This demo application shows how verifiable computations might be processed by a distributed cluster of nodes. It comes with a set of hardcoded operations that can be invoked by the client. Each requested operation is computed by every (ignoring failures or Byzantine cases) cluster node, and if any node disagrees with the computation outcome it can submit a dispute to an external Judge.

Results of each computation are stored on the cluster nodes and can be later on retrieved by the client. The storage of the results is secured with Merkle proofs, so malicious nodes can't substitute them with bogus data.

Because every computation is verified by the cluster nodes and computation outcomes are verified using Merkle proofs, the client normally doesn't have to interact with the entire cluster. Moreover, the client can interact with as little as a single node – this won't change safety properties. However, liveness might be compromised – for example, if the node the client is interacting with is silently dropping incoming requests.

Motivation
Overview
Installation and run
Sending queries
Implementation details
Incorrect behavior of the cluster nodes

Motivation

The application is a proof-of-concept of a decentralized system with the following properties:

Support of arbitrary deterministic operations: simple reads or writes as well as complex computations.
Total safety of operations when more than 2/3 of the cluster is non-Byzantine.
Ability to notice and dispute an incorrect behavior when there is at least one non-Byzantine node.
High availability: tolerance to simultaneous failures or Byzantine actions of some subset of nodes.
High throughput (up to 1000 transactions per second) and low latency (~1-2 seconds) of operations.
Reasonable blockchain finality time (few seconds).

Overview

There are following actors in the application network:

Cluster nodes which carry certain state and can run computations over it following requests sent by the client. All nodes normally have an identical state – the only exception is when some node is faulty, acting maliciously or has network issues. Computations can be effectful – which means they can change the state.

When the cluster has reached consensus on the computation outcome, the new state can be queried by the client – any up-to-date node can serve it. Consensus requires a 2/3 majority of the nodes to agree to avoid Byzantine nodes sneaking in incorrect results.
The client which can issue simple requests like put or get to update the cluster state as well as run complex computations. In this demo application an available computations set is limited to operations like sum or factorial but in principle can be extended by a developer.

The client is able to check whether the cluster has reached consensus over computation outcomes by checking cluster nodes signatures and validate responses to the queries using Merkle proofs. This means that unless the cluster is taken over by Byzantine nodes the client can be certain about results provided and in general about the cluster state.
The Judge which is in charge of resolving disputes over computations outcomes. Different nodes in the cluster might have different opinions on how their state should change when the computation is performed. Unless there is an unanimous consensus, any disagreeing node can escalate to the Judge for the final determination and penalization of uncomplying nodes.

The Judge is not represented by a single machine – actually, it can be as large as Ethereum blockchain to have the desired trustworthiness properties. For this showcase, however, it is imitated as a single process stub which can only notify the user if there is any disagreement.

Two major logical parts can be marked out in the demo application. One is a BFT consensus engine with a replicated transaction log which is provided by the Tendermint platform (Tendermint Core). Another is a state machine with domain-specific state transitions induced by transactions. Each node in the cluster runs an Tendermint Core instance and a state machine instance, and Tendermint connects nodes together. We will discuss both parts in more details below.

State machine

Each node carries a state which is updated using transactions furnished through the consensus engine. Assuming that more than 2/3 of the cluster nodes are honest, the BFT consensus engine guarantees correctness of state transitions. In other words, unless 1/3 or more of the cluster nodes are Byzantine there is no way the cluster will allow an incorrect transition.

If every transition made since the genesis was correct, we can expect that the state itself is correct too. Results obtained by querying such a state should be correct as well (assuming a state is a verifiable data structure). However, if at any moment in time there was an incorrect transition, all subsequent states can potentially be incorrect even if all later transitions were correct.

In this demo application the state is implemented as an hierarchical key-value tree which is combined with a Merkle tree. This allows a client that has obtained a correct Merkle root from a trusted location to query a single, potentially malicious, cluster node and validate results using Merkle proofs.

Such trusted location is provided by the Tendermint consensus engine. Cluster nodes reach consensus not only over the canonical order of transactions, but also over the Merkle root of the state – app_hash in Tendermint terminology. The client can obtain such Merkle root from any node in the cluster, verify cluster nodes signatures and check that more than 2/3 of the nodes have accepted the Merkle root change – i.e. that consensus was reached.

