tendermint/spec/light-client/detection/detection_003_reviewed.md

# Light Client Attack Detector

In this specification, we strengthen the light client to be resistant
against so-called light client attacks. In a light client attack, all
the correct Tendermint full nodes agree on the sequence of generated
blocks (no fork), but a set of faulty full nodes attack a light client
by generating (signing) a block that deviates from the block of the
same height on the blockchain. In order to do so, some of these faulty
full nodes must have been validators before and violate the assumption
of more than two thirds of "correct voting power"
[[TMBC-FM-2THIRDS]][TMBC-FM-2THIRDS-link], as otherwise, if
[[TMBC-FM-2THIRDS]][TMBC-FM-2THIRDS-link] would hold,
[verification][verification] would satisfy
[[LCV-SEQ-SAFE.1]][LCV-SEQ-SAFE-link].

An attack detector (or detector for short) is a mechanism that is used
by the light client [supervisor][supervisor] after
[verification][verification] of a new light block
with the primary, to cross-check the newly learned light block with
other peers (secondaries).  It expects as input a light block with some
height *root* (that serves as a root of trust), and a verification
trace (a sequence of lightblocks) that the primary provided.

In case the detector observes a light client attack, it computes
evidence data that can be used by Tendermint full nodes to isolate a
set of faulty full nodes that are still within the unbonding period
(more than 1/3 of the voting power of the validator set at some block
of the chain), and report them via ABCI (application/blockchain
interface)
to the application of a
Tendermint blockchain in order to punish faulty nodes.

## Context of this document

The light client [verification][verification] specification is
designed for the Tendermint failure model (1/3 assumption)
[[TMBC-FM-2THIRDS]][TMBC-FM-2THIRDS-link].  It is safe under this
assumption, and live if it can reliably (that is, no message loss, no
duplication, and eventually delivered) and timely communicate with a
correct full node. If [[TMBC-FM-2THIRDS]][TMBC-FM-2THIRDS-link]
assumption is violated, the light client can be fooled to trust a
light block that was not generated by Tendermint consensus.

This specification, the attack detector, is a "second line of
defense", in case the 1/3 assumption is violated.  Its goal is to
detect a light client attack (conflicting light blocks) and collect
evidence. However, it is impractical to probe all full nodes. At this
time we consider a simple scheme of maintaining an address book of
known full nodes from which a small subset (e.g., 4) are chosen
initially to communicate with. More involved book keeping with
probabilistic guarantees can be considered at later stages of the
project.

The light client maintains a simple address book containing addresses
of full nodes that it can pick as primary and secondaries.  To obtain
a new light block, the light client first does
[verification][verification] with the primary, and then cross-checks
the light block (and the trace of light blocks that led to it) with
the secondaries using this specification.

# Outline

- [Part I](#part-i---Tendermint-Consensus-and-Light-Client-Attacks):
  Formal definitions of lightclient attacks, based on basic
  properties of Tendermint consensus.
    - [Node-based characterization of
       attacks](#Node-based-characterization-of-attacks). The
       definition of attacks used in the problem statement of
    this specification.

    - [Block-based characterization of attacks](#Block-based-characterization-of-attacks). Alternative definitions
  provided for future reference.

- [Part II](#part-ii---problem-statement): Problem statement of
  lightclient attack detection
  
    - [Informal Problem Statement](#informal-problem-statement)
    - [Assumptions](#Assumptions)
    - [Definitions](#definitions)
    - [Distributed Problem statement](#Distributed-Problem-statement)
  
- [Part III](#part-iii---protocol): The protocol

    - [Functions and Data defined in other Specifications](#Functions-and-Data-defined-in-other-Specifications)
    - [Outline of Solution](#Outline-of-solution)
    - [Details of the functions](#Details-of-the-functions)
    - [Correctness arguments](#Correctness-arguments)

# Part I - Tendermint Consensus and Light Client Attacks

In this section we will give some mathematical definitions of what we
mean by light client attacks (that are considered in this
specification) and how they differ from main-chain forks. To this end,
we start by defining some properties of the sequence of blocks that is
decided upon by Tendermint consensus in normal operation (if the
Tendermint failure model holds
[[TMBC-FM-2THIRDS]][TMBC-FM-2THIRDS-link]),
and then define different
deviations that correspond to attack scenarios. We consider the notion
of [light blocks][LCV-LB-link] and [headers][LVC-HD-link].

