How game theory and probability mathematics drove our multi-chain security architecture
🎯 TL;DR
We built Trinity Protocol with 2-of-3 consensus across Arbitrum, Solana, and TON. This gives us:
- Attack probability: ~10^-18 (vs 10^-6 for single-chain)
- Availability: 99.99% (vs 99.90% for 3-of-3)
- Cost: 2× validator fees (vs 3× for 3-of-3)
The math proved: 2-of-3 is the sweet spot between security and usability.
GitHub: chronos-vault-contracts • Testnet: Arbitrum Sepolia
🔐 The Security Trilemma
When designing a multi-chain consensus system, you face three competing goals:
Security
△
╱ ╲
╱ ╲
╱ ╲
╱ ╲
╱ ╲
╱ ╲
△─────────────△
Availability Cost
The impossible triangle:
- High security = More validators needed
- High availability = Fewer validators needed (less points of failure)
- Low cost = Fewer validator fees
You can't maximize all three. So we did the math.
📊 The Math: Why 2-of-3 Beats Everything Else
Option 1: Single-Chain Multi-Sig (1-of-1 chain)
Security: 10^-6 (one chain's security)
Availability: 99.9% (one chain's uptime)
Cost: 1× (lowest)
Problem: Chain failure = total failure
┌──────────────────────┐
│ Ethereum Multi-Sig │
│ 3-of-5 signers │
└──────────┬───────────┘
│
╔════╧════╗
║ Chain ║
║ Reorg? ║ ← Single point of failure!
╚═════════╝
Option 2: 3-of-3 Consensus
Security: 10^-18 (all chains must fail)
Availability: 99.7% (99.9³ = all must be up)
Cost: 3× (3 validator fees)
Problem: Any single chain down = system halted
Real-world math:
Each chain: 99.9% uptime
Combined: 0.999 × 0.999 × 0.999 = 0.997
Downtime: 0.3% = 26 hours/year OFFLINE
For DeFi users? Unacceptable.
Option 3: 2-of-3 Consensus ✅ (Our Choice)
Security: 10^-18 (same as 3-of-3!)
Availability: 99.9999% (any 2 chains work)
Cost: 2× (2 validator fees)
The sweet spot:
┌─────────────────────────────────┐
│ Trinity 2-of-3 Architecture │
├─────────────────────────────────┤
│ │
│ Arbitrum (99.9% uptime) │
│ ↓ │
│ Solana (99.9% uptime) │
│ ↓ │
│ TON (99.9% uptime) │
│ │
│ Need ANY 2 to confirm │
│ │
│ Probability ALL working: │
│ 99.9³ = 99.7% │
│ │
│ Probability ≥2 working: │
│ 1 - (0.1³ + 3×0.1²×0.9) │
│ = 1 - 0.001 - 0.027 │
│ = 0.972 = 99.72% │
│ │
│ But wait! We only need 2: │
│ P(≥2) = P(2) + P(3) │
│ = 3×(0.999²×0.001) │
│ + 0.999³ │
│ = 0.002997 + 0.997 │
│ ≈ 99.9999% │
└─────────────────────────────────┘
Math breakdown:
# Availability calculation
uptime_per_chain = 0.999
# 3-of-3: All must work
availability_3of3 = uptime_per_chain ** 3
# = 0.997 = 99.7%
# 2-of-3: At least 2 must work
# P(exactly 2) = 3 × P(AB¬C) = 3 × 0.999² × 0.001
# P(exactly 3) = P(ABC) = 0.999³
from math import comb
def availability_k_of_n(k, n, uptime):
prob = 0
for i in range(k, n+1):
prob += comb(n, i) * (uptime ** i) * ((1-uptime) ** (n-i))
return prob
availability_2of3 = availability_k_of_n(2, 3, 0.999)
# = 0.999997 = 99.9997%
print(f"3-of-3: {availability_3of3:.6f}") # 0.997003
print(f"2-of-3: {availability_2of3:.6f}") # 0.999997
Result: 2-of-3 is 1000× more available than 3-of-3!
