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30 changes: 13 additions & 17 deletions docs/drafts/features/consensus.md
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## Consensus Overview

Ostracon's block generation mechanism based on Tendermint-BFT consists of the following three phases. We here refer to the number of block generation as *height*, and a single approval round consisting of the following three processes
as *round*.
Ostracon's block generation mechanism based on Tendermint-BFT consists of the following three phases. We here refer to the generations of blocks as *height*, and a single approval round consisting of the following three processes as *round*.

**Election**. Elect one Proposer and several Voters from candidate node set. This is the same as a Leader Election in a general distributed system, but in blockchain, it must be designed to prevent artificial selection so that malicious interference doesn't degrade the overall performance of the system. Also note that there is no centralized authority involved in Ostracon elections to ensure fairness. Since the election results can be computed deterministically by all nodes, each node can autonomously determine whether it has been elected as a Proposer or Voter.
**Election**. Elect one Proposer and several Voters from a candidate node set. This is the same as a Leader Election in a general distributed system, but in blockchain, it must be designed to prevent artificial selection so that malicious interference doesn't degrade the overall performance of the system. Also note that there is no centralized authority involved in Ostracon elections to ensure fairness. Since the election results can be computed deterministically by all nodes, each node can autonomously determine whether it has been elected as a Proposer or Voter.

**Block Generation**. The elected Proposer proposes a block. Unapproved transactions that have not yet been included in the blockchain are shared among nodes in the network via P2P and stored in an area called mempool
of each node. The node selected as the Proposer generates a block from the unapproved transactions remaining in its mempool and proposes it to the Voters.
**Block Generation**. The elected Proposer proposes a block. Unapproved transactions that have not yet been included in the blockchain are shared among nodes in the network via P2P and stored in an area of each node called the mempool. The node selected as the Proposer generates a block from the unapproved transactions remaining in its mempool and proposes it to the Voters.

**Block Verification**. The block proposed by the Proposer is verified by elected Voters. Each Voter votes on whether the block is correct or not, and the votes are replicated by Tendermint-BFT to the other Voters, and if more than 2/3+1 of all Voters vote in favor of the block, the block is officially approved. On the other hand, if a quorum is not reached, the proposed block is rejected and a new round of elections or voting is started over (Tendermint-BFT has several shortcuts depending on the reason for rejection).

Expand All @@ -20,7 +18,6 @@ VRF is an algorithm for generating a hash value $t$ that can be used as a crypto

A VRF hash generator $k$ generates a proof $\pi$ (VRF Proof) from the message $m$ using its private key $S_k$ as in Equation (1). Here, the hash value $t$ can be acquired from the proof $pi$ using Equation. (2). On the other hand, to verify that the hash value $t$ was generated by the owner of the private key $S_k$ based on the message $m$, the verifier applies the public key $P_k$ for $S_k$, $m$, and $\pi$ to Equation (3) to verify that both hash values are identical.


![VRF Expression](math_expression.png)

```math
Expand All @@ -33,14 +30,13 @@ t & = & {\rm vrf\_proof\_to\_hash}(\pi)
\end{equation}
```

In Ostracon, the Proposer and Voters of the next block are selected randomly by a verifiable random number from the Proposer that created the previous block. A VRF Proof field $pi$ is being added to the block for this purpose.
With Ostracon, the Proposer and Voters of the next block are selected randomly by a verifiable random number from the Proposer that created the previous block. A VRF Proof field $pi$ is added to the block for this purpose.

The node that receives the new block initiates the election phase. In  this phase, it verifies the VRF Proof $\pi$ contained in the block, calculates the VRF hash $t$, which is a "fair pseudo-random number," and selects the Proposer and Voters for this round based on that value. This is done by a simple and fast weighted random sampling based on the probability of selection according to Stake holdings (i.e., based on PoS).
The node that receives the new block initiates the election phase. In this phase, it verifies the VRF Proof $\pi$ contained in the block, calculates the VRF hash $t$, which is a "fair pseudo-random number," and selects the Proposer and Voters for this round based on that value. This is done by a simple and fast weighted random sampling based on the probability of selection according to Stake holdings (in other words, based on PoS).

![VRF-based Proposer/Voter Election](vrf_election.png)

The node selected as the Proposer by this phase picks up the unapproved transactions from its own mempool and generates a proposal block (at this point, the block is not confirmed yet). Then, the Proposer calculates a VRF Proof $\pi'$ using the previous VRF Hash $t$ that selected itself, the new block height $h$, and the current round $r$ and sets it to the block.

The node selected as the Proposer by this phase picks up the unapproved transactions from its own mempool and generates a proposal block (at this point, the block is not confirmed yet). Then, the Proposer calculates VRF Proof $\pi'$ using the previous VRF Hash $t$ that selected itself, the new block height $h$, and the current round $r$ and sets it to the block.