#### **[TMBC-GENESIS.1]**

Let *Genesis* be the agreed-upon initial block (file).

#### **[TMBC-FUNC-SIGN.1]**

Let *b* and *c* be two light blocks with *b.Header.Height + 1 =
c.Header.Height*. We define the predicate **signs(b,c)** to hold
iff *c.Header.LastCommit* is in *PossibleCommit(b)*.
[[TMBC-SOUND-DISTR-POSS-COMMIT.1]][TMBC-SOUND-DISTR-POSS-COMMIT-link].

> The above encodes sequential verification, that is, intuitively,
> b.Header.NextValidators = c.Header.Validators and 2/3 of
> these Validators signed c.

#### **[TMBC-FUNC-SUPPORT.1]**

Let *b* and *c* be two light blocks. We define the predicate
**supports(b,c,t)** to hold iff

- *t - trustingPeriod < b.Header.Time < t*
- the voting power in *b.NextValidators* of nodes in *c.Commit*
  is more than 1/3 of *TotalVotingPower(b.Header.NextValidators)*

> That is, if the [Tendermint failure model][TMBC-FM-2THIRDS-link]
> holds, then *c* has been signed by at least one correct full node, cf.
> [[TMBC-VAL-CONTAINS-CORR.1]][TMBC-VAL-CONTAINS-CORR-link].
> The following formalizes that *b* was properly generated by
> Tendermint; *b* can be traced back to genesis.

#### **[TMBC-SEQ-ROOTED.1]**

Let *b* be a light block.
We define *sequ-rooted(b)* iff for all *i*, *1 <= i < h = b.Header.Height*,
there exist light blocks *a(i)* s.t.

- *a(1) = Genesis* and
- *a(h) = b* and
- *signs( a(i) , a(i+1) )*.

> The following formalizes that *c* is trusted based on *b* in
> skipping verification. Observe that we do not require here (yet)
> that *b* was properly generated.

#### **[TMBC-SKIP-TRACE.1]**

Let *b* and *c* be light blocks. We define *skip-trace(b,c,t)* if at
time t there exists an integer *h* and a sequence *a(1)*, ... *a(h)* s.t.

- *a(1) = b* and
- *a(h) = c* and
- *supports( a(i), a(i+1), t)*, for all i, *1 <= i < h*.

We call such a sequence *a(1)*, ... *a(h)* a **verification trace**.

> The following formalizes that two light blocks of the same height
> should agree on the content of the header. Observe that *b* and *c*
> may disagree on the Commit. This is a special case if the canonical
> commit has not been decided on yet, that is, if b.Header.Height is the
> maximum height of all blocks decided upon by Tendermint at this
> moment.

#### **[TMBC-SIGN-SKIP-MATCH.1]**

Let *a*, *b*, *c*, be light blocks and *t* a time, we define
*sign-skip-match(a,b,c,t) = true* iff the following implication
evaluates to true:

- *sequ-rooted(a)* and
- *b.Header.Height = c.Header.Height* and
- *skip-trace(a,b,t)*
- *skip-trace(a,c,t)*

implies *b.Header = c.Header*.

> Observe that *sign-skip-match* is defined via an implication. If it
> evaluates to false this means that the left-hand-side of the
> implication evaluates to true, and the right-hand-side evaluates to
> false. In particular, there are two **different** headers *b* and
> *c* that both can be verified from a common block *a* from the
> chain. Thus, the following describes an attack.

#### **[TMBC-ATTACK.1]**

If there exists three light blocks a, b, and c, with
*sign-skip-match(a,b,c,t) = false* then we have an *attack*.  We say
we have **an attack at height** *b.Header.Height* and write
*attack(a,b,c,t)*.

> The lightblock *a* need not be unique, that is, there may be
> several blocks that satisfy the above requirement for the same
> blocks *b* and *c*.

[[TMBC-ATTACK.1]](#TMBC-ATTACK1) is a formalization of the violation
of the agreement property based on the result of consensus, that is,
the generated blocks.