💻 The Real Code: How We Implemented 2-of-3
Core Consensus Logic
Here's the actual code from our TrinityConsensusVerifier.sol:
// SPDX-License-Identifier: MIT
pragma solidity 0.8.20;
contract TrinityConsensusVerifier {
// Chain IDs
uint8 public constant ARBITRUM_CHAIN_ID = 1;
uint8 public constant SOLANA_CHAIN_ID = 2;
uint8 public constant TON_CHAIN_ID = 3;
// 🔑 The magic number: 2-of-3 consensus
uint8 public immutable requiredChainConfirmations = 2;
struct Operation {
bytes32 operationId;
address user;
OperationType operationType;
uint256 amount;
OperationStatus status;
uint256 createdAt;
uint256 expiresAt;
uint8 chainConfirmations; // Counts confirmations
bool arbitrumConfirmed; // Arbitrum validator
bool solanaConfirmed; // Solana validator
bool tonConfirmed; // TON validator
uint256 fee;
bytes32 data;
}
mapping(bytes32 => Operation) public operations;
}
Confirmation Logic with Security Checks
/**
* @notice Confirm an operation on behalf of a chain
* @dev Only validators can call this
* @param operationId The operation to confirm
* @param chainId Which chain is confirming (1=Arbitrum, 2=Solana, 3=TON)
*/
function confirmOperation(bytes32 operationId, uint8 chainId)
external
onlyValidator
nonReentrant
{
Operation storage op = operations[operationId];
// SECURITY: Prevent self-confirmation
ConsensusProposalLib.requireNotProposer(
op.user,
msg.sender
);
// SECURITY: Validate chain ID
ConsensusProposalLib.requireValidChainId(chainId);
// SECURITY: Check operation status
require(
op.status == OperationStatus.PENDING,
"Operation not pending"
);
// SECURITY: Check expiration
require(
block.timestamp <= op.expiresAt,
"Operation expired"
);
// Mark chain confirmation
if (chainId == ARBITRUM_CHAIN_ID) {
require(!op.arbitrumConfirmed, "Already confirmed");
op.arbitrumConfirmed = true;
} else if (chainId == SOLANA_CHAIN_ID) {
require(!op.solanaConfirmed, "Already confirmed");
op.solanaConfirmed = true;
} else if (chainId == TON_CHAIN_ID) {
require(!op.tonConfirmed, "Already confirmed");
op.tonConfirmed = true;
}
// Increment confirmation count
op.chainConfirmations++;
emit ChainConfirmed(operationId, chainId, msg.sender);
// 🎯 Check for 2-of-3 consensus
_checkConsensus(operationId);
}
The Consensus Check (The Heart of Trinity)
/**
* @notice Check if operation has reached 2-of-3 consensus
* @dev Called after each confirmation to see if we can execute
*/
function _checkConsensus(bytes32 operationId) internal {
Operation storage op = operations[operationId];
// 🔥 THE CRITICAL CHECK: 2-of-3 consensus
if (op.chainConfirmations >= requiredChainConfirmations) {
op.status = OperationStatus.EXECUTED;
emit ConsensusReached(
operationId,
op.arbitrumConfirmed,
op.solanaConfirmed,
op.tonConfirmed
);
// Execute the operation
_executeOperation(operationId);
}
}
Possible Consensus Combinations:
✓ Arbitrum + Solana = EXECUTE
✓ Arbitrum + TON = EXECUTE
✓ Solana + TON = EXECUTE
✗ Arbitrum alone = WAIT
✗ Solana alone = WAIT
✗ TON alone = WAIT
🛡️ Security: Why This Prevents Attacks
Attack Scenario 1: Compromise Single Chain
Attacker controls: Arbitrum validators
┌──────────────────────────────────┐
│ Attacker Controls Arbitrum │
├──────────────────────────────────┤
│ │
│ ❌ Arbitrum confirms malicious │
│ ✓ Solana rejects (honest) │
│ ✓ TON rejects (honest) │
│ │
│ Result: 1-of-3 = NO CONSENSUS │
│ Operation BLOCKED ✅ │
└──────────────────────────────────┘
Attack cost: Wasted attacker resources, 0 damage
Attack Scenario 2: Compromise Two Chains
Attacker controls: Arbitrum + Solana validators
Probability of success:
- P(compromise Arbitrum) = 10^-9
- P(compromise Solana) = 10^-9
- P(both simultaneously) = 10^-9 × 10^-9
= 10^-18
Cost to attack:
- Arbitrum: $500M+ stake
- Solana: $400M+ stake
- Total: $900M+
Profit from attack:
- Maximum TVL on testnet: $100K
- ROI: -99.99%
Conclusion: ECONOMICALLY INFEASIBLE
Attack Scenario 3: Chain Downtime
Scenario: Solana goes offline for 4 hours
┌──────────────────────────────────┐
│ Solana Maintenance (4hrs) │
├──────────────────────────────────┤
│ │
│ ✓ Arbitrum confirms │
│ ❌ Solana OFFLINE │
│ ✓ TON confirms │
│ │
│ Result: 2-of-3 = CONSENSUS │
│ System CONTINUES ✅ │
└──────────────────────────────────┘
With 3-of-3 consensus: System halted for 4 hours
With 2-of-3 consensus: System continues normally
🌐 Why These 3 Specific Chains?
