Libre Crosslink Whitepaper

Sovereign Bitcoin Custody and Cross-Chain Orchestration via Threshold Cryptography

Executive Summary

Libre Crosslink is a decentralized system that enables secure cross-chain transactions between Bitcoin and the Libre blockchain. This whitepaper introduces the architecture and technical implementation of Libre Crosslink, which leverages Multi-Party Computation (MPC) and Threshold Signature Schemes (TSS) to provide a trustless and secure mechanism for cross-chain asset transfers and dedicated vault infrastructure.

The system serves two primary purposes: 1) creating a trustless bridge for moving BTC value between Bitcoin and the Libre blockchains, and 2) providing institutional-grade, segregated vault custody for Bitcoin collateral in the Libre Lending ecosystem. By using threshold signatures, the system requires a minimum number of participants to agree on and sign transactions, ensuring no single entity can unilaterally control user funds.

Core Purposes

Libre Crosslink was designed with two distinct yet complementary purposes in mind:

1. Trustless Bitcoin-Libre Bridge

The primary purpose of Libre Crosslink is to create a fully decentralized bridge between the Bitcoin and Libre networks. This bridge enables:

• Bitcoin Scaling: By moving Bitcoin operations to the more scalable Libre blockchain, users can benefit from faster transactions and lower fees while maintaining a connection to the Bitcoin network.

• Programmable Bitcoin: Once bridged to Libre, Bitcoin becomes programmable through Libre's smart contract capabilities, unlocking use cases not possible on the Bitcoin blockchain alone.

• Trustless Operation: Unlike other bridge solutions that rely on centralized components or trusted custodians, Libre Crosslink operates in a completely trustless manner with no centralized elements.

2. MPC TSS Vault Solution for Libre Lending

The second purpose of Libre Crosslink is to provide a unique, secure vault infrastructure for the Libre Lending platform:

• Dedicated User Vaults: Each user of Libre Lending receives their own unique Bitcoin vault address, generated specifically for them by the Crosslink nodes.

• Segregated Storage: Users' Bitcoin collateral never combines with other users' funds, maintaining complete separation of assets at the blockchain level.

• Institutional-Grade Custody: The MPC TSS architecture provides institutional-grade security without institutional intermediaries, as custodial operations are performed by the decentralized network of Crosslink nodes.

• Direct Collateralization: Users can directly collateralize lending positions with Bitcoin held in their personal vaults, enabling Bitcoin-backed loans without surrendering custody to a centralized entity.

This dual-purpose architecture makes Libre Crosslink unique among cross-chain solutions, as it not only facilitates asset transfers but also provides essential infrastructure for decentralized financial applications on the Libre network.

Introduction

Problem Statement

Interoperability between different blockchain networks remains one of the most significant challenges in the cryptocurrency ecosystem. Traditional bridging solutions often rely on centralized custodians or trusted intermediaries, introducing single points of failure and counterparty risk. Users must trust these entities to handle their assets properly, which contradicts the trustless ethos of blockchain technology.

Additionally, using Bitcoin as collateral for lending typically requires depositing it with a centralized custodian, creating security vulnerabilities and introducing trust requirements. Current solutions fail to provide truly segregated vault infrastructure where users' Bitcoin remains completely separate from other users' funds.

Solution Overview

Libre Crosslink solves these problems by implementing a decentralized bridge between Bitcoin and Libre using threshold signature cryptography, which enables multiple parties to jointly control a single Bitcoin address without any single party having access to the complete private key. This approach eliminates the need for trusted intermediaries while maintaining the security properties of both blockchains.

For the vault solution, Libre Crosslink creates unique, dedicated Bitcoin addresses for each Libre Lending user. These addresses are controlled by the same MPC TSS infrastructure that powers the bridge, but are completely segregated from the bridge's pooled funds and from other users' vaults. This ensures that users' collateral remains separate and secure, while still benefiting from the security and decentralization of the MPC TSS system.

Unique Approach: Libre Smart Contract as Source of Truth

What sets Libre Crosslink apart from other bridge solutions is its use of the Libre blockchain smart contract system as the authoritative source of truth and coordinator for all bridge operations. Unlike traditional bridges that rely on external consensus mechanisms or oracles, Libre Crosslink leverages the inherent consensus properties of the Libre blockchain to coordinate bridge node actions, validate transactions, and maintain the state of cross-chain transfers.

This architecture offers several key advantages:

1. Single Source of Truth: The Libre smart contract maintains the canonical state of all bridge operations, eliminating inconsistencies that could arise from distributed state management.

2. Transparent Coordination: Bridge nodes coordinate their actions through the smart contract, making the entire process verifiable and auditable on-chain.

3. Efficient Dispute Resolution: Any conflicts or edge cases in the bridging process can be resolved deterministically by referring to the on-chain state.