**Remark.**
Violation of agreement is only possible if more than 1/3 of the validators (or
next validators) of some previous block deviated from the protocol. The
upcoming "accountability" specification will describe how to compute
a set of at least 1/3 faulty nodes from two conflicting blocks. []

There are different ways to characterize forks
and attack scenarios. This specification uses the "node-based
characterization of attacks" which focuses on what kinds of nodes are
affected (light nodes vs. full nodes). For future reference and
discussion we also provide a
"block-based characterization of attacks" below.

## Node-based characterization of attacks

#### **[TMBC-MC-FORK.1]**

We say there is a (main chain) fork at time *t* if

- there are two correct full nodes *i* and *j* and
- *i* is different from *j* and
- *i* has decided on *b* and
- *j* has decided on *c* and
- there exist *a* such that *attack(a,b,c,t)*.

#### **[TMBC-LC-ATTACK.1]**

We say there is a light client attack at time *t*, if

- there is **no** (main chain) fork [[TMBC-MC-FORK.1]](#TMBC-MC-FORK1), and
- there exist nodes that have computed light blocks *b* and *c* and
- there exist *a* such that *attack(a,b,c,t)*.

We say the attack is at height *a.Header.Height*.

> In this specification we consider detection of light client
> attacks. Intuitively, the case we consider is that
> light block *b* is the one from the
> blockchain, and some attacker has computed *c* and tries to wrongly
> convince
> the light client that *c* is the block from the chain.

#### **[TMBC-LC-ATTACK-EVIDENCE.1]**

We consider the following case of a light client attack
[[TMBC-LC-ATTACK.1]](#TMBC-LC-ATTACK1):

- *attack(a,b,c,t)*
- there is a peer p1 that has a sequence *chain* of blocks from *a* to *b*
- *skip-trace(a,c,t)*: by [[TMBC-SKIP-TRACE.1]](#TMBC-SKIP-TRACE1) there is a
  verification trace *v* of the form *a = v(1)*, ... *v(h) = c*

Evidence for p1 (that proves an attack to p1) consists for index i
of v(i) and v(i+1) such that

- E1(i). v(i) is equal to the block of *chain* at height v(i).Height, and
- E2(i). v(i+1) that is different from  the block of *chain* at
  height v(i+1).height

> Observe p1 can
>
> - check that v(i+1)  differs from its block at that height, and
> - verify v(i+1) in one step from v(i) as v is a verification trace.

#### **[TMBC-LC-EVIDENCE-DATA.1]**

To prove the attack to p1, because of Point E1, it is sufficient to
submit

- v(i).Height (rather than v(i)).
- v(i+1)

This information is *evidence for height v(i).Height*.

## Block-based characterization of attacks

In this section we provide a different characterization of attacks. It
is not defined on the nodes that are affected but purely on the
content of the blocks. In that sense these definitions are less
operational.

> They might be relevant for a closer analysis of fork scenarios on the
> chain, which is out of the scope of this specification.
  
#### **[TMBC-SIGN-UNIQUE.1]**

Let *b* and *c* be  light blocks, we define the predicate
*sign-unique(b,c)* to evaluate to true iff the following implication
evaluates to true:

- *b.Header.Height =  c.Header.Height* and
- *sequ-rooted(b)* and
- *sequ-rooted(c)*

implies *b = c*.

#### **[TMBC-BLOCKS-MCFORK.1]**

If there exists two light blocks b and c, with *sign-unique(b,c) =
false* then we have a *fork*.

> The difference of the above definition to
> [[TMBC-MC-FORK.1]](#TMBC-MC-FORK1) is subtle. The latter requires a
> full node being affected by a bad block while
> [[TMBC-BLOCKS-MCFORK.1]](#TMBC-BLOCKS-MCFORK1) just requires that a
> bad block exists, possibly in memory of an attacker.
> The following captures a light client fork. There is no fork up to
> the height of block b. However, c is of that height, is different,
> and passes skipping verification. It is a stricter property than
> [[TMBC-LC-ATTACK.1]](#TMBC-LC-ATTACK1), as
> [[TMBC-LC-ATTACK.1]](#TMBC-LC-ATTACK1) requires that no correct full
> node is affected.