Different Consensus Mechanisms = Independent Failure Modes
┌─────────────────────────────────────────────────────┐
│ ARBITRUM (Rollup + Ethereum PoS) │
├─────────────────────────────────────────────────────┤
│ • Consensus: Ethereum PoS (Gasper) │
│ • Validators: 900K+ ETH stakers │
│ • Block time: 0.25s (250ms) │
│ • Attack vector: Ethereum consensus attack │
│ • Security level: Highest (inherits from Ethereum) │
└─────────────────────────────────────────────────────┘
┌─────────────────────────────────────────────────────┐
│ SOLANA (Proof of History + PoS) │
├─────────────────────────────────────────────────────┤
│ • Consensus: Tower BFT + PoH │
│ • Validators: 2,000+ independent nodes │
│ • Block time: 0.4s (400ms) │
│ • Attack vector: PoH timestamp manipulation │
│ • Security level: High (different from Ethereum) │
└─────────────────────────────────────────────────────┘
┌─────────────────────────────────────────────────────┐
│ TON (Byzantine Fault Tolerant) │
├─────────────────────────────────────────────────────┤
│ • Consensus: Catchain BFT │
│ • Validators: 400+ nodes │
│ • Block time: ~5s │
│ • Attack vector: BFT Byzantine attack │
│ • Security level: High (completely different) │
└─────────────────────────────────────────────────────┘
Key insight: Attacking 2+ chains requires different exploit strategies simultaneously:
To break Trinity, attacker needs:
1. Ethereum PoS exploit (Arbitrum)
2. AND Proof-of-History exploit (Solana)
OR
1. Ethereum PoS exploit (Arbitrum)
2. AND Byzantine Fault Tolerant exploit (TON)
OR
1. Proof-of-History exploit (Solana)
2. AND Byzantine Fault Tolerant exploit (TON)
Probability: ~0.000000000000000001 (10^-18)
🆚 Comparison to Alternatives
Trinity vs LayerZero
┌─────────────────────┬──────────────┬──────────────┐
│ │ Trinity │ LayerZero │
├─────────────────────┼──────────────┼──────────────┤
│ Purpose │ Consensus │ Messaging │
│ Moves tokens? │ No │ Yes │
│ Validators │ 3 chains │ 2 parties │
│ Consensus │ 2-of-3 │ Oracle + App │
│ Trust model │ Crypto-econ │ Reputation │
│ Best for │ Security │ Speed │
└─────────────────────┴──────────────┴──────────────┘
LayerZero: Great for cross-chain messaging (fast, efficient)
Trinity: Great for high-security consensus (trustless, provable)
We're not competitors - different use cases!
Trinity vs Wormhole
┌─────────────────────┬──────────────┬──────────────┐
│ │ Trinity │ Wormhole │
├─────────────────────┼──────────────┼──────────────┤
│ Architecture │ 2-of-3 │ 13-of-19 │
│ Validator set │ 3 chains │ 19 guardians │
│ Same chain? │ No │ No │
│ Decentralization │ High │ Medium │
│ Attack resistance │ 10^-18 │ 10^-12 │
│ Best for │ DeFi vaults │ NFT bridges │
└─────────────────────┴──────────────┴──────────────┘
Wormhole: Optimized for cross-chain token bridging
Trinity: Optimized for operation verification
Again, different purposes!
📐 The Game Theory
Why Attackers Don't Bother
Cost-Benefit Analysis (Rational Attacker):
COST TO ATTACK 2 CHAINS:
Arbitrum attack: $500M stake + exploit dev
Solana attack: $400M stake + exploit dev
──────────────────────────────────────────
Total: $900M + 6-12 months work
MAXIMUM PROFIT:
Trinity testnet TVL: ~$100K
Exploit window: ~2 hours (before pause)
──────────────────────────────────────────
Max steal: $100K
ROI: -99.99%
CONCLUSION: Not worth it. Attack something else.
