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

The focus is not merely on the internal components of such systems, like signatures, identity verification, ledger states, and cryptographic proofs, but more critically on the interaction between these off-chain elements and the Layer 1 (L1) blockchain, which still relies on classical cryptographic methods such as ECDSA/Schnorr over secp256k1. This situation presents a vulnerability, as even if every off-chain component is secured against quantum attacks, the system's reliance on a non-post-quantum secure L1 for settlement exposes it to potential quantum threats.

The distinction between 'peg-out' and 'peg-in' processes highlights different levels of challenge in achieving post-quantum security. The peg-out process, involving the transfer of assets from the blockchain to an external system, appears somewhat more manageable. It could potentially be streamlined to involve a commitment-based claim where a classical signature is required only at the final withdrawal stage, thereby minimizing exposure. Conversely, the peg-in process, which covers the depositing of assets into the blockchain, inherently demands a classical signature to construct the transaction itself. This requirement embeds a fundamental difficulty, as altering this would necessitate changes to Bitcoin’s core signature scheme itself.

The discussion also touches on broader applications beyond the specific project, applicable to any BitVM-based bridge, Lightning Network transactions, or similar setups performing substantial cryptographic operations off-chain yet settling on a blockchain that is not quantum-resistant. This ongoing concern invites further investigation and discussion within the community to evaluate whether the current strategies are sufficient or if new approaches need to be developed to ensure future-proof security in the evolving landscape of quantum computing.