#### **[TMBC-BLOCKS-LCFORK.1]**

Let *a*, *b*, *c*, be light blocks and *t* a time. We define
*light-client-fork(a,b,c,t)* iff

- *sign-skip-match(a,b,c,t) = false* and
- *sequ-rooted(b)* and
- *b* is "unique", that is, for all *d*,  *sequ-rooted(d)* and
     *d.Header.Height = b.Header.Height* implies *d = b*

> Finally, let us also define bogus blocks that have no support.
> Observe that bogus is even defined if there is a fork.
> Also, for the definition it would be sufficient to restrict *a* to
> *a.height < b.height* (which is implied by the definitions which
> unfold until *supports()*).

#### **[TMBC-BOGUS.1]**

Let *b* be a light block and *t* a time. We define *bogus(b,t)* iff

- *sequ-rooted(b) = false* and
- for all *a*, *sequ-rooted(a)* implies *skip-trace(a,b,t) = false*
  
# Part II - Problem Statement
  
## Informal Problem statement

There is no sequential specification: the detector only makes sense
in a distributed systems where some nodes misbehave.

We work under the assumption that full nodes and validators are
responsible for detecting attacks on the main chain, and the evidence
reactor takes care of broadcasting evidence to communicate
misbehaving nodes via ABCI to the application, and halt the chain in
case of a fork. The point of this specification is to shield a light
clients against attacks that cannot be detected by full nodes, and
are fully addressed at light clients (and consequently IBC relayers,
which use the light client protocols to observe the state of a
blockchain). In order to provide full nodes the incentive to follow
the protocols when communicating with the light client, this
specification also considers the generation of evidence that will
also be processed by the Tendermint blockchain.

#### **[LCD-IP-MODEL.1]**

The detector is designed under the assumption that

- [[TMBC-FM-2THIRDS]][TMBC-FM-2THIRDS-link] may be violated
- there is no fork on the main chain.

> As a result some faulty full nodes may launch an attack on a light
> client.

The following requirements are operational in that they describe how
things should be done, rather than what should be done. However, they
do not constitute temporal logic verification conditions. For those,
see [LCD-DIST-*] below.

The detector is called in the [supervisor][supervisor] as follows

```go
Evidences := AttackDetector(root_of_trust, verifiedLS);`
```

where

- `root-of-trust` is a light block that is trusted (that is,
except upon initialization, the primary and the secondaries
agreed on in the past), and
- `verifiedLS` is a lightstore that contains a verification trace that
  starts from a lightblock that can be verified with the
  `root-of-trust` in one step and ends with a lightblock of the height
  requested by the user
- `Evidences` is a list of evidences for misbehavior

#### **[LCD-IP-STATEMENT.1]**

Whenever AttackDetector is called, the detector should for each
secondary cross check the largest header in verifiedLS with the
corresponding header of the same height provided by the secondary. If
there is a deviation, the detector should
try to replay the verification trace `verifiedLS` with the
secondary
  
- in case replaying leads to detection of a light client attack
  (one of the lightblocks differ from the one in verifiedLS with
  the same height), we should return evidence
- if the secondary cannot provide a verification trace, we have no
  proof for an attack. Block *b* may be bogus. In this case the
  secondary is faulty and it should be replaced.

## Assumptions

It is not in the interest of faulty full nodes to talk to the
detector as long as the  detector is connected to at least one
correct full node. This would only increase the likelihood of
misbehavior being detected. Also we cannot punish them easily
(cheaply). The absence of a response need not be the fault of the full
node.

Correct full nodes have the incentive to respond, because the
detector may help them to understand whether their header is a good
one. We can thus base liveness arguments of the  detector on
the assumptions that correct full nodes reliably talk to the
detector.

#### **[LCD-A-CorrFull.1]**

At all times there is at least one correct full
node among the primary and the secondaries.

> For this version of the detection we take this assumption. It
> allows us to establish the invariant that the lightblock
> `root-of-trust` is always the one from the blockchain, and we can
> use it as starting point for the evidence computation. Moreover, it
> allows us to establish the invariant at the supervisor that any
> lightblock in the (top-level) lightstore is from the blockchain.  
> In the future we might design a lightclient based on the assumption
> that at least in regular intervals the lightclient is connected to a
> correct full node. This will require the detector to reconsider
> `root-of-trust`, and remove lightblocks from the top-level
> lightstore.

