Analysis and Optimization Ideas of DLC Technology

1. Introduction

Discrete Log Contracts ( DLC ) are a type of contract execution scheme based on oracle technology, allowing both parties to make conditional payments based on predefined conditions. Compared to the Lightning Network, DLC has significant advantages in privacy protection, support for complex financial contracts, and reducing counterparty risk.

However, there are still some issues and risks associated with DLC:

• The risk of leakage or loss of the oracle private key and random number
• The centralization trust issue of Oracles
• Decentralized oracles cannot directly perform key derivation.
• Risk of collusion among oracle nodes
• There is a fixed denomination change issue during asset redistribution.

This article will explore some optimization solutions to address these issues and enhance the security of the Bitcoin ecosystem.

2. DLC Principle

The basic principle of DLC is to construct conditional signatures by transmitting information through oracles, allowing the correct party to win the assets. The main steps include:

1. Initialization: Generate elliptic curve parameters
2. Key Generation: Oracles and participants generate private and public keys
3. Capital Injection Transaction: Locking funds into multi-signature outputs
4. Contract Execution Transaction: Create transactions for spending capital injection transactions.
5. Oracle Calculation Commitment
6. Settlement: The oracle generates a signature based on the result.
7. Withdraw: The winning party calculates the new private key and withdraws the assets

3. DLC Optimization Plan

3.1 Key Management

To enhance the security of the oracle private key, the following measures can be adopted:

• Use BIP32 to derive child or grandchild keys for signing
• Use the private key and counter hash value as random numbers to prevent duplication or loss.

3.2 Decentralized Oracle

Using Schnorr threshold signatures to implement decentralized oracles, with the following advantages:

• Enhance security, reduce single point of failure risk
• Achieve distributed control to avoid excessive concentration of power.
• Improve system availability and flexibility
• Has good scalability
• Achieve accountability

3.3 Decentralization and Key Management Coupling

In the scenario of decentralized oracles, the absence of a complete private key prevents the direct use of BIP32 for key derivation. A distributed key derivation method can be employed, which establishes a correspondence between private key shares and the complete private key based on Lagrange interpolation polynomials, thereby enabling the derivation of child private key shares.

3.4 OP-DLC: Oracle Trust Minimization

Propose the OP-DLC mechanism, introducing the optimistic challenge mechanism:

• The oracle needs to stake in advance to build on-chain OP games.
• Any honest participant can initiate a challenge.
• Successfully challenging can punish the evil oracle.
• Implement mutual supervision among oracle nodes, minimizing trust.

3.5 OP-DLC + BitVM Dual Bridge

Combine OP-DLC and BitVM to solve the issues of DLC when used for cross-chain bridges:

• Solve the issues of fund change and granularity limits
• Provide multiple deposit and withdrawal channels
• Achieve oracle trust minimization
• Improve capital utilization rate

4. Conclusion

DLC combines technologies such as Taproot and BitVM to enable more complex off-chain contract validation and settlement. Through the OP challenge mechanism, it further achieves oracle trust minimization, bringing more application possibilities to the Bitcoin ecosystem.