Consensus Mechanisms: Detailed Documentation

Overview

The ArthaChain blockchain employs several advanced consensus mechanisms to achieve high throughput, security, and cross-shard capabilities. The primary consensus algorithms include Quantum SVBFT (Scalable Byzantine Fault Tolerance), adaptive consensus, and specialized cross-shard coordination.

Architecture

The consensus module is organized into several specialized components:

blockchain_node/src/consensus/
├── adaptive.rs              # Adaptive consensus parameters
├── block_manager.rs         # Block creation and management
├── byzantine.rs             # Byzantine fault tolerance implementation
├── cross_shard/             # Cross-shard transaction coordination
│   ├── coordinator.rs       # Shard coordination logic
│   ├── integration.rs       # Integration with main consensus
│   ├── mod.rs               # Module definition
│   ├── protocol.rs          # Cross-shard protocol implementation
│   ├── resource.rs          # Resource management
│   ├── routing.rs           # Transaction routing
│   ├── sharding.rs          # Sharding logic
│   └── tests/               # Test implementations
├── ltl.rs                   # Linear Temporal Logic for consensus verification
├── mod.rs                   # Main module definition
├── parallel_processor.rs    # Parallel transaction processing
├── parallel_tx.rs           # Parallel transaction validation
├── petri_net.rs             # Petri net modeling for consensus
├── quantum_svbft.rs         # Quantum-resistant SVBFT implementation
├── reputation.rs            # Validator reputation system
├── svcp.rs                  # Scalable Verifiable Consensus Protocol
└── view_change.rs           # View change protocol for leader rotation

Core Consensus Algorithms

1. Quantum SVBFT (quantum_svbft.rs)

The Quantum SVBFT algorithm is an advanced Byzantine Fault Tolerant consensus mechanism designed to be resistant to quantum computing attacks.

pub struct QuantumSVBFT {
    // Current validator set
    validators: Vec<Validator>,
    
    // Current view (round) number
    view: u64,
    
    // Current primary (leader) validator
    primary: ValidatorId,
    
    // Quantum-resistant cryptographic components
    crypto: QuantumCrypto,
    
    // State of the consensus
    state: ConsensusState,
    
    // Configuration parameters
    config: QuantumSVBFTConfig,
}

impl QuantumSVBFT {
    // Creates a new instance of the Quantum SVBFT
    pub fn new(validators: Vec<Validator>, config: QuantumSVBFTConfig) -> Self { ... }
    
    // Processes a consensus message
    pub fn process_message(&mut self, message: ConsensusMessage) -> Result<ConsensusAction, ConsensusError> { ... }
    
    // Proposes a new block as the primary validator
    pub fn propose_block(&mut self, transactions: Vec<Transaction>) -> Result<Block, ConsensusError> { ... }
    
    // Prepares for a block (prepare phase)
    pub fn prepare(&mut self, block_hash: &Hash) -> Result<PrepareMessage, ConsensusError> { ... }
    
    // Commits to a block (commit phase)
    pub fn commit(&mut self, block_hash: &Hash) -> Result<CommitMessage, ConsensusError> { ... }
    
    // Finalizes a block, making it part of the chain
    pub fn finalize_block(&mut self, block: &Block) -> Result<(), ConsensusError> { ... }
    
    // Initiates a view change when the primary is suspected to be faulty
    pub fn initiate_view_change(&mut self) -> Result<ViewChangeMessage, ConsensusError> { ... }
}

Key characteristics:

• Quantum Resistance: Uses post-quantum cryptographic primitives
• High Throughput: Optimized for processing thousands of transactions per second
• Low Latency: Achieves finality in 2-3 seconds under normal conditions
• Byzantine Fault Tolerance: Can tolerate up to f faulty nodes in a 3f+1 system
• Adaptive Difficulty: Adjusts consensus parameters based on network conditions

2. Adaptive Consensus (adaptive.rs)

The adaptive consensus component dynamically adjusts consensus parameters based on network conditions.