#### **[LCD-A-RelComm.1]**

Communication between the  detector 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 processed 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.

## Definitions

### Evidence

Following the definition of
[[TMBC-LC-ATTACK-EVIDENCE.1]](#TMBC-LC-ATTACK-EVIDENCE1), by evidence
we refer to a variable of the following type

#### **[LC-DATA-EVIDENCE.1]**

```go
type LightClientAttackEvidence struct {
    ConflictingBlock   LightBlock
    CommonHeight       int64
}
```

As the above data is computed for a specific peer, the following
data structure wraps the evidence and adds the peerID.

#### **[LC-DATA-EVIDENCE-INT.1]**

```go
type InternalEvidence struct {
    Evidence           LightClientAttackEvidence
    Peer               PeerID
}
```

#### **[LC-SUMBIT-EVIDENCE.1]**

```go
func submitEvidence(Evidences []InternalEvidence)
```

- Expected postcondition
    - for each `ev` in `Evidences`: submit `ev.Evidence` to `ev.Peer`

---

### LightStore

Lightblocks and LightStores are defined in the verification
specification [[LCV-DATA-LIGHTBLOCK.1]][LCV-LB-link]
and [[LCV-DATA-LIGHTSTORE.2]][LCV-LS-link]. See
the [verification specification][verification] for details.

## Distributed Problem statement

> As the attack detector is there to reduce the impact of faulty
> nodes, and faulty nodes imply that there is a distributed system,
> there is no sequential specification to which this distributed
> problem statement may refer to.

The detector gets as input a trusted lightblock called *root* and an
auxiliary lightstore called *primary_trace* with lightblocks that have
been verified before, and that were provided by the primary.

#### **[LCD-DIST-INV-ATTACK.1]**

If the detector returns evidence for height *h*
[[TMBC-LC-EVIDENCE-DATA.1]](#TMBC-LC-EVIDENCE-DATA1), then there is an
attack at height *h*. [[TMBC-LC-ATTACK.1]](#TMBC-LC-ATTACK1)

#### **[LCD-DIST-INV-STORE.1]**

If the detector does not return evidence, then *primary_trace*
contains only blocks from the blockchain.

#### **[LCD-DIST-LIVE.1]**

The detector eventually terminates.

#### **[LCD-DIST-TERM-NORMAL.1]**

If

- the *primary_trace* contains only blocks from the blockchain, and
- there is no attack, and
- *Secondaries* is always non-empty, and
- the age of *root* is always less than the trusting period,

then the detector does not return evidence.

#### **[LCD-DIST-TERM-ATTACK.1]**

If

- there is an attack, and
- a secondary reports a block that conflicts
  with one of the blocks in *primary_trace*, and
- *Secondaries* is always non-empty, and
- the age of *root* is always less than the trusting period,

then the detector returns evidence.

> Observe that above we require that "a secondary reports a block that
> conflicts". If there is an attack, but no secondary tries to launch
> it against the detector (or the message from the secondary is lost
> by the network), then there is nothing to detect for us.

#### **[LCD-DIST-SAFE-SECONDARY.1]**

No correct secondary is ever replaced.

#### **[LCD-DIST-SAFE-BOGUS.1]**

If

- a secondary reports a bogus lightblock,
- the age of *root* is always less than the trusting period,

then the secondary is replaced before the detector terminates.

> The above property is quite operational (e.g., the usage of
> "reports"), but it captures closely the requirement. As the
> detector only makes sense in a distributed setting, and does not
> have a sequential specification, a less "pure" specification are
> acceptable.

# Part III - Protocol

## Functions and Data defined in other Specifications

### From the [supervisor][supervisor]

[[LC-FUNC-REPLACE-SECONDARY.1]][repl]

```go
Replace_Secondary(addr Address, root-of-trust LightBlock)
```

### From the [verifier][verification]

[[LCV-FUNC-MAIN.2]][vtt]

```go
func VerifyToTarget(primary PeerID, root LightBlock,
                    targetHeight Height) (LightStore, Result)
```

Observe that `VerifyToTarget` does communication with the secondaries
via the function [FetchLightBlock][fetch].

