DLC Technology Analysis and Optimization Ideas

1. Overview

The Discrete Logarithm Contract ( DLC ) is a contract execution scheme based on oracles, proposed by Tadge Dryja from MIT in 2018. DLC allows both parties to make conditional payments based on predefined conditions, with participants pre-determining possible outcomes and pre-signing them, executing payments when the oracle signs the result. Compared to the Lightning Network, DLC has advantages in privacy protection, support for complex financial contracts, and reduction of counterparty risk.

Although DLC has broad application prospects in the Bitcoin ecosystem, there are still some issues:

• Risk of oracle private key and random number leakage
• The trust issues brought about by centralized oracles
• The decentralized oracle cannot directly derive BIP32 keys.
• Oracle Node Collusion Risk
• Fixed denomination change limit

This article will propose some optimization solutions to address these issues, in order to improve the security and practicality of DLC.

2. How DLC Works

Taking the example of Alice and Bob betting on the parity of the hash value of the n+k-th block, the basic workflow of the DLC is as follows:

1. Key Generation: Oracle, Alice, and Bob each generate their private and public keys.

2. Capital injection transaction: Alice and Bob create a 2-of-2 multi-signature output, each locking 1 BTC.

3. Contract execution transaction: Create two CET for spending injection transaction

4. The oracle computes the commitments R, S, S' and broadcasts them.

5. Alice and Bob calculate the new public keys PK^Alice and PK^Bob

6. Settlement: The oracle broadcasts s or s' based on the block hash value.

7. Withdraw: The winning party calculates the new private key using s or s' and withdraws the assets.

In addition, a time lock needs to be added to prevent one party from holding onto the coins for an extended period.

3. DLC Optimization Plan

3.1 Key Management

To enhance the security of oracle private keys and random numbers:

• Use BIP32 to derive child keys or grandchild keys for signing
• Use the private key and counter hash value as a random number

3.2 Decentralized Oracle

The decentralized oracle is implemented using Schnorr threshold signatures, which has the following advantages:

• Enhance security and reduce single point of failure risks
• Implement distributed control
• Enhance system availability and flexibility
• Scalable
• Support for accountability mechanisms

3.3 Decentralization and Key Management Coupling

Using distributed key derivation methods to achieve BIP32 key derivation in decentralized oracle scenarios. However, compatibility issues between enhanced and non-enhanced BIP32 need to be considered.

3.4 OP-DLC: Oracle Trust Minimization

Introducing an optimistic challenge mechanism, oracles need to stake in advance to build on-chain OP games. Any honest participant can challenge the malicious oracle, and upon winning the case, punish the wrongdoer and confiscate their deposit.

3.5 OP-DLC + BitVM dual bridge

Combine OP-DLC and BitVM to solve the fixed denomination change problem of DLC:

• Support for any granularity of change
• Provide multiple deposit and withdrawal channels
• Achieve trust minimization for oracles
• Improve capital utilization

4. Conclusion

DLC combines new technologies such as Taproot and BitVM, enabling more complex off-chain contract verification and settlement. Through the OP challenge mechanism, it minimizes trust in oracles. In the future, DLC is expected to play a greater role in the Bitcoin ecosystem.