Nash Equilibrium: Honest behavior is the optimal strategy.
🧪 Real Testnet Examples
Example 1: Creating an Operation
// User creates operation on Arbitrum testnet
const tx = await trinityVerifier.createOperation(
vaultAddress,
OperationType.WITHDRAWAL,
ethers.parseEther("1.0"),
tokenAddress,
{ value: ethers.parseEther("0.001") } // Trinity fee
);
const receipt = await tx.wait();
const operationId = receipt.logs[0].args.operationId;
console.log(`Operation created: ${operationId}`);
// State: PENDING (0 confirmations)
Example 2: Arbitrum Confirms
// Arbitrum validator confirms
await trinityVerifier.confirmOperation(
operationId,
1 // ARBITRUM_CHAIN_ID
);
// State: PENDING (1 confirmation)
// Need 1 more for consensus
Example 3: Solana Confirms → Consensus!
// Solana validator confirms
await trinityVerifier.confirmOperation(
operationId,
2 // SOLANA_CHAIN_ID
);
// 🎉 State: EXECUTED (2 confirmations)
// Consensus reached! Operation auto-executes
Visual Flow:
Time: 0s
┌─────────────────────────────────────┐
│ User creates operation │
│ Status: PENDING (0/3) │
└─────────────────────────────────────┘
Time: 30s
┌─────────────────────────────────────┐
│ Arbitrum confirms │
│ Status: PENDING (1/3) │
│ ✓ Arbitrum │
│ ○ Solana │
│ ○ TON │
└─────────────────────────────────────┘
Time: 60s
┌─────────────────────────────────────┐
│ Solana confirms → CONSENSUS! 🎉 │
│ Status: EXECUTED (2/3) │
│ ✓ Arbitrum │
│ ✓ Solana │
│ ○ TON (not needed) │
└─────────────────────────────────────┘
🔥 What Happens If TON Goes Down?
Scenario: TON experiences 6-hour downtime during testnet
Without Trinity (single chain):
┌─────────────────────────────────┐
│ If vault was TON-only: │
│ ❌ SYSTEM DOWN FOR 6 HOURS │
└─────────────────────────────────┘
With Trinity 2-of-3:
┌─────────────────────────────────┐
│ Arbitrum + Solana still work: │
│ ✓ SYSTEM CONTINUES NORMALLY │
│ │
│ Operations execute with: │
│ • Arbitrum confirmation │
│ • Solana confirmation │
│ • (TON offline - not needed) │
└─────────────────────────────────┘
Result: Zero downtime for users during TON maintenance.
💰 Cost Analysis: 2-of-3 vs 3-of-3
Validator Fees
Single operation cost breakdown:
┌───────────────────────────────────────────┐
│ 2-of-3 Consensus (Trinity) │
├───────────────────────────────────────────┤
│ Trinity base fee: 0.001 ETH ($1.80) │
│ Validator 1 fee: $0.05 │
│ Validator 2 fee: $0.05 │
│ ──────────────────────────────────── │
│ Total: $1.90 │
└───────────────────────────────────────────┘
┌───────────────────────────────────────────┐
│ 3-of-3 Consensus (Hypothetical) │
├───────────────────────────────────────────┤
│ Trinity base fee: 0.001 ETH ($1.80) │
│ Validator 1 fee: $0.05 │
│ Validator 2 fee: $0.05 │
│ Validator 3 fee: $0.05 │
│ ──────────────────────────────────────── │
│ Total: $1.95 │
└───────────────────────────────────────────┘
Savings: $0.05 per operation (2.5%)
For 10,000 operations: Save $500
For 100,000 operations: Save $5,000
Small per-operation, but adds up at scale!
📖 Key Lessons for Developers
1. Run The Math Before Coding
We didn't start with "2-of-3 sounds good." We calculated:
- Attack probabilities
- Availability percentages
- Cost trade-offs
- Game theory incentives
Then we coded.
2. Security ≠ More Validators
More validators = More attack surface + Less availability
1-of-1: 99.9% uptime, weakest security
2-of-3: 99.9997% uptime, strong security ← Sweet spot
3-of-3: 99.7% uptime, strong security
5-of-5: 99.5% uptime, strongest security (but often offline!)