### Shared data of the light client

- a pool of full nodes *FullNodes* that have not been contacted before
- peer set called *Secondaries*
- primary

> Note that the lightStore is not needed to be shared.

## Outline of solution

The problem laid out is solved by calling the function `AttackDetector`
with a lightstore that contains a light block that has just been
verified by the verifier.

Then `AttackDetector` downloads headers from the secondaries. In case
a conflicting header is downloaded from a secondary, it calls
`CreateEvidenceForPeer` which computes evidence in the case that
indeed an attack is confirmed. It could be that the secondary reports
a bogus block, which means that there need not be an attack, and the
secondary is replaced.
  
## Details of the functions

#### **[LCD-FUNC-DETECTOR.2]:**

```go
func AttackDetector(root LightBlock, primary_trace []LightBlock)
                   ([]InternalEvidence) {

    Evidences := new []InternalEvidence;

    for each secondary in Secondaries {
        lb, result := FetchLightBlock(secondary,primary_trace.Latest().Header.Height);
        if result != ResultSuccess {
            Replace_Secondary(root);
        }
        else if lb.Header != primary_trace.Latest().Header {
  
            // we replay the primary trace with the secondary, in
            // order to generate evidence that we can submit to the
            // secondary. We return the evidence + the trace the
            // secondary told us that spans the evidence at its local store

            EvidenceForSecondary, newroot, secondary_trace, result :=
                    CreateEvidenceForPeer(secondary,
                                          root,
                                          primary_trace);
            if result == FaultyPeer {
                Replace_Secondary(root);
            }
            else if result == FoundEvidence {
                // the conflict is not bogus
                Evidences.Add(EvidenceForSecondary);
                // we replay the secondary trace with the primary, ...
                EvidenceForPrimary, _, result :=
                        CreateEvidenceForPeer(primary,
                                              newroot,
                                              secondary_trace);
                if result == FoundEvidence {
                    Evidences.Add(EvidenceForPrimary);
                }
                // At this point we do not care about the other error
                // codes. We already have generated evidence for an
                // attack and need to stop the lightclient. It does not
                // help to call replace_primary. Also we will use the
                // same primary to check with other secondaries in
                // later iterations of the loop
            }
            // In the case where the secondary reports NoEvidence
            // after initially it reported a conflicting header.
            // secondary is faulty
            Replace_Secondary(root);
        }
    }
    return Evidences;
}
```

- Expected precondition
    - root and primary trace are a verification trace
- Expected postcondition
    - solves the problem statement (if attack found, then evidence is reported)
- Error condition
    - `ErrorTrustExpired`: fails if root expires (outside trusting
    period) [[LCV-INV-TP.1]][LCV-INV-TP1-link]
    - `ErrorNoPeers`: if no peers are left to replace secondaries, and
    no evidence was found before that happened

---

```go
func CreateEvidenceForPeer(peer PeerID, root LightBlock, trace LightStore)
                          (Evidence, LightBlock, LightStore, result) {

    common := root;

    for i in 1 .. len(trace) {
        auxLS, result := VerifyToTarget(peer, common, trace[i].Header.Height)
  
        if result != ResultSuccess {
            // something went wrong; peer did not provide a verifiable block
            return (nil, nil, nil, FaultyPeer)
        }
        else {
            if auxLS.LatestVerified().Header != trace[i].Header {
                // the header reported by the peer differs from the
                // reference header in trace but both could be
                // verified from common in one step.
                // we can create evidence for submission to the secondary
                ev := new InternalEvidence;
                ev.Evidence.ConflictingBlock := trace[i];
                ev.Evidence.CommonHeight := common.Height;
                ev.Peer := peer
                return (ev, common, auxLS, FoundEvidence)
            }
            else {
                // the peer agrees with the trace, we move common forward.
                // we could delete auxLS as it will be overwritten in
                // the next iteration
                common := trace[i]
            }
        }
    }
    return (nil, nil, nil, NoEvidence)
}
```

