# Light Client Verification The light client implements a read operation of a [header][TMBC-HEADER-link] from the [blockchain][TMBC-SEQ-link], 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][TMBC-FM-2THIRDS-link]: starting at time *Time* of the [header][TMBC-HEADER-link], 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][TMBC-FM-2THIRDS-link]. # 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](https://github.com/informalsystems/tendermint-rs/pull/479) we established the need for an update in the data structures in [Issue 499](https://github.com/informalsystems/tendermint-rs/issues/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](#part-i---tendermint-blockchain): Introduction of relevant terms of the Tendermint blockchain. - [Part II](#part-ii---sequential-definition-of-the-verification-problem): Introduction of the problem addressed by the Lightclient Verification protocol. - [Verification Informal Problem statement](#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](#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](#part-iii---light-client-as-distributed-system): Distributed aspects of the light client, system assumptions and temporal logic specifications. - [Incentives](#incentives): how faulty full nodes may benefit from misbehaving and how correct full nodes benefit from cooperating. - [Computational Model](#Computational-Model): timing and correctness assumptions. - [Distributed Problem Statement](#Distributed-Problem-Statement): temporal properties that formalize safety and liveness properties in the distributed setting. - [Part IV](#part-iv---light-client-verification-protocol): Specification of the protocols. - [Definitions](#Definitions): Describes inputs, outputs, variables used by the protocol, auxiliary functions - [Core Verification](#core-verification): gives an outline of the solution, and details of the functions used (with preconditions, postconditions, error conditions). - [Liveness Scenarios](#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](#part-v---supporting-the-ibc-relayer): 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][block]). 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][arXiv]. 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]**][TMBC-SEQ-link]. ## 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][arXiv]: 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]][TMBC-VAL-CONTAINS-CORR-link] and [[TMBC-VAL-COMMIT]][TMBC-VAL-COMMIT-link] 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][block]. 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][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]**][TMBC-FM-2THIRDS-link]. #### **[LCV-A-VAL.1]** The system satisfies [**[TMBC-AUTH-BYZ.1]**][TMBC-Auth-Byz-link] and [**[TMBC-FM-2THIRDS.1]**][TMBC-FM-2THIRDS-link]. 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]**](#lcv-vc-inv) must hold. > The invariant [**[LCV-DIST-SAFE.1]**](#lcv-dist-safe) and the liveness > requirement [**[LCV-DIST-LIVE.1]**](#lcv-dist-life) > 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](#liveness-scenarios). ### 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-vc-inv) => [**[LCV-SEQ-SAFE.1]**](#lcv-seq-inv) 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]**](#lcv-a-comm) ⋀ ( ( [**[TMBC-CorrFull.1]**][TMBC-CorrFull-link] ⋀ [**[LCV-DIST-LIVE.1]**](#lcv-vc-live) ) ⟹ [**[LCV-SEQ-LIVE.1]**](#lcv-seq-live) ) # 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]** ```go 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. ```go type LightStore struct { ... } ``` Each LightBlock is in one of the following states: ```go 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. ```go 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. ```go func (ls LightStore) LatestVerified() LightBlock ``` - Expected postcondition - returns the highest light block whose state is `StateVerified` or `StateTrusted` #### **[LCV-FUNC-UPDATE.1]** ```go func (ls LightStore) Update(lightBlock LightBlock, verfiedState VerifiedState) ``` - Expected postcondition - The state of the LightBlock is set to *verifiedState*. > The following function is used only in the detector specification > listed here for completeness. ```go func (ls LightStore) LatestTrusted() LightBlock ``` - Expected postcondition - returns the highest light block that has been verified and checked by the detector. ### 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]**][TMBC-TIME_PARAMS-link]. - *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][RPC]. ```go func Commit(height int64) (SignedHeader, error) ``` - Implementation remark - RPC to full node *n* - JSON sent: ```javascript // 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 ---- ```go func Validators(height int64) (ValidatorSet, error) ``` - Implementation remark - RPC to full node *n* - JSON sent: ```javascript // 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]** ```go 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]**][TMBC-Auth-Byz-link] - 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]** ```go 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 == OK { lightStore.Update(current, StateVerified) } else if verdict == CANNOT_VERIFY { // 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]**](#LCV-INV-TP.1) is violated ### Details of the Functions #### **[LCV-FUNC-VALID.1]** ```go func ValidAndVerified(trusted LightBlock, untrusted LightBlock) Result ``` - Expected precondition: - *untrusted* is valid, that is, satisfies the soundness [checks][block] - *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 `OK`: - 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]**][TMBC-VAL-CONTAINS-CORR-link] and [**[TMBC-VAL-COMMIT.1]**][TMBC-VAL-COMMIT-link]) - Returns `CANNOT_VERIFY` 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]**][TMBC-VAL-CONTAINS-CORR-link] fails and header is does not violate the soundness checks [[block]]). - Error condition: - if precondition violated ---- #### **[LCV-FUNC-SCHEDULE.1]** ```go 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]**](#lcv-dist-safe) - `ValidAndVerified` implements the soundness checks and the checks [**[TMBC-VAL-CONTAINS-CORR.1]**][TMBC-VAL-CONTAINS-CORR-link] and [**[TMBC-VAL-COMMIT.1]**][TMBC-VAL-COMMIT-link] under the assumption [**[TMBC-FM-2THIRDS.1]**][TMBC-FM-2THIRDS-link] - Only if `ValidAndVerified` returns with `OK`, the state of a light block is set to *StateVerified*. #### Argument for [**[LCV-DIST-LIVE.1]**](#lcv-dist-life) - 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]**](#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](#liveness-scenarios). - 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]**](#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 `OK`, 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][TMBC-FM-2THIRDS-link] 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][ibc-rs] 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](#part-iv---light-client-verification-protocol). ```go 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*. ```go 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]** ```go 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]** ```go 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]. [RPC]: https://docs.tendermint.com/master/rpc/ [block]: https://github.com/tendermint/spec/blob/d46cd7f573a2c6a2399fcab2cde981330aa63f37/spec/core/data_structures.md [TMBC-HEADER-link]: #tmbc-header1 [TMBC-SEQ-link]: #tmbc-seq1 [TMBC-CorrFull-link]: #tmbc-corr-full1 [TMBC-Auth-Byz-link]: #tmbc-auth-byz1 [TMBC-TIME_PARAMS-link]: #tmbc-time-params1 [TMBC-FM-2THIRDS-link]: #tmbc-fm-2thirds1 [TMBC-VAL-CONTAINS-CORR-link]: #tmbc-val-contains-corr1 [TMBC-VAL-COMMIT-link]: #tmbc-val-commit1 [TMBC-SOUND-DISTR-POSS-COMMIT-link]: #tmbc-sound-distr-poss-commit1 [lightclient]: https://github.com/interchainio/tendermint-rs/blob/e2cb9aca0b95430fca2eac154edddc9588038982/docs/architecture/adr-002-lite-client.md [fork-detector]: https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/detection/detection_001_reviewed.md [ibc-rs]:https://github.com/informalsystems/ibc-rs [blockchain-validator-set]: https://github.com/tendermint/spec/blob/master/spec/blockchain/blockchain.md#data-structures [fullnode-data-structures]: https://github.com/tendermint/spec/blob/master/spec/core/data_structures.md [arXiv]: https://arxiv.org/abs/1807.04938