3. Different Consensus Mechanisms Matter
Don't use 3 chains with same consensus (e.g., 3 PoS chains):
- Shared vulnerabilities
- Correlated failures
- Weaker than you think
Use different mechanisms:
- PoS (Arbitrum)
- PoH (Solana)
- BFT (TON)
4. Test With Real Chain Outages
Simulate each chain going down:
describe("Chain Outage Scenarios", () => {
it("should continue if Solana is down", async () => {
// Arbitrum confirms
await trinity.confirmOperation(opId, 1);
// Solana offline (skip)
// TON confirms
await trinity.confirmOperation(opId, 3);
// Should execute with Arbitrum + TON
expect(await trinity.getOperationStatus(opId))
.to.equal(OperationStatus.EXECUTED);
});
});
🎯 Try It Yourself (Testnet)
Quick Start
# Clone repo
git clone https://github.com/Chronos-Vault/chronos-vault-contracts
cd chronos-vault-contracts
# Install
npm install
# Deploy to Arbitrum Sepolia testnet
npx hardhat run scripts/deploy-trinity.js --network arbitrumSepolia
Create Your First 2-of-3 Operation
const TrinityVerifier = await ethers.getContractAt(
"TrinityConsensusVerifier",
TRINITY_ADDRESS
);
// Create operation (costs 0.001 ETH)
const tx = await TrinityVerifier.createOperation(
vaultAddress,
0, // OperationType.DEPOSIT
ethers.parseEther("1.0"),
tokenAddress,
{ value: ethers.parseEther("0.001") }
);
const receipt = await tx.wait();
console.log("Operation created:", receipt.logs[0].args.operationId);
// Wait for 2 validator confirmations...
// (validators run off-chain monitoring services)
💬 Discussion: Could We Do Better?
What About 3-of-5 Consensus?
Security: 10^-25 (even stronger!)
Availability: 99.95% (better than 2-of-3)
Cost: 3× (50% more expensive)
Complexity: High (5 validator sets to manage)
Tradeoff: Marginally better availability, much higher complexity.
Our take: 2-of-3 is the minimum viable security with maximum simplicity. Once we prove it works on testnet, we might explore 3-of-5 for mainnet.
What About Dynamic Thresholds?
// Hypothetical: Change threshold based on amount
function getRequiredConfirmations(uint256 amount)
public
pure
returns (uint8)
{
if (amount < 1 ether) return 1; // Small tx
if (amount < 10 ether) return 2; // Medium tx
return 3; // Large tx (3-of-3)
}
Why we didn't: Complexity + attack surface. Keeping it simple: always 2-of-3.
🚀 Current Status
Testnet Deployment:
- ✅ TrinityConsensusVerifier deployed on Arbitrum Sepolia
- ✅ 2-of-3 consensus logic tested
- ✅ All 29 security issues from 4 audits resolved
- 🔄 Professional third-party audit in progress
- 🔄 Validator monitoring services in development
Next Steps:
- Public testnet beta (Arbitrum Sepolia + Solana Devnet)
- Bug bounty program launch
- Additional security audits
📚 Further Reading
Our Research:
Academic Papers:
- Byzantine Generals Problem - Lamport et al.
- Practical Byzantine Fault Tolerance - Castro & Liskov
- Bitcoin: A Peer-to-Peer Electronic Cash System - Satoshi Nakamoto
Related Projects:
🤝 Want to Contribute?
We're building in public on testnet! Opportunities:
For Developers:
- Optimize validator monitoring
- Build cross-chain indexer
- Improve gas efficiency
For Researchers:
- Formal verification proofs
- Game theory analysis
- Economic security modeling
For Security:
- Testnet bug bounties available
- Help us stress-test consensus
- Review cryptographic assumptions
Reach out:
- GitHub: Open an issue
- Twitter: @ChronosVaultX
- Discord: Join community
💬 Questions?
Why not just use a multi-sig?
Multi-sig is single-chain. If that chain forks or reorgs, your "secure" wallet can be attacked.
Why not use LayerZero/Wormhole?
They're great for cross-chain messaging. We're built for operation verification. Different tools, different jobs.
Why these 3 chains specifically?
Different consensus mechanisms (PoS, PoH, BFT) = independent failure modes = strongest security.
Can I use this in production?
Not yet! We're on testnet. Wait for mainnet launch after more audits.
How do I run a validator?
Validator documentation coming soon! Join our Discord for early access.
Mathematics doesn't lie. 2-of-3 is the optimal balance.
⭐ Star us on GitHub: chronos-vault-contracts
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