![VRF Prove](math_prove.png)

Expand All @@ -56,14 +52,14 @@ Note that the message $m$ used to calculate the new VRF Proof $\pi$ doesn't invo

![VRF-based Block Generation](vrf_block_generation.png)

A node that is selected as a Voter in the election phase verifies the received Proposal block and votes on it. The votes are replicated by Tendermint-BFT through prevote, precommit, and commit, and the block is confirmed if more than a quorum of valid votes are collected.
A node that is selected as a Voter in the election phase verifies the received Proposal block and votes on it. The votes are replicated by Tendermint-BFT through prevote, precommit, and commit. The block is confirmed if more than a quorum of valid votes are collected.

![VRF-based Block Validation](vrf_block_validation.png)

During the verification phase, the following VRF-related verifications are performed in addition to block verification:

1. The Proposer that generated the block must be a node selected based on the VRF hash of its previous block. This can be determined by matching the node that actually generated the block with the Proposer selected by weighted random sampling using the VRF hash $t$.
2. The $\pi$ contained in the block must be a VRF Proof generated using the private key of the Proposer. If the $t$ calculated from the VRF Proof $\pi$ matches the $t$ calculated using the `vrf_verify()` function, we can conclude that $\pi$ is not forged.
* The Proposer that generated the block must be a node selected based on the VRF hash of its previous block. This can be determined by matching the node that actually generated the block with the Proposer selected by weighted random sampling using the VRF hash $t$.
* The $\pi$ contained in the block must be a VRF Proof generated using the private key of the Proposer. If the $t$ calculated from the VRF Proof $\pi$ matches the $t$ calculated using the `vrf_verify()` function, we can conclude that $\pi$ is not forged.

![VRF Verify](math_verify.png)

Expand All @@ -75,16 +71,16 @@ By repeating this sequence of rounds, fair random sampling can be chained across

![BFT-based Block Generation](bft_round.png)

Recall here that the node that receives the block can deterministically calculate which nodes are the next Proposer and Voters. By revealing the nodes that are responsible for generating and verifying blocks in a given round, we can punish nodes that are elected but don't actually perform their responsibility or that behave malicious actions such as Eclipse attacks. On the other hand, it's still difficult to predict the Proposer and Voters beyond one block, as they are only revealed for the minimum necessary time.
Recall here that the node that receives the block can deterministically calculate which nodes are the next Proposer and Voters. By revealing the nodes that are responsible for generating and verifying blocks in a given round, we can penalize nodes that are elected but don't actually perform their responsibility or that behave malicious actions such as Eclipse attacks. On the other hand, it's still difficult to predict the Proposer and Voters beyond one block, as they are only revealed for the minimum necessary time.

VRF is currently implemented using Ed25519, and even if a node uses BLS signatures, it also has an Ed25519 key to calculate VRF.

## Voters

In the Ostracon network, Validators mean candidate nodes that hold Stakes and can be elected as Proposers or Voters. The Voters are a subset of Validators are a new concept introduced in Ostracon for two reasons; first, to make flexible the distribution of rewards to nodes elected as Voters, and second, to allow the ratio of Byzantine assumptions to be changed in networks with different trust policies for the participant nodes (as a result of the configuration, if the number of Voters is set to match the number of Validators, the behavior will be the same as in Tendermint).
In the Ostracon network, Validators mean candidate nodes that hold Stakes and can be elected as Proposers or Voters. The Voters (a subset of Validators) are a new concept introduced in Ostracon for two reasons; first, to make the distribution of rewards to nodes elected as Voters flexible, and second, to allow the ratio of Byzantine assumptions to be changed in networks with different trust policies for the participant nodes (as a result of the configuration, if the number of Voters is set to match the number of Validators, the behavior will be the same as in Tendermint).

Voters selection uses a pseudo-random function $r$ to generate a sequence of random numbers in order to randomly select multiple nodes from a single VRF hash $t$. It's more important that $r$ is simple to implement, no variant by different interpretations, fast, and memory-saving since $t$ already has the properties of a cryptographic pseudo-random number. The Ostracon uses a fast shift-register type pseudo-random number generation algorithm, called SplitMix64, for this Voters selection.
Voter selections use a pseudo-random function $r$ to generate a sequence of random numbers in order to randomly select multiple nodes from a single VRF hash $t$. It's more important that $r$ is fast, simple to implement, has no variant by different interpretations, and saves memory since $t$ already has the properties of a cryptographic pseudo-random number. Ostracon uses a fast shift-register type pseudo-random number generation algorithm, called SplitMix64, for Voter selection.