Computations correctness

It's not possible to expect that a cluster can't be taken over by Byzantine nodes. Let's assume that n nodes in the cluster were independently sampled from a large enough pool of the nodes containing a fraction of q Byzantine nodes. In this case the number of Byzantine nodes in the cluster (denoted by X) approximately follows a Binomial distribution B(n, q). The probability of the cluster failing BFT assumptions is Pr(X >= ceil(1/3 * n)) which for 10 cluster nodes and 20% of Byzantine nodes in the network pool is ~0.1.

This a pretty high probability, and if we want to keep the cluster size reasonably low to have desired cost efficiency another trick should work. We can allow any node in the cluster to escalate to the external trusted Judge if it disagrees with state transitions made by the rest of the nodes. In this case, all nodes in the cluster need to be Byzantine to keep the Judge uninformed. For the considered case the probability of such event is ~1E-7.

This way it's possible to improve the probability of noticing an incorrect behavior almost by six orders of magnitude. However, there is a significant difference between the two approaches. Once the cluster has reached consensus, the state transition is made and potentially incorrect results can be immediately used by the client. An escalation mechanism allows to notice an incorrect cluster behavior only post factum.

To compensate, a Judge can penalize malicious nodes by forfeiting their security deposits for the benefit of the client. However, even in this case a client can't be a mission critical application where no amount of compensation would offset the damage made.

Tendermint

Tendermint platform provides a Byzantine-resistant consensus engine (Tendermint Core) which roughly consists of the following parts:

distributed transaction cache (mempool)
blockchain to store transactions
Byzantine-resistant сonsensus module (to reach the agreement on the order of transactions)
peer-to-peer layer to communicate with other nodes
RPC endpoint to serve client requests
query processor for making requests to the state

To execute domain-specific logic the application state machine implements Tendermint's ABCI interface. It is written in Scala 2.12, compatible with Tendermint v0.19.x and uses the jabci library providing ABCI definitions for JVM languages.

Tendermint orders incoming transactions, passes them to the application and stores them persistently. It also combines transactions into ordered lists – blocks. Besides the transaction list, a block also has some metadata that helps to provide integrity and verifiability guarantees. Basically this metadata consists of two major parts:

metadata related to the current block
- height – an index of this block in the blockchain
- block creation time
- hash of the transaction list in the block
- hash of the previous block
metadata related to the previous block
- app_hash – hash of the state machine state that was achieved at the end of the previous block
- previous block voting process information

To create a new block a single node – the block proposer is chosen. The proposer composes the transaction list, prepares the metadata and initiates the voting process. Then other nodes make votes accepting or declining the proposed block. If enough number of votes accepting the block exists (i.e. the quorum was achieved – more than 2/3 of the nodes in the cluster voted positively), the block is considered committed.

Once this happens, every node's state machine applies newly committed block transactions to the state in the same order those transactions are present in the block. Once all block transactions are applied, the new state machine app_hash is memorized by the node and will be used in the next block formation.

If for some reason a quorum was not reached the proposer is changed and a new round of a block creation for the same height as was in the previous attempt is started. This might happen, for example, if there was an invalid proposer, or a proposal containing incorrect hashes, a timed out voting and so on.

Note that the information about the voting process and the app_hash achieved during the block processing by the state machine are not stored in the current block. The reason is that this part of metadata is not known to the proposer at time of block creation and becomes available only after successful voting. That's why the app_hash and voting information for the current block are stored in the next block. That metadata can be received by external clients only upon the next block commit event.

Grouping transactions together significantly improves performance by reducing the storage and computational overhead per transaction. All metadata including app_state and nodes signatures is associated with blocks, not transactions.

It's important to mention that block height is a primary identifier of a specific state version. All non-transactional queries to the state machine (e.g. get operations) refer to a particular height. Also, some blocks might be empty – contain zero transactions. By committing empty blocks, Tendermint maintains the freshness of the state without creating dummy transactions.