pub struct AdaptiveConsensus {
    // Network metrics collector
    metrics: NetworkMetrics,
    
    // Current parameter set
    parameters: ConsensusParameters,
    
    // Parameter adjustment rules
    adjustment_rules: Vec<AdjustmentRule>,
    
    // History of parameter changes
    parameter_history: VecDeque<ParameterChange>,
}

impl AdaptiveConsensus {
    // Creates a new adaptive consensus component
    pub fn new(initial_parameters: ConsensusParameters) -> Self { ... }
    
    // Updates network metrics
    pub fn update_metrics(&mut self, new_metrics: NetworkMetrics) { ... }
    
    // Computes optimal parameters based on current conditions
    pub fn compute_optimal_parameters(&self) -> ConsensusParameters { ... }
    
    // Applies a parameter change
    pub fn apply_parameter_change(&mut self, change: ParameterChange) -> Result<(), ConsensusError> { ... }
    
    // Gets the current parameters
    pub fn get_current_parameters(&self) -> &ConsensusParameters { ... }
}

Key characteristics:

• Dynamic Timeout Adjustment: Adapts timeout values based on network latency
• Batch Size Optimization: Adjusts transaction batch sizes for optimal throughput
• Validator Set Scaling: Dynamically adjusts the active validator set size
• Progressive Difficulty: Increases security during high-value transaction periods

3. Cross-Shard Consensus (cross_shard/)

The cross-shard consensus enables atomic transactions across multiple shards.

Coordinator (coordinator.rs)

pub struct CrossShardCoordinator {
    // Shard this coordinator belongs to
    shard_id: ShardId,
    
    // Cross-shard transactions being coordinated
    active_transactions: HashMap<TransactionId, CrossShardTransaction>,
    
    // Connections to other shard coordinators
    shard_connections: HashMap<ShardId, ShardConnection>,
    
    // Protocol for cross-shard communication
    protocol: CrossShardProtocol,
}

impl CrossShardCoordinator {
    // Creates a new cross-shard coordinator
    pub fn new(shard_id: ShardId, protocol: CrossShardProtocol) -> Self { ... }
    
    // Initiates a cross-shard transaction
    pub fn initiate_transaction(&mut self, transaction: Transaction) -> Result<TransactionId, CrossShardError> { ... }
    
    // Prepares resources for a cross-shard transaction
    pub fn prepare_resources(&mut self, tx_id: &TransactionId) -> Result<ResourceLockResult, CrossShardError> { ... }
    
    // Commits a cross-shard transaction
    pub fn commit_transaction(&mut self, tx_id: &TransactionId) -> Result<(), CrossShardError> { ... }
    
    // Aborts a cross-shard transaction
    pub fn abort_transaction(&mut self, tx_id: &TransactionId) -> Result<(), CrossShardError> { ... }
    
    // Processes a message from another shard
    pub fn process_message(&mut self, message: CrossShardMessage) -> Result<CrossShardAction, CrossShardError> { ... }
}

Protocol (protocol.rs)

pub struct CrossShardProtocol {
    // Protocol version
    version: u32,
    
    // Message authentication
    authenticator: MessageAuthenticator,
    
    // Timeout settings
    timeouts: CrossShardTimeouts,
    
    // Retry policy
    retry_policy: RetryPolicy,
}

impl CrossShardProtocol {
    // Creates a new cross-shard protocol instance
    pub fn new(version: u32, timeouts: CrossShardTimeouts) -> Self { ... }
    
    // Prepares a cross-shard message
    pub fn prepare_message(&self, content: CrossShardContent) -> CrossShardMessage { ... }
    
    // Validates a received cross-shard message
    pub fn validate_message(&self, message: &CrossShardMessage) -> Result<(), ValidationError> { ... }
    
    // Handles a timeout for a cross-shard operation
    pub fn handle_timeout(&self, operation: &CrossShardOperation) -> TimeoutAction { ... }
}