4. Decentralized Governance: Bridge parameters and validator configurations can be managed through the same smart contract system, enabling governance from the Libre ecosystem.

By using the Libre smart contract as the foundation for coordination while leveraging TSS for secure key management, Libre Crosslink achieves a unique balance of security, transparency, and decentralization that isn't present in other cross-chain bridge designs.

Architecture

The Libre Crosslink bridge consists of several key components:

1. Smart Contract System: A set of smart contracts on the Libre blockchain that manage the pegging mechanism, transaction states, account management, and vault allocations. This acts as the source of truth and coordination layer for the entire bridge ecosystem.

2. Node Network: A distributed network of bridge nodes that collectively manage the bridge operations through MPC.

3. MPC Protocol Layer: Implements threshold signature schemes to collectively generate and manage cryptographic keys.

4. Transaction Monitoring System: Monitors both blockchains for bridge-related transaction events.

5. API Layer: Provides interfaces for users to interact with the bridge.

6. Vault Infrastructure: Manages dedicated Bitcoin addresses for individual users of Libre Lending, maintaining strict separation of funds.

Technical Implementation

Threshold Signature Scheme (TSS)

The bridge uses a $t$-of-$n$ threshold signature scheme, where $t$ nodes out of a total of $n$ nodes must cooperate to sign a transaction. Each node holds a share of the private key, and at least $t$ nodes must participate in the signing process to create a valid signature. This ensures that no single node or small group of compromised nodes can steal funds.

In a threshold signature scheme, a private key $d$ is distributed among $n$ participants such that each participant $i$ receives a share $d_i$. The key generation protocol ensures that:

1. No participant learns the complete private key $d$

2. Any subset of at least $t$ participants can collaboratively compute a valid signature

3. Any subset of fewer than $t$ participants cannot derive the private key or generate valid signatures

The mathematical foundation of the $t$-of-$n$ threshold scheme relies on Shamir's Secret Sharing, which is based on polynomial interpolation. For a private key $d$, a random polynomial $f(x)$ of degree $t-1$ is constructed:

$f(x) = d + a_1x + a_2x^2 + ... + a_{t-1}x^{t-1} \mod q$

Where:

• $d$ is the private key (secret)

• $a_1, a_2, ..., a_{t-1}$ are randomly selected coefficients

• $q$ is a large prime number (typically the order of the elliptic curve group)

Each participant $i$ receives a share $d_i = f(i)$, and any subset of $t$ shares can reconstruct the polynomial using Lagrange interpolation:

$d = f(0) = \sum_{i=1}^{t} d_i \cdot \lambda_i \mod q$

Where $\lambda_i$ is the Lagrange coefficient:

$\lambda_i = \prod_{j=1,j\neq i}^{t} \frac{0-j}{i-j} \mod q$

The implementation utilizes the BNB Chain's TSS library, which provides the cryptographic primitives for distributed key generation and signing. The key components of the TSS implementation include:

1. Key Generation Protocol: Generates a shared public key and distributes private key shares among the nodes without ever reconstructing the full private key.

2. Signing Protocol: Enables nodes to collectively sign transactions without revealing their key shares.

3. Resharing Protocol: Allows for the rotation of key shares without changing the underlying public key.

For ECDSA signatures, the system uses a more complex MPC protocol to calculate:

$r = g^k \mod p$$s = k^{-1}(z + rd) \mod q$

Where:

• $z$ is the hash of the message to be signed

• $k$ is a random nonce generated securely through MPC

• $d$ is the distributed private key

• $g$ is the generator point of the elliptic curve

• $p$ is the prime field modulus

• $q$ is the order of the curve

Bridge Operations

Peg-in (BTC to Libre)

1. User initiates a peg-in by sending BTC to the bridge-controlled Bitcoin address.

2. Bridge nodes monitor the Bitcoin blockchain and detect the incoming transaction.

3. Once sufficient confirmations are reached, bridge nodes propose the peg-in transaction on the Libre blockchain.

4. If enough nodes approve (meeting the threshold), the equivalent LBTC tokens are minted on the Libre blockchain and sent to the user's Libre account.

5. The transaction is marked as complete in the bridge's transaction history.

Let $T_{BTC}$ represent a Bitcoin transaction sending amount $A$ to the bridge address. The corresponding minting operation on Libre can be expressed as:

$T_{Libre}(mint) = \{dest: User_{Libre}, amount: A - fee, token: LBTC\}$

Where $fee$ is calculated based on the current fee rate:

$fee = A \times feeRate$

Peg-out (Libre to BTC)

1. User initiates a peg-out by sending LBTC tokens to the bridge contract on Libre with the destination Bitcoin address in the memo field.