Another critical thing to keep in mind is that once the k block is committed, only the presence and the order of its transactions is verified, but not the state achieved by their execution. Because the app_hash resulted from the block k execution is only available when the block k + 1 is committed, the client has to wait for the next block to trust a result computed by the transaction in the block k. To avoid making the client wait if there were no transactions for a while, Tendermint makes the next block (possibly empty) in a short time after the previous block was committed.

Operations

There are few different operations that can be invoked using the bundled command-line client:

put operations which request to assign a constant value to the key: put a/b=10
computational put operations which request to assign the function result to the key: put a/c=factorial(a/b)
get operations which read the value associated with a specified key: get a/b
run operations which await for the cluster to respond with the function result: run factorial(a/b)

put operations are effectful and are explicitly changing the application state. To process such operation, Tendermint sends a transaction to the state machine which applies this transaction to its state, typically changing the associated value of the specified key. If requested operation is a computational put, state machine finds the corresponding function from a set of previously hardcoded ones, executes it and then assigns the result to the target key.

Correctness of put operations can be verified by the presence of a corresponding transaction in a correctly formed block and an undisputed app_hash in the next block. Basically, this would mean that a cluster has reached quorum regarding this transaction processing.

get operations do not change the application state and are implemented as Tendermint ABCI queries. As the result of such query the state machine returns the value associated with the requested key. Correctness of get operations can be verified by matching the Merkle proof of the returned result with the app_hash confirmed by consensus.

run operations are just a shortcut to the combination of put and get requests. To perform such operation, the client first requests to assign the result of the specified function to a certain key and then queries the value associated with this key.

Installation and run

To run the application, the node machine needs Scala 2.12 with sbt, Tendermint and GNU screen.
To execute operations the client machine needs Python 2.7 with sha3 package installed.

This demo contains scripts that automate running a cluster of 4 nodes (the smallest BFT ensemble possible) on the local machine. To prepare configuration files, run source local-cluster-init.sh.

To start the cluster, run local-cluster-start.sh which starts 9 screen instances: app[1-4] – application backends, tm[1-4] – corresponding Tendermint instances and judge – Judge stub. Cluster initialization might take few seconds, after which the client can query Tendermint RPC endpoints using any of 46158, 46258, 46358 or 46458 ports.

Other scripts allow to temporarily stop (local-cluster-stop.sh), delete (local-cluster-delete.sh) and reinitialize (local-cluster-reset.sh) the cluster.

Sending queries

Examples below use localhost:46157 to query TM Core on 1st local "node", to access other nodes one needs to use other endpoints (46257, 46357, 46457). In normal conditions, all endpoints behave the same way.

Writing operations (`put`)

To set a new key-value mapping, use:

> python query.py localhost:46157 put a/b=10
RESULT:    10
OK

This creates hierarchical key a/b (if necessary) and maps it to 10.

copy operation allows to assign a value from one key to another:

> python query.py localhost:46157 put "a/c=copy(a/b)"
RESULT:    10
OK

Submitting an increment operation increments the referenced key value and copies the old referenced key value to target key:

> python query.py localhost:46157 put "a/d=increment(a/c)"
RESULT:    10
OK

sum operation sums the values of references keys and assigns the result to the target key:

> python query.py localhost:46157 put "a/e=sum(a/c,a/d)"
RESULT:    23
OK

factorial operation calculates the factorial of the referenced key value:

> python query.py localhost:46157 put "a/f=factorial(a/b)"
RESULT:    3628800
OK

hiersum operation calculates the sum of non-empty values for the referenced key and its descendants by hierarchy (all non-empty values should be integer):

> python query.py localhost:46157 put "c/asum=hiersum(a)"
RESULT:    3628856
OK

Simple queries (`get`, `ls`)

get reads value associated with the argument:

> python query.py localhost:46157 get a/e
RESULT:    23
OK

Another non-changing request, ls, can be used to obtain argument key's immediate children list:

> python query.py localhost:46157 ls a
...
RESULT:    e f b c d
OK

Computations without target key (`run`)

Below is the example (note that no target key specified here):

> python query.py localhost:46157 run "factorial(a/b)"
RESULT:    3628800
OK

Operation verbose mode and proofs

Now let's examine operations output in verbose mode. It allows to trace information about the blockchain structure and verifications.

