.Height = targetHeight then
     H = targetHeight

Case i. captures the case where the light block at height nextHeight has been verified, and we can choose a height closer to the targetHeight. As we get the lightStore as parameter, the choice of the next height can depend on the lightStore, e.g., we can pick a height for which we have already downloaded a light block. In Case ii. the header of nextHeight could not be verified, and we need to pick a smaller height. In Case iii. is a special case when we have verified the targetHeight.

Solving the distributed specification

trustedStore is implemented by the light blocks in lightStore that have the state StateVerified.

Argument for **[LCV-DIST-SAFE.1]**

• ValidAndVerified implements the soundness checks and the checks [TMBC-VAL-CONTAINS-CORR.1]** and [TMBC-VAL-COMMIT.1]** under the assumption **[TMBC-FM-2THIRDS.1]**
• Only if ValidAndVerified returns with SUCCESS, the state of a light block is set to StateVerified.

Argument for **[LCV-DIST-LIVE.1]**

• If primary is correct,
  • FetchLightBlock will always return a light block consistent with the blockchain
  • ValidAndVerified either verifies the header using the trusting period or falls back to sequential verification
  • If **[LCV-INV-TP.1]** holds, eventually every header will be verified and core verification terminates successfully.
  • successful termination depends on the age of lightStore.LatestVerified (for instance, initially on the age of trustedHeader) and the changes of the validator sets on the blockchain. We will give some examples below.
• If primary is faulty,
  • it either provides headers that pass all the tests, and we return with the header
  • it provides one header that fails a test, core verification terminates with failure.
  • it times out and core verification terminates with failure.

Liveness Scenarios

The liveness argument above assumes **[LCV-INV-TP.1]**

which requires that there is a header that does not expire before the target height is reached. Here we discuss scenarios to ensure this.

Let startHeader be LightStore.LatestVerified when core verification is called (trustedHeader) and startTime be the time core verification is invoked.

In order to ensure liveness, LightStore always needs to contain a verified (or initially trusted) header whose time is within the trusting period. To ensure this, core verification needs to add new headers to LightStore and verify them, before all headers in LightStore expire.

Many changes in validator set

Let's consider Schedule implements bisection, that is, it halves the distance. Assume the case where the validator set changes completely in each block. Then the method in this specification needs to sequentially verify all headers. That is, for

• W = log_2 (targetHeight - startHeader.Height),

W headers need to be downloaded and checked before the header of height startHeader.Height + 1 is added to LightStore.

• Let Comp be the local computation time needed to check headers and signatures for one header.

• Then we need in the worst case Comp + 2 Delta to download and check one header.

• Then the first time a verified header could be added to LightStore is startTime + W * (Comp + 2 Delta)

• [TP.1] However, it can only be added if we still have a header in LightStore, which is not expired, that is only the case if

  • startHeader.Time > startTime + WCG * (Comp + 2 Delta) - trustingPeriod,
  • that is, if core verification is started at
    startTime < startHeader.Time + trustingPeriod - WCG * (Comp + 2 Delta)

• one may then do an inductive argument from this point on, depending on the implementation of Schedule. We may have to account for the headers that are already downloaded, but they are checked against the new LightStore.LatestVerified.

We observe that the worst case time it needs to verify the header of height targetHeight depends mainly on how frequent the validator set on the blockchain changes. That core verification terminates successfully crucially depends on the check [TP.1], that is, that the headers in LightStore do not expire in the time needed to download more headers, which depends on the creation time of the headers in LightStore. That is, termination of core verification is highly depending on the data stored in the blockchain. The current light client core verification protocol exploits that, in practice, changes in the validator set are rare. For instance, consider the following scenario.

No change in validator set

If on the blockchain the validator set of the block at height targetHeight is equal to startHeader.NextValidators:

• there is one round trip in FetchLightBlock to download the light block of height targetHeight, and Comp to check it.
• as the validator sets are equal, Verify returns SUCCESS, if startHeader.Time > now - trustingPeriod.
• that is, if startTime < startHeader.Header.Time + trustingPeriod - 2 Delta - Comp, then core verification terminates successfully

Part V - Supporting the IBC Relayer

The above specification focuses on the most common case, which also constitutes the most challenging task: using the Tendermint security model to verify light blocks without downloading all intermediate blocks. To focus on this challenge, above we have restricted ourselves to the case where targetHeight is greater than the height of any trusted header. This simplified presentation of the algorithm as initially lightStore.LatestVerified() is less than targetHeight, and in the process of verification lightStore.LatestVerified() increases until targetHeight is reached.