4. Reputation System (reputation.rs)

The reputation system tracks validator performance and reliability.

pub struct ReputationSystem {
    // Validator reputation scores
    validator_scores: HashMap<ValidatorId, ReputationScore>,
    
    // History of reputation changes
    reputation_history: VecDeque<ReputationChange>,
    
    // Reputation update rules
    update_rules: Vec<ReputationRule>,
}

impl ReputationSystem {
    // Creates a new reputation system
    pub fn new(validators: &[ValidatorId]) -> Self { ... }
    
    // Updates a validator's reputation
    pub fn update_reputation(&mut self, validator_id: &ValidatorId, event: ReputationEvent) { ... }
    
    // Gets a validator's current reputation score
    pub fn get_reputation(&self, validator_id: &ValidatorId) -> Option<ReputationScore> { ... }
    
    // Selects validators for the next consensus round based on reputation
    pub fn select_validators(&self, count: usize) -> Vec<ValidatorId> { ... }
    
    // Determines if a validator should be excluded due to poor reputation
    pub fn should_exclude(&self, validator_id: &ValidatorId) -> bool { ... }
}

Consensus Flow

1. Block Proposal Phase

1. The current primary validator collects transactions from the mempool
2. Transactions are validated and organized into a block proposal
3. The block proposal is signed using quantum-resistant cryptography
4. The proposal is broadcast to all validators

// Primary validator creates a block proposal
let transactions = mempool.get_transactions(max_tx_count);
let block_proposal = BlockProposal::new(
    previous_block_hash,
    block_height,
    transactions,
    timestamp,
    primary_validator_id,
);

// Sign the proposal with quantum-resistant signature
let signature = quantum_crypto.sign(&block_proposal.hash(), &primary_private_key);
block_proposal.set_signature(signature);

// Broadcast to all validators
network.broadcast(ConsensusMessage::Proposal(block_proposal));

2. Preparation Phase

1. Validators receive the block proposal and verify its validity
2. Each validator sends a PREPARE message if the proposal is valid
3. Validators collect PREPARE messages from other validators
4. Once 2f+1 PREPARE messages are collected, the validator moves to the commit phase

// Validator receives a block proposal
fn handle_proposal(&mut self, proposal: BlockProposal) -> Result<(), ConsensusError> {
    // Verify proposal validity
    if !self.verify_proposal(&proposal) {
        return Err(ConsensusError::InvalidProposal);
    }
    
    // Create and sign PREPARE message
    let prepare_message = PrepareMessage::new(
        proposal.hash(),
        self.view,
        self.validator_id,
    );
    let signature = self.crypto.sign(&prepare_message.hash(), &self.private_key);
    prepare_message.set_signature(signature);
    
    // Broadcast PREPARE message
    self.network.broadcast(ConsensusMessage::Prepare(prepare_message));
    
    // Update internal state
    self.state = ConsensusState::Preparing(proposal.hash());
    
    Ok(())
}

// Validator collects PREPARE messages
fn handle_prepare(&mut self, prepare: PrepareMessage) -> Result<ConsensusAction, ConsensusError> {
    // Verify the PREPARE message
    if !self.verify_prepare(&prepare) {
        return Err(ConsensusError::InvalidPrepare);
    }
    
    // Add to collected PREPAREs
    self.prepare_messages.insert(prepare.validator_id(), prepare);
    
    // Check if we have enough PREPARE messages (2f+1)
    if self.prepare_messages.len() >= self.quorum_size() {
        // Move to COMMIT phase
        let commit_message = self.create_commit_message(prepare.block_hash());
        self.network.broadcast(ConsensusMessage::Commit(commit_message));
        self.state = ConsensusState::Committing(prepare.block_hash());
        
        return Ok(ConsensusAction::MoveToCommit);
    }
    
    Ok(ConsensusAction::None)
}

3. Commit Phase

1. Once in the commit phase, validators send COMMIT messages
2. Validators collect COMMIT messages from other validators
3. Once 2f+1 COMMIT messages are collected, the block is finalized
4. The block is added to the blockchain and state is updated