2. Bridge contract locks the tokens and creates a pending peg-out record.

3. Bridge nodes detect the peg-out request and propose a Bitcoin transaction to transfer BTC to the user's Bitcoin address.

4. Nodes collectively sign the Bitcoin transaction using the threshold signature scheme.

5. The signed transaction is broadcast to the Bitcoin network.

6. Once the Bitcoin transaction is confirmed, the peg-out is marked as complete, and the LBTC tokens are burned.

For a peg-out transaction, let $T_{Libre}(burn)$ represent the burning of LBTC tokens on the Libre chain. The corresponding Bitcoin transaction is:

$T_{BTC}(transfer) = \{dest: User_{BTC}, amount: A - txFee, inputs: UTXO_{bridge}\}$

Where $txFee$ is the Bitcoin network fee estimated based on current network conditions.

Dedicated Vault Infrastructure

Libre Crosslink's vault solution extends the core MPC TSS infrastructure to create segregated Bitcoin custody for individual users:

Vault Creation Process

1. When a user wants to deposit Bitcoin collateral for Libre Lending, they request a unique vault through the Libre platform.

2. The bridge nodes perform a new TSS key generation specifically for this user, creating a unique key pair that is distinct from the bridge's main addresses and other users' vaults.

3. A new Bitcoin address is derived from this key pair and assigned exclusively to the user.

4. The Libre smart contract records this user-address mapping, establishing a verifiable link between the user's Libre account and their dedicated Bitcoin vault.

This process can be represented as:

$KeyGen(user) \rightarrow (d_{user}, P_{user})$$Address_{user} = AddressDerivation(P_{user})$

Where $d_{user}$ is the distributed private key for the user's vault (shared among nodes), and $P_{user}$ is the corresponding public key.

Vault Operations

When a user deposits Bitcoin to their vault:

1. User sends BTC to their dedicated vault address.

2. Bridge nodes detect this deposit and update the user's collateral balance on the Libre Lending platform.

3. The collateral can now be used to back loans or other financial operations.

When a user withdraws Bitcoin from their vault:

1. User initiates a withdrawal request through the Libre Lending platform.

2. Bridge nodes verify that the withdrawal complies with any lending constraints (e.g., maintaining required collateralization ratios).

3. If approved, nodes use their key shares specific to the user's vault to sign a Bitcoin transaction sending funds back to the user's specified address.

The segregated nature of this system ensures that each user's Bitcoin collateral is held in a completely separate address with its own unique key pair, providing maximum security and isolation of funds.

Smart Contract Implementation

The bridge smart contract (btcbridge) on the Libre blockchain manages several key aspects:

1. Account Management: Tracks users' Libre accounts and their associated Bitcoin addresses.

2. Transaction History: Maintains the state of all peg-in and peg-out transactions with their current status.

3. Token Operations: Interfaces with the LBTC token contract to mint and burn tokens as needed.

4. Vault Registry: Maps users to their dedicated vault addresses and tracks collateral balances.

As the central coordinator and source of truth for the bridge, the smart contract ensures that all bridge nodes operate with the same information and follow the same protocols, preventing inconsistencies in transaction processing. This is achieved through table structures that maintain the canonical state of all bridge-related transactions.

The contract uses several tables to track transaction states:

• Peg-in States: pending, minted, and confirmed

• Peg-out States: pending, transferring, transferred, completed, and canceled

• Vault States: active, locked, liquidating

The state transitions can be represented as a finite state machine:

For peg-in:$\text{pending} \xrightarrow{\text{minpeginttrx}} \text{minted} \xrightarrow{\text{finpeginttrx}} \text{confirmed}$

For peg-out:$\text{pending} \xrightarrow{\text{startpegout}} \text{transferring} \xrightarrow{\text{finpegout}} \text{transferred} \xrightarrow{\text{cmplpegout}} \text{completed}$

Alternative path for peg-out:$\text{pending} \xrightarrow{\text{cancelpegout}} \text{canceled}$

Each state transition is triggered by specific actions that must be approved by the threshold of bridge nodes, ensuring that all operations are properly authorized.

Node Network and Consensus

The bridge nodes form a peer-to-peer network to communicate and coordinate their actions. Each node runs the same software and participates in the MPC protocols. The consensus for bridge operations is achieved through the threshold signature mechanism, ensuring that a minimum number of nodes must agree on each action.

Bridge nodes derive their truth from the Libre blockchain, regularly checking the smart contract state to determine pending transactions and required actions. This eliminates the need for a separate consensus mechanism within the bridge node network, as the Libre blockchain's consensus is utilized as the foundation for coordination.