For IBC it might be that some "older" header is needed, that is, targetHeight < lightStore.LatestVerified(). In this section we present a preliminary design, and we mark some remaining open questions. If targetHeight < lightStore.LatestVerified() our design separates the following cases:

• A previous instance of VerifyToTarget has already downloaded the light block of targetHeight. There are two cases
  • the light block has been verified
  • the light block has not been verified yet
• No light block of targetHeight had been downloaded before. There are two cases:
  • there exists a verified light block of height less than targetHeight
  • otherwise. In this case we need to do "backwards verification" using the hash of the previous block in the LastBlockID field of a header.

Open Question: what are the security assumptions for backward verification. Should we check that the light block we verify from (and/or the checked light block) is within the trusting period?

The design just presents the above case distinction as a function, and defines some auxiliary functions in the same way the protocol was presented in Part IV.

func (ls LightStore) LatestPrevious(height Height) (LightBlock, bool)

• Expected postcondition
  • returns a light block lb that satisfies:
    • lb is in lightStore
    • lb is verified and not expired
    • lb.Header.Height < height
    • for all b in lightStore s.t. b is verified and not expired it holds lb.Header.Height >= b.Header.Height
  • false in the second argument if the LightStore does not contain such an lb.

func (ls LightStore) MinVerified() (LightBlock, bool)

• Expected postcondition
  • returns a light block lb that satisfies:
    • lb is in lightStore
    • lb is verified Open Question: replace by trusted?
    • lb.Header.Height is minimal in the lightStore
    • Open Question: according to this, it might be expired (outside the trusting period). This approach appears safe. Are there reasons we should not do that?
  • false in the second argument if the LightStore does not contain such an lb.

If a height that is smaller than the smallest height in the lightstore is required, we check the hashes backwards. This is done with the following function:

[LCV-FUNC-BACKWARDS.1]

func Backwards (primary PeerID, lightStore LightStore, targetHeight Height)
               (LightStore, Result) {
  
    lb,res = lightStore.MinVerified()
    if res = false {
        return (lightStore, ResultFailure)
    }

    latest := lb.Header
    for i := lb.Header.height - 1; i >= targetHeight; i-- {
        // here we download height-by-height. We might first download all
        // headers down to targetHeight and then check them.
        current := FetchLightBlock(primary,i)
        if (hash(current) != latest.Header.LastBlockId) {
            return (lightStore, ResultFailure)
        }
        else {
            lightStore.Update(current, StateVerified)
            // **Open Question:** Do we need a new state type for
            // backwards verified light blocks?
        }
        latest = current
    }
    return (lightStore, ResultSuccess)
}

The following function just decided based on the required height which method should be used.

[LCV-FUNC-IBCMAIN.1]

func Main (primary PeerID, lightStore LightStore, targetHeight Height)
          (LightStore, Result) {

    b1, r1 = lightStore.Get(targetHeight)
    if r1 = true and b1.State = StateVerified {
        // block already there
        return (lightStore, ResultSuccess)
    }

    if targetHeight > lightStore.LatestVerified.height {
     // case of Part IV
        return VerifyToTarget(primary, lightStore, targetHeight)
    }
    else {
        b2, r2 = lightStore.LatestPrevious(targetHeight);
        if r2 = true {
            // make auxiliary lightStore auxLS to call VerifyToTarget.
   // VerifyToTarget uses LatestVerified of the given lightStore
            // For that we need:
            // auxLS.LatestVerified = lightStore.LatestPrevious(targetHeight)
            auxLS.Init;
            auxLS.Update(b2,StateVerified);
            if r1 = true {
                // we need to verify a previously downloaded light block.
                // we add it to the auxiliary store so that VerifyToTarget
                // does not download it again
                auxLS.Update(b1,b1.State);
            }
            auxLS, res2 = VerifyToTarget(primary, auxLS, targetHeight)
            // move all lightblocks from auxLS to lightStore,
            // maintain state
   // we do that whether VerifyToTarget was successful or not
            for i, s range auxLS {
                lighStore.Update(s,s.State)
            }
            return (lightStore, res2)
        }
        else {
            return Backwards(primary, lightStore, targetHeight)
        }
    }
}

References

[block] Specification of the block data structure.

[RPC] RPC client for Tendermint

[fork-detector] The specification of the light client fork detector.

[fullnode] Specification of the full node API

[ibc-rs] Rust implementation of IBC modules and relayer.

[lightclient] The light client ADR [77d2651 on Dec 27, 2019].