Observe the output of put operation with -v option:

> python query.py localhost:46157 put -v c/a=20
HEIGHT:    21
APP_HASH:  8FA7A9819479B06B49F7DE770764F353F7492545D182FD9A8F4C4732EC1FC824
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
RESULT:    20
OK

HEIGHT corresponds to height of block in which the writing transaction eventually included. APP_HASH is app_hash of HEIGHT-th block. PROOF is comma-separated list of Merkle hash from the root key to the target key.

The blockchain contents can be viewed by running a dedicated command:

> python parse_chain.py localhost:46157
height                 block time     txs acc.txs app_hash                            tx1
...
   20: 2018-06-19 20:43:30.943104       0       9 0x49C941
   21: 2018-06-19 20:45:28.161980       1      10 0x49C941                         c/a=20
   22: 2018-06-19 20:45:29.478594       0      10 0x8FA7A9

This command outputs the latest blocks in the blockchain with a short summary about transactions. Here one can ensure that the provided transaction c/a=20 indeed included in the block with height from the response. This fact verifies that Tendermint majority (more than 2/3 of configured validator nodes) agreed on including this transaction in the mentioned block which certified by their signatures.

The output of parse_chain.py also shows that the Tendermint blockchain stores app_hash from the block not in this block itself, but in the next block. For example, compare HEIGHT (21) and HASH (0x8FA7A9) from the previous query with parse_chain summary for 21st and 22nd blocks. Also note that app_hash is not changed after empty block's commit as expected, because empty blocks do not change the App state.

Implementation details

Operation processing in the cluster

To initiate an operation the Client needs to connect only a single node of the cluster in normal conditions.

Reading get requests are processed on a single node entirely. The node State machine has all required information to process such query because the state with key-value tree and their proofs is fully replicated. The node TM Core also has everything to process get query because the blockchain is also fully replicated and contains all information not only about blocks but also about the blocks signatures of other nodes and therefore can prove to the client that the provided response is consistent with those nodes signed the blockchain data.

Writing run and put requests implemented via Tendermint transactions, so a cluster-wide interaction is required in order to:

TM Core spreads the transaction to other nodes.
TM Cores reach consensus about including this transaction in a particular block.
TM Cores request their local State machine to apply this transaction to the state.
TM Cores obtain the app_hash from their local State machines.

Transaction processing on the single node

A single transaction is processing primarily by 2 TM Core modules: Mempool and Consensus.

A transaction appears in Mempool after one of TM Core RPC broadcast method invoked. Mempool then invokes the State machine CheckTx ABCI method. The State machine might reject the transaction if it is invalid, in this case, the node does not need to connect other nodes and the rejected transaction removed. Otherwise, the transaction starts spreading through other nodes.

The transaction remains some time in Mempool until Consensus module of the current TM proposer consumes it, includes to the newly created block (possibly together with other transactions) and initiates the voting process for this proposal block. If the transaction rate is intensive enough or even exceed the node throughput, it is possible that the transaction may 'wait' during several block formation before it is eventually consumed by proposer's Consensus. Note that the transaction broadcast and the block proposal are processed independently, it is possible but not required that the proposer is the node initially processed the broadcast.

If more than 2/3 of the nodes voted for the proposal in a timely manner, the voting process ends successfully. In this case, every TM Core starts the block synchronization with its local State machine. During this phase, the proposer and other nodes behave the same way. TM Core consecutively invokes the State machine's ABCI methods: BeginBlock, DeliverTx (for each transaction), EndBlock, and Commit. The State machine applies the block's transactions from DeliverTx sequence in their order, calculates the new app_hash and returns it to TM Core. At that moment the current block processing ends and the block becomes available outside (via RPC methods like block and blockchain). TM Core keeps app_hash and the information about a voting process for including in the next block's metadata.

ABCI query processing on the single node

ABCI queries that serve non-changing operations are described by the target key and the target height. They are initially processed by TM Core's Query processor which reroutes them to the State machine.