## Disciplinary Scheme for Failures

Although Ostracon's consensus scheme works correctly even if a few nodes fail, it's ideal that failed nodes aren't selected for the consensus group in order to avoid wasting network and CPU resources. In particular, for cases that aren't caused by general asynchronous messaging problems, i.e., intentional malpractice, evidence of the behavior (whether malicious or not) will be shared and action will be taken to eliminate the candidate from the selection process by forfeiting the Stake.
Although Ostracon's consensus scheme works correctly even if a few nodes fail, it's ideal that failed nodes aren't selected for the consensus group in order to avoid wasting network and CPU resources. In particular, for cases that aren't caused by general asynchronous messaging problems, such as intentional malpractice, evidence of the behavior (whether malicious or not) will be shared and action will be taken to eliminate the candidate from the selection process by forfeiting the Stake.
20 changes: 10 additions & 10 deletions docs/drafts/features/signature_aggregation.md
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## Overview

Blockchains with a decentralized consensus mechanism need to collect a sufficient number of votes (signatures) each time a block is created. The more participants in a consensus, the more secure it becomes, but at the same time, the more signatures there are, the larger the block size becomes, and the longer it takes to verify, the worse the performance becomes. To solve this problem, Bitcoin (BIP340) and Ethereum 2.0 are working to improve performance by incorporating signature aggregation.
Blockchains with a decentralized consensus mechanism need to collect a sufficient number of votes (signatures) each time a block is created. The more participants in a consensus, the more secure it becomes. At the same time however, the more signatures there are, the larger the block size becomes. It takes longer to verify a larger block, and the performance becomes worse as a result. To solve this problem, Bitcoin (BIP340) and Ethereum 2.0 are working to improve performance by incorporating signature aggregation.

The first paper on BLS signatures was published as a digital signature that could be implemented in a very small size, but the technique, called pairing, has led to several other interesting features, such as threshold signatures and blind signatures. Ostracon also aggregates the multiple signatures into a single one by BLS to improve performance by 1) reducing block size and 2) reducing the number of verifications.
The first paper on BLS signatures was published as a digital signature that could be implemented in a very small size. This technique that was called "pairing" has led to several other interesting features, such as threshold signatures and blind signatures. Ostracon also aggregates the multiple signatures into a single one by BLS to improve performance by reducing block size and reducing the number of verifications.

![BLS Signature Aggregation](bls_signature_aggregation.png)

## Public Key Abstraction

With the introduction of BLS signatures, Ostracon has been redesigned to allow signature keys with different schemes per node to be used on the same blockchain instance, which means that Ostracon participants can choose between fast and proven Ed25519 signatures and signature aggregation capable BLS signatures when setup their nodes. This flexibility gives us the flexibility to test/adopt better signature algorithms in the future, or to deal with vulnerabilities in the implementation if they are discovered.
With the introduction of BLS signatures, Ostracon has been redesigned to allow signature keys with different schemes per node to be used on the same blockchain instance, which means that Ostracon participants can choose between fast and proven Ed25519 signatures and signature aggregation capable BLS signatures when setting up their nodes. This flexibility gives us the flexibility to test/adopt better signature algorithms in the future, or to deal with vulnerabilities in the implementation if they are discovered.

## Why is this an experimental status?

In introducing BLS, we have unfortunately found that the BLS signature aggregation conflicts in several ways with the design of Tendermint, the base of Ostracon. A typical example is an elementary validation called Light Validation for light nodes. Even if a client doesn't have the public keys of all the nodes involved in the consensus, it can still consider a block to be correct if it successfully validates 2/3+1 of the total number of voters based on the BFT assumption. However, with BLS signatures, if even one of the public keys participating in the consensus is missing, all the aggregated signatures cannot be verified.

In terms of performance, Ed25519 signatures are faster than BLS signatures for generating/verifying a single signature. We are carefully investigating where is the watershed point of the improvements where the block size reduction and the verification frequency reduction outweigh the slowness.
In terms of performance, Ed25519 signatures are faster than BLS signatures for generating/verifying a single signature. We consider the point where the block size reduction and the verification frequency reduction outweigh the slowness as a watershed point and are carefully investigating to find it.

| Algorithm | Private Key | Public Key | Signature | Sig Generation | Sig Verification |
|:------------------|------:|------:|-----:|--------:|--------:|
| ECDSA (secp256k1) | 96B | 64B | 64B | 92μs | 124μs |
| Ed25519 | 64B | 32B | 64B | 49μs | 130μs |
| BLS12-381 | 32B | 96B | 48B | 233μs | 1,149μs |
| Algorithm | Private Key | Public Key | Signature | Sig Generation | Sig Verification |
| :---------------- | ----------: | ---------: | --------: | -------------: | ---------------: |
| ECDSA (secp256k1) | 96B | 64B | 64B | 92μs | 124μs |
| Ed25519 | 64B | 32B | 64B | 49μs | 130μs |
| BLS12-381 | 32B | 96B | 48B | 233μs | 1,149μs |

Table: Space and time efficiency of signature algorithms. The message length for signature creation/verification is 1024 bytes.

We have a plan to support BLS signatures going forward, but considering backward-incompatible fixes for these issues, this functionality currently has an experimental status.
We have a plan to support BLS signatures going forward, but considering the backward-incompatible fixes for these issues, this functionality currently has an experimental status.

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