// Validator handles COMMIT messages
fn handle_commit(&mut self, commit: CommitMessage) -> Result<ConsensusAction, ConsensusError> {
    // Verify the COMMIT message
    if !self.verify_commit(&commit) {
        return Err(ConsensusError::InvalidCommit);
    }
    
    // Add to collected COMMITs
    self.commit_messages.insert(commit.validator_id(), commit);
    
    // Check if we have enough COMMIT messages (2f+1)
    if self.commit_messages.len() >= self.quorum_size() {
        // Finalize the block
        let block = self.pending_blocks.get(&commit.block_hash()).unwrap();
        self.finalize_block(block);
        
        // Reset consensus state for next round
        self.reset_consensus_state();
        
        return Ok(ConsensusAction::FinalizeBlock(block.clone()));
    }
    
    Ok(ConsensusAction::None)
}

// Finalizing a block
fn finalize_block(&mut self, block: &Block) -> Result<(), ConsensusError> {
    // Add block to blockchain
    self.blockchain.add_block(block.clone())?;
    
    // Update state with transactions in the block
    for tx in block.transactions() {
        self.state_manager.apply_transaction(tx)?;
    }
    
    // Update validator set if needed
    if block.has_validator_changes() {
        self.update_validator_set(block.validator_changes());
    }
    
    // Notify other components
    self.event_bus.publish(BlockchainEvent::BlockFinalized(block.clone()));
    
    Ok(())
}

4. View Change

If the primary validator is suspected to be faulty (e.g., no proposal for too long), a view change is initiated:

1. Validators send VIEW-CHANGE messages
2. Once 2f+1 VIEW-CHANGE messages are collected, a new view begins
3. The primary for the new view is selected based on a deterministic formula

// Initiating a view change
fn initiate_view_change(&mut self) -> Result<(), ConsensusError> {
    // Create VIEW-CHANGE message
    let view_change = ViewChangeMessage::new(
        self.view,
        self.view + 1,
        self.validator_id,
        self.last_finalized_block_hash,
    );
    
    // Sign and broadcast VIEW-CHANGE message
    let signature = self.crypto.sign(&view_change.hash(), &self.private_key);
    view_change.set_signature(signature);
    self.network.broadcast(ConsensusMessage::ViewChange(view_change));
    
    // Update internal state
    self.state = ConsensusState::ViewChanging(self.view + 1);
    
    Ok(())
}

// Handling VIEW-CHANGE messages
fn handle_view_change(&mut self, view_change: ViewChangeMessage) -> Result<ConsensusAction, ConsensusError> {
    // Verify VIEW-CHANGE message
    if !self.verify_view_change(&view_change) {
        return Err(ConsensusError::InvalidViewChange);
    }
    
    // Add to collected VIEW-CHANGEs
    self.view_change_messages.insert(view_change.validator_id(), view_change);
    
    // Check if we have enough VIEW-CHANGE messages (2f+1)
    if self.view_change_messages.len() >= self.quorum_size() {
        // Execute view change
        self.execute_view_change(view_change.new_view());
        
        return Ok(ConsensusAction::ViewChanged(view_change.new_view()));
    }
    
    Ok(ConsensusAction::None)
}

// Executing a view change
fn execute_view_change(&mut self, new_view: ViewNumber) -> Result<(), ConsensusError> {
    // Update view number
    self.view = new_view;
    
    // Select new primary
    self.primary = self.select_primary_for_view(new_view);
    
    // Reset consensus state
    self.reset_consensus_state();
    
    // If I am the new primary, start a new round
    if self.primary == self.validator_id {
        self.start_new_round()?;
    }
    
    Ok(())
}

Cross-Shard Transaction Flow

Cross-shard transactions follow a two-phase commit protocol:

