Discussion on the Technical Principles and Optimization Ideas of DLC

1. Introduction

Discrete Log Contracts ( DLC ) are a type of condition payment scheme based on oracles, proposed by MIT's Tadge Dryja in 2018. DLC allows both parties to make conditional payments based on predefined conditions, with participants pre-signing possible outcomes and executing payments when the oracle signs the result. This enables DLC to facilitate new decentralized financial applications while ensuring the security of Bitcoin deposits.

Compared to the Lightning Network, DLC has the following advantages:

• Better privacy protection, contract details are only shared between the participating parties.
• Support more complex and flexible financial contracts, such as derivatives, insurance, etc.
• Reduce counterparty risk, with funds locked in a multi-signature contract.
• No need to manage payment channels
• Provide better scalability in complex contracts.

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

• Risk of oracle key leakage or loss
• Centralization issues of oracle
• Decentralized oracles cannot directly perform key derivation.
• Oracle node collusion risk
• Fixed denomination change problem

This article will propose some optimization solutions to these issues in order to enhance the security of the Bitcoin ecosystem.

2. DLC Principle

Taking Alice and Bob signing a betting agreement as an example, the bet is on the parity of the hash value of the n+k-th block. DLC constructs conditional signatures by transmitting block information through oracles, allowing the winning party to win the assets.

The main steps include:

1. All parties generate key pairs
2. Create Funding Transaction
3. Create Contract Execution Transactions
4. Oracle Computation Commitment
5. Participants calculate the new public key
6. The oracle generates a signature based on the results.
7. The winning party withdraws assets

Analysis shows that only the correct party can calculate the new private key and successfully withdraw the tokens. A time lock also needs to be added to prevent the assets from being withdrawn by the other party.

3. DLC Optimization

3.1 Key Management

The private key and random number of the oracle in DLC are crucial; leakage or loss may result in:

• Unable to settle, refund contract needs to be executed.
• Facing the risk of fraudulent settlement
• Leak oracle private key
• Corresponding DLC cannot be settled.

It is recommended to use BIP32 to derive child keys or grandchild keys, and to use the hash value of the private key and counter as a random number to enhance security.

3.2 Decentralized Oracle

Using Schnorr threshold signatures can achieve decentralized oracles, with the following advantages:

• Enhance security
• Distributed Control
• Improve availability
• Flexibility and Scalability
• Accountability

3.3 Decentralization and Key Management Coupling

In the scenario of decentralized oracles, the complete private key does not appear, making it impossible to directly use BIP32 to derive keys. A distributed key derivation method can be employed, implemented based on Lagrange interpolation polynomials. However, the compatibility issues between enhanced and non-enhanced BIP32 must be considered.

3.4 OP-DLC: Oracle Trust Minimization

Propose the OP-DLC scheme and introduce an optimistic challenge mechanism. The oracle needs to stake in advance to build on-chain OP games and commit to not acting maliciously. Any honest participant can initiate a challenge to punish the malicious oracle. This allows oracle nodes to supervise each other and achieve minimal trust.

3.5 OP-DLC + BitVM dual bridge

Combining OP-DLC and BitVM to solve the limitations of DLC in fund distribution:

• Achieve any granularity of change
• Improve capital liquidity
• Users can freely choose deposit and withdrawal methods.
• Reduce reliance on oracle trust

4. Conclusion

DLC technology combined with new technologies like Taproot and BitVM can achieve more complex off-chain contract verification and settlement. Through the OP challenge mechanism, it can further achieve oracle trust minimization, bringing more possibilities to the Bitcoin ecosystem.