The State machine processed the query by looking up for the target key in a state corresponding to the height-th block. So the State machine maintains several Query states to be able to process different target heights.

Note that the State machine handles Mempool (CheckTx), Consensus (DeliverTx, Commit) and Query request pipelines concurrently. Also, it maintains separate states for those pipelines, so none of the Query states might be affected by 'real-time' Consensus state which is possibly modified by delivered transactions at the same time. This design, together with making the target height explicit, allows to isolate different states and avoid race conditions between transactions and queries.

Client implementation details

To make a reading (get) request, the Client first gets the latest verifiable height and its app_hash from the blockchain RPC. This is the last but one height (because the latest one could never be verifiable, its app_hash is not available). Then a single ABCI Query call with the get target key and the latest verifiable height is enough to get the required value together with Merkle proof and check that the value and the proof are consistent with app_hash.

To make a writing (put) requests, the Client broadcasts the transaction to the cluster. Upon successful broadcast and insertion of the transaction into some block, the Client knows the corresponding block height. This height becomes verifiable as soon as the next block is committed (as mentioned earlier normally this happens in a short time, by default 1 second at most). Then to verify successful put (and to get computation result in case of the computational put), the Client just needs to make the ABCI Query with the target key and height, like it is described in the previous paragraph for the get request.

run requests processing is very similar to put processing. The only difference that the Client generates a 'hidden' target key and use it to invoke the calculation via Tendermint transaction and then to read it via ABCI Query.

Transactions and Merkle hashes

The State machine does not recalculate Merkle hashes during DeliverTx processing. In case block consists of several transactions, the State machine modifies key tree and marks changed paths by clearing Merkle hashes until ABCI Commit processing.

On Commit the State machine recalculates Merkle hash along changed paths only. Finally, the app returns the resulting root Merkle hash to TM Core and this hash is stored as app_hash for a corresponding block.

Note that described merkelized structure is just for demo purposes and not self-balanced, it remains efficient only until it the user transactions keep it relatively balanced. Something like Patricia tree should be more appropriate to achieve self-balancing.

Incorrect behavior of the cluster nodes

As any viable distributed system, this Application is designed to handle incorrect or even malicious behavior of the cluster nodes. To avoid the over-complication the following statements considered:

The Client is correct.
The Judge is correct. This might look as a serious limitation but using some highly trusted source like Ethereum smart contract as the Judge in the real life scenario might be a valid solution. This App implements the Judge as a very simple program just for demo purposes.
The nodes' public keys are known to all cluster participants.
The set of nodes in the cluster is immutable. A mutable node set might be handled too, but this is out of the scope of this demo Application.
At least one cluster node is correct (both the node's TM Core and the State machine are correct). If the cluster size if large enough (20 and more nodes), the probability of such condition might be very high.
The correct nodes can communicate with the client and the Judge.
It is needless to consider situations when some nodes are partly correct (correct TM Core and incorrect State machine or vice versa).

A. Cases which the client can detect and handle

The node is not available or RPC request to the node is timed out. In this case the Client just retries request to another node, its possible that the rest of nodes is enough to have a quorum and keep the App alive.
The TM Core blockchain RPCs (block, blockchain) return response with inconsistent information: falsified transactions in the blocks, incorrect block hashes, incorrect vote signatures or signatures that are not matched with known public keys. In this case, the Client treats the node as incorrect (possibly Byzantine) and retries request to another node. Not implemented yet.
The TM Core ABCI Query returns wrong result/proof combination (inconsistent with the target height's app_hash). Like for Case 2, in this case, the Client treats the node as incorrect (possibly Byzantine) and retries request to another node.
The TM Core blockchain RPCs return stale data. The Client expects some maximum time between the blocks, so observing the larger time since the latest block is the reason to retry the request to another node. Note that the current node cannot be considered Byzantine for sure because it might experience connection problems with the rest of the cluster. Not implemented yet.

B. Cases which the client can detect, but cannot handle

After detecting those cases the Client is sure that the cluster liveness is violated. An external interference is required to restore it.