1. Preparation Phase

1. The originating shard coordinator initiates the transaction
2. Resource requirements are identified across all involved shards
3. Each shard attempts to lock the required resources
4. If all resources are successfully locked, the preparation phase is complete

// Initiating a cross-shard transaction
fn initiate_cross_shard_tx(&mut self, tx: Transaction) -> Result<(), CrossShardError> {
    // Identify involved shards
    let involved_shards = self.identify_involved_shards(&tx);
    
    // Create cross-shard transaction record
    let cross_shard_tx = CrossShardTransaction::new(
        tx.id(),
        self.shard_id,
        involved_shards.clone(),
        tx.clone(),
    );
    
    // Store the transaction
    self.active_transactions.insert(tx.id(), cross_shard_tx);
    
    // Send PREPARE messages to all involved shards
    for shard_id in involved_shards {
        if shard_id != self.shard_id {
            let prepare_message = CrossShardMessage::Prepare(
                tx.id(),
                self.shard_id,
                shard_id,
                tx.resource_requirements_for_shard(shard_id),
            );
            
            self.send_to_shard(shard_id, prepare_message);
        }
    }
    
    // Lock local resources
    self.resource_manager.lock_resources(tx.resource_requirements_for_shard(self.shard_id))?;
    
    Ok(())
}

// Handling a PREPARE message from another shard
fn handle_prepare(&mut self, prepare: CrossShardPrepareMessage) -> Result<(), CrossShardError> {
    // Try to lock requested resources
    match self.resource_manager.try_lock_resources(prepare.resource_requirements()) {
        Ok(_) => {
            // Resources locked successfully, send PREPARED response
            let prepared_message = CrossShardMessage::Prepared(
                prepare.tx_id(),
                self.shard_id,
                prepare.originating_shard(),
            );
            
            self.send_to_shard(prepare.originating_shard(), prepared_message);
            
            // Record the prepared transaction
            let tx_record = CrossShardTransactionRecord::new(
                prepare.tx_id(),
                prepare.originating_shard(),
                prepare.resource_requirements(),
            );
            
            self.prepared_transactions.insert(prepare.tx_id(), tx_record);
            
            Ok(())
        },
        Err(e) => {
            // Failed to lock resources, send ABORT
            let abort_message = CrossShardMessage::Abort(
                prepare.tx_id(),
                self.shard_id,
                prepare.originating_shard(),
                format!("Failed to lock resources: {}", e),
            );
            
            self.send_to_shard(prepare.originating_shard(), abort_message);
            
            Err(e)
        }
    }
}

2. Commit Phase

1. If preparation is successful, the coordinator sends COMMIT messages
2. Each shard executes its portion of the transaction
3. Results are reported back to the coordinator
4. The coordinator finalizes the transaction

// Coordinator decides to commit after all shards are prepared
fn commit_cross_shard_tx(&mut self, tx_id: &TransactionId) -> Result<(), CrossShardError> {
    // Get the cross-shard transaction
    let tx = self.active_transactions.get(tx_id)
        .ok_or(CrossShardError::TransactionNotFound)?;
    
    // Verify all shards are prepared
    if !tx.all_shards_prepared() {
        return Err(CrossShardError::NotAllShardsPrepared);
    }
    
    // Send COMMIT messages to all involved shards
    for shard_id in tx.involved_shards() {
        if shard_id != self.shard_id {
            let commit_message = CrossShardMessage::Commit(
                *tx_id,
                self.shard_id,
                shard_id,
            );
            
            self.send_to_shard(shard_id, commit_message);
        }
    }
    
    // Execute local portion of the transaction
    self.transaction_executor.execute(&tx.transaction())?;
    
    // Update transaction state
    tx.set_state(CrossShardTransactionState::Committing);
    