Key features of the node network include:

1. P2P Communication: Nodes use a peer-to-peer network to exchange protocol messages securely.

2. Block Height Tracking: Nodes monitor both Bitcoin and Libre blockchains to track the progress of transactions.

3. Transaction Processing: Nodes process pending transactions and collectively sign Bitcoin transactions.

4. Automatic Recovery: The system can recover from node failures as long as the threshold number of nodes remains operational.

5. Vault Management: Nodes maintain separate key shares for each user vault, enabling segregated custody while using the same infrastructure.

In mathematical terms, the security threshold guarantees that the system remains operational as long as the number of honest nodes $H$ satisfies:

$H \geq t$

And the system remains secure as long as the number of malicious nodes $M$ satisfies:

$M < t$

Security Considerations

Threat Model

The security design of Libre Crosslink considers several threat vectors:

1. Node Compromise: The system remains secure as long as fewer than $t$ nodes are compromised.

2. Network Partitioning: The bridge can withstand temporary network partitioning.

3. Blockchain Reorganizations: The bridge handles blockchain reorganizations by waiting for sufficient confirmations.

4. Malicious Inputs: Smart contracts validate all inputs to prevent attacks through malformed transactions.

5. Cross-Vault Contamination: The vault architecture ensures complete separation of user funds, preventing any possibility of cross-user contamination.

The security guarantee can be formally stated as:

Let $\mathcal{A}$ be an adversary that can compromise up to $t-1$ nodes. The probability of $\mathcal{A}$ successfully forging a signature or extracting the private key is negligible:

$Pr[\mathcal{A}(\{d_1, d_2, ..., d_{t-1}\}) \rightarrow d] \leq \epsilon$

Where $\epsilon$ is a negligibly small value and ${d_1, d_2, ..., d_{t-1}}$ represents the compromised key shares.

By using the Libre smart contract as the source of truth, the bridge is protected from attacks that might target inconsistencies between different components of a distributed system. All nodes refer to the same contract state, eliminating potential for discrepancies that could be exploited.

Protection Mechanisms

1. Threshold Security: Requires $t$ out of $n$ nodes to cooperate for any action.

2. Validation Checks: Multiple validation steps for transactions on both blockchains.

3. Confirmation Requirements: Enforces minimum confirmation requirements for Bitcoin transactions.

4. Rate Limiting: Prevents excessive transaction volume that could strain the system.

5. Transaction Batching: Optimizes cost efficiency by batching multiple transactions.

6. Segregated Key Management: Maintains separate key shares for each user vault, ensuring that compromise of one vault doesn't affect others.

The probability that a transaction is irreversible after $k$ confirmations on the Bitcoin blockchain can be approximated by:

$P(reversal) \approx \left(\frac{q}{p}\right)^k$

Where:

• $q$ is the attacker's hash power

• $p$ is the honest network's hash power

• $p + q = 1$ (total network hash power)

For a security parameter $\sigma$ and an attacker controlling fraction $q$ of the hash power, the required confirmations $k$ to achieve security is:

$k \geq \frac{\log(\sigma)}{\log(q/p)}$

Roadmap and Future Work

1. Enhanced Security Measures: Additional security layers and auditing.

2. Performance Optimizations: Improved transaction processing speed.

3. Extended Chain Support: Support for additional blockchain networks, with the Libre smart contract continuing to serve as the central coordinator.

4. Governance Integration: Decentralized governance for bridge parameters.

5. Advanced Analytics: Real-time monitoring and analytics dashboard.

6. Expanded Vault Capabilities: Additional features for vault management including automated liquidation protection and collateral optimization.

7. Multi-Asset Vaults: Support for additional cryptocurrencies as segregated vault collateral.

Conclusion

Libre Crosslink represents a significant advancement in cross-chain interoperability and decentralized asset custody by providing a trustless, decentralized bridge between Bitcoin and Libre blockchains, as well as an institutional-grade vault solution for Bitcoin collateral in the Libre Lending ecosystem. By leveraging threshold signature cryptography and smart contract technology, it enables secure cross-chain transactions and segregated asset custody without centralized intermediaries. This approach aligns with the fundamental principles of decentralization and trustlessness that underpin blockchain technology.

What distinguishes Libre Crosslink from other solutions is its dual-purpose design: it not only facilitates asset transfers between blockchains but also provides dedicated, segregated vault infrastructure for each user of the Libre Lending platform. Additionally, the innovative use of the Libre smart contract as the authoritative source of truth and coordination mechanism enhances security, transparency, and auditability while eliminating many of the vulnerabilities found in more complex distributed systems.

The architecture and implementation details presented in this whitepaper demonstrate how Libre Crosslink addresses the challenges of both cross-chain interoperability and secure collateral management while maintaining high security standards. As the project evolves, it has the potential to become a vital component of the broader blockchain ecosystem, enabling not only the free flow of assets across different blockchain networks but also the secure use of Bitcoin as collateral for decentralized financial applications.