- Expected precondition
    - root and trace are a verification trace
- Expected postcondition
    - finds evidence where trace and peer diverge
- Error condition
    - `ErrorTrustExpired`: fails if root expires (outside trusting
       period) [[LCV-INV-TP.1]][LCV-INV-TP1-link]
    - If `VerifyToTarget` returns error but root is not expired then return
 `FaultyPeer`

---

## Correctness arguments

#### On the existence of evidence

**Proposition.** In the case of attack,
evidence [[TMBC-LC-ATTACK-EVIDENCE.1]](#TMBC-LC-ATTACK-EVIDENCE1)
 exists.  
*Proof.* First observe that

- (A). (NOT E2(i)) implies E1(i+1)

Now by contradiction assume there is no evidence. Thus

- for all i, we have NOT E1(i) or NOT E2(i)
- for i = 1 we have E1(1) and thus NOT E2(1)
  thus by induction on i, by (A) we have for all i that **E1(i)**
- from attack we have E2(h-1), and as there is no evidence for
  i = h - 1 we get **NOT E1(h-1)**. Contradiction.
QED.

#### Argument for [[LCD-DIST-INV-ATTACK.1]](#LCD-DIST-INV-ATTACK1)

Under the assumption that root and trace are a verification trace,
when in `CreateEvidenceForPeer` the detector creates
evidence, then the lightclient has seen two different headers (one via
`trace` and one via `VerifyToTarget`) for the same height that can both
be verified in one step.

#### Argument for [[LCD-DIST-INV-STORE.1]](#LCD-DIST-INV-STORE1)

We assume that there is at least one correct peer, and there is no
fork. As a result, the correct peer has the correct sequence of
blocks. Since the primary_trace is checked block-by-block also against
each secondary, and at no point evidence was generated that means at
no point there were conflicting blocks.

#### Argument for [[LCD-DIST-LIVE.1]](#LCD-DIST-LIVE1)

At the latest when [[LCV-INV-TP.1]][LCV-INV-TP1-link] is violated,
`AttackDetector` terminates.

#### Argument for [[LCD-DIST-TERM-NORMAL.1]](#LCD-DIST-TERM-NORMAL1)

As there are finitely many peers, eventually the main loop
terminates. As there is no attack no evidence can be generated.

#### Argument for [[LCD-DIST-TERM-ATTACK.1]](#LCD-DIST-TERM-ATTACK1)

Argument similar to  [[LCD-DIST-TERM-NORMAL.1]](#LCD-DIST-TERM-NORMAL1)

#### Argument for [[LCD-DIST-SAFE-SECONDARY.1]](#LCD-DIST-SAFE-SECONDARY1)

Secondaries are only replaced if they time-out or if they report bogus
blocks. The former is ruled out by the timing assumption, the latter
by correct peers only reporting blocks from the chain.

#### Argument for [[LCD-DIST-SAFE-BOGUS.1]](#LCD-DIST-SAFE-BOGUS1)

Once a bogus block is recognized as such the secondary is removed.

# References

> links to other specifications/ADRs this document refers to

[[verification]] The specification of the light client verification.

[[supervisor]] The specification of the light client supervisor.

[verification]: https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md

[supervisor]: https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/supervisor/supervisor_001_draft.md

[block]: https://github.com/tendermint/spec/blob/d46cd7f573a2c6a2399fcab2cde981330aa63f37/spec/core/data_structures.md

[TMBC-FM-2THIRDS-link]: https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#tmbc-fm-2thirds1

[TMBC-SOUND-DISTR-POSS-COMMIT-link]: https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#tmbc-sound-distr-poss-commit1

[LCV-SEQ-SAFE-link]:https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#lcv-seq-safe1

[TMBC-VAL-CONTAINS-CORR-link]:
https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#tmbc-val-contains-corr1

[fetch]:
https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#lcv-func-fetch1

[LCV-INV-TP1-link]:
https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#lcv-inv-tp1

[LCV-LB-link]:
https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#lcv-data-lightblock1

[LCV-LS-link]:
https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#lcv-data-lightstore2

[LVC-HD-link]:
https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#tmbc-header-fields2

[repl]:
https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/supervisor/supervisor_001_draft.md#lc-func-replace-secondary1

[vtt]:
https://github.com/tendermint/spec/blob/master/rust-spec/lightclient/verification/verification_002_draft.md#lcv-func-main2