    Ok(())
}

// Handling a COMMIT message from the coordinator
fn handle_commit(&mut self, commit: CrossShardCommitMessage) -> Result<(), CrossShardError> {
    // Get the prepared transaction
    let tx_record = self.prepared_transactions.get(&commit.tx_id())
        .ok_or(CrossShardError::TransactionNotFound)?;
    
    // Execute the transaction
    match self.transaction_executor.execute_prepared(tx_record) {
        Ok(result) => {
            // Send COMMITTED message back to coordinator
            let committed_message = CrossShardMessage::Committed(
                commit.tx_id(),
                self.shard_id,
                commit.originating_shard(),
                result,
            );
            
            self.send_to_shard(commit.originating_shard(), committed_message);
            
            // Clean up resources
            self.resource_manager.convert_locks_to_permanent(tx_record.resource_requirements());
            self.prepared_transactions.remove(&commit.tx_id());
            
            Ok(())
        },
        Err(e) => {
            // Send FAILED message back to coordinator
            let failed_message = CrossShardMessage::Failed(
                commit.tx_id(),
                self.shard_id,
                commit.originating_shard(),
                format!("Execution failed: {}", e),
            );
            
            self.send_to_shard(commit.originating_shard(), failed_message);
            
            // Release resources
            self.resource_manager.release_locks(tx_record.resource_requirements());
            self.prepared_transactions.remove(&commit.tx_id());
            
            Err(e.into())
        }
    }
}

3. Abort Handling

If any shard fails during preparation or commit, the transaction is aborted:

// Coordinator aborts a cross-shard transaction
fn abort_cross_shard_tx(&mut self, tx_id: &TransactionId, reason: &str) -> Result<(), CrossShardError> {
    // Get the cross-shard transaction
    let tx = self.active_transactions.get(tx_id)
        .ok_or(CrossShardError::TransactionNotFound)?;
    
    // Send ABORT messages to all involved shards
    for shard_id in tx.involved_shards() {
        if shard_id != self.shard_id {
            let abort_message = CrossShardMessage::Abort(
                *tx_id,
                self.shard_id,
                shard_id,
                reason.to_string(),
            );
            
            self.send_to_shard(shard_id, abort_message);
        }
    }
    
    // Release local resources
    self.resource_manager.release_locks(tx.local_resource_requirements());
    
    // Update transaction state and record reason
    tx.set_state(CrossShardTransactionState::Aborted(reason.to_string()));
    
    // Clean up after timeout
    self.scheduler.schedule_cleanup(*tx_id, Duration::from_secs(60));
    
    Ok(())
}

// Handling an ABORT message
fn handle_abort(&mut self, abort: CrossShardAbortMessage) -> Result<(), CrossShardError> {
    // Get the prepared transaction
    if let Some(tx_record) = self.prepared_transactions.remove(&abort.tx_id()) {
        // Release locked resources
        self.resource_manager.release_locks(tx_record.resource_requirements());
        
        // Log the abort
        self.logger.info(
            "Cross-shard transaction aborted: {} from shard {} reason: {}",
            abort.tx_id(),
            abort.originating_shard(),
            abort.reason(),
        );
    }
    
    Ok(())
}

Performance Characteristics

The consensus algorithms are optimized for the following performance targets:

• Transaction Throughput: Up to 22,680,000 TPS for small transactions (100 bytes) and 608,000 TPS for large transactions (10KB)
• Block Time: 1-3 seconds under normal network conditions
• Finality: Absolute finality after 2-3 blocks
• Fault Tolerance: Can tolerate up to f Byzantine nodes in a 3f+1 system
• Shard Count: Support for up to 64 independent shards
• Cross-Shard Latency: 2-4 seconds for cross-shard transactions

Security Considerations

• Adaptive Security: Security parameters adjust based on transaction value
• Quantum Resistance: All cryptographic operations use post-quantum algorithms
• Leader Selection: Leader selection uses verifiable random functions to prevent manipulation
• Reputation System: Validators with poor performance or suspicious behavior are excluded
• Formal Verification: Critical consensus paths are formally verified