The Client retried the request for cases A1-A4 for all cluster nodes and they all are failed.
The cluster cannot commit height+1-th block while the Client waits for it to have height-th block verifiable. This is actually a subcase of the previous case, but it appears if the cluster recently committed height-th block during put or run processing. The failure to progress in this case probably means that the nodes have different app_hash-es for height-th block, so this is likely an evidence of the dispute in the cluster.

C. Dispute cases

Dispute cases, in general, cannot be detected by the client, because the client is normally satisfied by the first successful response while retrying response to the cluster nodes. The external Judge is available to the correct nodes in order to prevent such situations (instead of multicasting the client requests to all cluster nodes and comparing the responses).

Another, even more important, reason is that the dispute case might violate the cluster safety! When there is a Byzantine quorum, Byzantine nodes might provide to the client as wrong responses as they want, but the client keeps trusting the cluster because no Cases B and even Cases A evidence is observed. So the external Judge should also be able to replay the computations that caused the dispute.

Dispute case C1: some nodes correct, some not, no quorum

When the last block is height-th and there is no quorum (neither correct nor Byzantine) for height+1-th block's voting, liveness is violated and new blocks cannot be formed. Such situation might happen if the cluster cannot reach an agreement about next block. Even if TM Core works as expected, different State machines on different nodes might provide to local TM Cores different app hashes for height-th block. As already said, Case B2 is usually an aftermath of this case.

To simulate disputes in the local cluster the special key wrong might be used. If some node's State machine (indexed 1 to 4 which corresponds to their ports 46158, 46258, 46358, 46458) get put request targeted to wrong and a provided value contains node's index, it prepends a prefix wrong to this value. For example, after put wrong=13 request, the 2nd and 4th nodes map wrong to 13, but 1st and 2rd nodes map it to wrong13. Consequently, those 'wrong' nodes obtain 'wrong' app_hash which disputes with correct app_hash.

This convention works well to illustrate Dispute case C1. First, let's try using fastput, an unchecked alternative to put (it does not wait for the next block with the current block's app_hash) to submit new wrong value:

> python query.py localhost:46157 fastput -v wrong=34
HEIGHT:    3
INFO:      34
OK

This invocation return info 34 and OK status. At first glance, everything is well because height-th (the 3rd actually) block formed and INFO equal to new value 34 got. However, this INFO should be considered as tentative because despite successful the 3rd block formation it's needed to wait for the 4th block that should contain app_hash for 3rd block. Note that the source of INFO is just output of DeliverTx from single App and this output is neither merkelized nor signed by other nodes.

Now the blockchain has inconsistent state. Let's reset it via local-cluster-reset.sh, wait some time for cluster initialization and instead of unchecked fastput use checked put:

> python query.py localhost:46157 put -v wrong=34
HEIGHT:    3
APP_HASH:  NOT_READY
PROOF:     NO_PROOF
RESULT:    EMPTY
BAD:       Cannot verify tentative '34'! Height is not verifiable

put waits for height+1-th block before responding. As before, 3rd block formation is successful but it's not enough for put, it waits for 4th block. After some timeout, it responds that this block is still not available, so tentative 34 value is not confirmed.

The State machine itself also monitors block creation. The Monitor thread of the App that checks the following condition periodically: if 1 second elapsed from last non-empty block in the blockchain there must be an empty block after that block. In case this does not hold, the Monitors detects a dispute and signals the Judge that cluster needs to be fixed. Of course, the timeout value (default is 1 second) is configurable. This might be checked by querying the Judge status:

> curl -s "localhost:8080/status" | jq
{
  "1": {
    "status": "No quorum",
    "app_hash": "366D393BAD6563C067CBF8F7CF582EB7FE61217C8FC0264903789E307FC95EFB",
    "height": 3
  },
  "3": {
    "status": "No quorum",
    "app_hash": "A35CF646E011DCBA103705B1BCA2AB196AE8FA1F46A662E086A33C6DD518CC22",
    "height": 3
  },
  "2": {
    "status": "No quorum",
    "app_hash": "366D393BAD6563C067CBF8F7CF582EB7FE61217C8FC0264903789E307FC95EFB",
    "height": 3
  },
  "4": {
    "status": "No quorum",
    "app_hash": "A35CF646E011DCBA103705B1BCA2AB196AE8FA1F46A662E086A33C6DD518CC22",
    "height": 3
  }
}

Here it might be noticed that every node detects the absence of quorum and provides its own version of app_hash. Half of the nodes have the correct app_hash whereas the rest of nodes has a wrong one.

