What does "post-quantum" actually mean for a Bitcoin L2 when settlement still happens on a non-PQ L1?

The discussion centers around the potential for a post-quantum (PQ) second-layer (L2) solution to operate securely atop a first-layer (L1) blockchain, such as Bitcoin, that is still susceptible to quantum attacks. This scenario contemplates the use of scripthash addresses on L1 where users "peg in" by transferring their assets into these addresses under specific script conditions. The core concern addressed is whether these funds remain secure, especially if an effective quantum attack occurs after the assets have been locked in the L1 but before the L2 can achieve consensus on a security update.

The security of the overall system hinges on multiple factors, including how each layer handles quantum threats and the interaction between these layers. Even with PQ-resistant mechanisms at the L2 level, the integrity of the system could be compromised if the base layer (L1) remains vulnerable. Concerns are raised about the ability of the bridge connecting L1 and L2 to authenticate deposits accurately and ensure that only legitimate transactions are processed. This authentication process must itself be resilient against quantum attacks to prevent unauthorized access or theft of funds.

A potential solution discussed involves the use of one-time signature (OTS) schemes, which might offer robust security enhancements when integrated within a blockchain context. However, simply implementing an OTS within the existing framework is insufficient. It requires a carefully designed signature verification logic to ensure that it complements the existing security measures effectively and provides genuine quantum resistance.

Overall, examining the feasibility of PQ-resistant L2 solutions settling on a quantum-vulnerable L1 reveals a complex interplay of technological and security considerations. Each component's resilience contributes to the system's overall security posture, necessitating a comprehensive and well-integrated approach to safeguard against both current and emerging threats.