Configuration Parameters

The consensus mechanisms can be configured through the following parameters:

pub struct ConsensusConfig {
    // Maximum block size in bytes
    pub max_block_size: usize,
    
    // Maximum number of transactions per block
    pub max_transactions_per_block: usize,
    
    // Block time target in milliseconds
    pub block_time_ms: u64,
    
    // View change timeout in milliseconds
    pub view_change_timeout_ms: u64,
    
    // Minimum number of validators
    pub min_validators: usize,
    
    // Maximum number of validators
    pub max_validators: usize,
    
    // Number of blocks after which a block is considered final
    pub finality_depth: u64,
    
    // Cross-shard transaction timeout in milliseconds
    pub cross_shard_timeout_ms: u64,
    
    // Quantum security level (bits)
    pub quantum_security_bits: u32,
}

Usage Examples

Basic Consensus Operation

// Initialize consensus with validators
let validators = vec![
    Validator::new(ValidatorId(1), PublicKey::from_hex("...")),
    Validator::new(ValidatorId(2), PublicKey::from_hex("...")),
    Validator::new(ValidatorId(3), PublicKey::from_hex("...")),
    Validator::new(ValidatorId(4), PublicKey::from_hex("...")),
];

let config = QuantumSVBFTConfig {
    block_time_ms: 2000,
    view_change_timeout_ms: 10000,
    max_transactions_per_block: 10000,
    quantum_security_bits: 256,
};

let mut consensus = QuantumSVBFT::new(validators, config);

// Primary validator proposes a block
if consensus.is_primary() {
    let transactions = mempool.get_pending_transactions(1000);
    let block = consensus.propose_block(transactions)?;
    network.broadcast(ConsensusMessage::Proposal(block));
}

// Non-primary validators process messages
while let Some(message) = network.next_message() {
    match message {
        ConsensusMessage::Proposal(proposal) => {
            consensus.process_proposal(proposal)?;
        },
        ConsensusMessage::Prepare(prepare) => {
            consensus.process_prepare(prepare)?;
        },
        ConsensusMessage::Commit(commit) => {
            consensus.process_commit(commit)?;
        },
        ConsensusMessage::ViewChange(view_change) => {
            consensus.process_view_change(view_change)?;
        },
    }
}

Cross-Shard Transaction

// Create a cross-shard transaction
let input1 = TransactionInput {
    shard_id: ShardId(1),
    account: AccountId(0x123),
    amount: 100,
};

let output1 = TransactionOutput {
    shard_id: ShardId(2),
    account: AccountId(0x456),
    amount: 100,
};

let cross_shard_tx = Transaction::new(
    vec![input1],
    vec![output1],
    NetworkId(1),
);

// Submit the transaction to the originating shard
let shard1_coordinator = network.get_shard_coordinator(ShardId(1));
shard1_coordinator.submit_transaction(cross_shard_tx)?;

// The coordinator handles the cross-shard protocol
// 1. Preparation phase
shard1_coordinator.prepare_transaction(&cross_shard_tx.id())?;

// 2. Wait for all shards to be prepared
while !shard1_coordinator.all_shards_prepared(&cross_shard_tx.id()) {
    thread::sleep(Duration::from_millis(100));
}

// 3. Commit phase
shard1_coordinator.commit_transaction(&cross_shard_tx.id())?;

// 4. Wait for all shards to commit
while !shard1_coordinator.all_shards_committed(&cross_shard_tx.id()) {
    thread::sleep(Duration::from_millis(100));
}

println!("Cross-shard transaction completed successfully!");

Future Developments

Planned enhancements for the consensus mechanisms include:

1. Parallel Consensus: Running multiple consensus instances in parallel
2. Hierarchical Consensus: Consensus at multiple levels for scalability
3. Threshold Signatures: Reducing communication complexity with threshold cryptography
4. Validator Rotation: Dynamic rotation of validators for improved security
5. Deep Sharding: Nested shards for extreme scalability