Dispute case C2: Byzantine quorum, minority of correct nodes

This case can also be illustrated using wrong key:

> python query.py localhost:46157 put -v wrong=123
HEIGHT:    3
APP_HASH:  3E5B81D6C436A5319577637A005FDA99EAA632C360ACA23AE9BB3BD3766CFE02
PROOF:     A7FFC6F8BF1ED76651C14756A061D662F580FF4DE43B49FA82D80A4B80F8434A 1AACEE49E178FF7836873CB0D520C5C7D82B772D28997A0EE51A837A5AA5683C 672896E0A9F15E323B6D2166A520701F8423198E0AB3D33415F7E2A844D18454, 10A1E4BF410C6BFD3455EF467700B24842ABE6F9ED6D24C816741F43A8FA8D58
RESULT:    wrong123
OK

The 'wrong' nodes (1st, 2nd, and 3rd) have a quorum (despite the 4th disagrees with them) and provide their version of state and corresponding app_hash. The Client validates the blockchain information and provided response and treats it correct. From the Client's point of view it is impossible in general case to discriminate a correct response and a falsified response in presence of a Byzantine quorum.

This example is pretty artificial because the trivial comparison of the target value 123 with the result wrong123 might be done. However, in case of a non-trivial operation the client is unable to reproduce an arbitrary computation and cannot detect the incorrect response.

Node 4 is able to detect the disagreement, which might be checked via the Judge status

> curl -s "localhost:8080/status" | jq
{
  "1": {
    "status": "OK",
    "app_hash": "3E5B81D6C436A5319577637A005FDA99EAA632C360ACA23AE9BB3BD3766CFE02",
    "height": 4
  },
  "3": {
    "status": "OK",
    "app_hash": "3E5B81D6C436A5319577637A005FDA99EAA632C360ACA23AE9BB3BD3766CFE02",
    "height": 4
  },
  "2": {
    "status": "OK",
    "app_hash": "3E5B81D6C436A5319577637A005FDA99EAA632C360ACA23AE9BB3BD3766CFE02",
    "height": 4
  },
  "4": {
    "status": "Disagreement with quorum",
    "app_hash": "431ED90111F3A4D5349DF955B664CA63950CB768526DD9F5105C26A3723CBB53",
    "height": 3
  }
}

To achieve this detection the State machine Monitor periodically requests its peer's TM Core RPC's for the next block and compares their app_hash-es with its own app_hash. In case of a disagreement the Monitor immediately raises the dispute to the Judge.

Dispute case C3: correct quorum, some nodes Byzantine or not available

This case is symmetric to the previous, but the quorum is correct now.

When a quorum (2/3+ nodes of the cluster) exists, the availability of other nodes does not influence cluster's safety or liveness. This demo app does not implement any special checks for the existence of nodes absent or Byzantine during operation processing. Let's illustrate this using wrong key:

> python query.py localhost:46157 put -v wrong=4
HEIGHT:    3
APP_HASH:  7B840A448231110FC3746EE06C0053E6EADE213189BDFDB902E7FBA6A486643B
PROOF:     A7FFC6F8BF1ED76651C14756A061D662F580FF4DE43B49FA82D80A4B80F8434A 1AACEE49E178FF7836873CB0D520C5C7D82B772D28997A0EE51A837A5AA5683C B103DC8A5244FD6548F7C0DE617EE66D25F79007A993BC15C6EA11D8390E6279, B410677B84ED73FAC43FCF1ABD933151DD417D932A0EF9B0260ECF8B7B72ECB9
RESULT:    4
OK

Here the 4th Node is 'wrong'. It detects a disagreement and might raise the dispute to the Judge. But in this case the Judge would detect this Node as incorrect and punish it.

README.md Unescape Escape

Tendermint Verifiable Computations and Storage Demo

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