QCAP: A Bitcoin-Native Quantum Canary Alert

The Quantum Canary Address Generation Protocol (QCAP) is an innovative solution addressing the potential risks posed by quantum computers to the security of Bitcoin's digital signature schemes. The protocol leverages the computational difficulty of the discrete logarithm problem on elliptic curves, a principle upon which the security of Bitcoin currently rests. With the advent of quantum computing, this underlying security feature faces potential threats, as quantum computers could solve these problems more efficiently than classical computers.

QCAP introduces a novel method involving a taproot address on the Bitcoin blockchain that can only be accessed by solving the discrete logarithm problem on a specifically chosen weaker elliptic curve. This method not only maintains compatibility with Bitcoin’s existing protocols but also ensures that solving the weaker curve does not compromise the security of the primary Bitcoin curve. The dual-curve approach utilized in QCAP involves using the same secret scalar across both the main Bitcoin curve and the weaker curve. This scalar is collaboratively generated through multi-party computation among various participants, ensuring no single participant knows the complete scalar, thus maintaining secrecy and security.

The integrity of QCAP hinges on a zero-knowledge proof technique known as Discrete Logarithm Equality Across Groups (DLEQAG). This technique ensures that the public keys generated on both curves indeed correspond to the same secret scalar without revealing what that scalar is. The protocol aggregates these keys only if they come with valid DLEQAG proofs, mitigating the risk of any participant introducing discrepancies in the secret scalar used.

For integration into the Bitcoin network, QCAP uses a tweaked taproot address, which embeds a commitment to all protocol data. This allows for verification that the address was derived honestly and enables spending by those who can solve the discrete logarithm problem on the weaker curve and adjust for the tweak in the secret scalar. The protocol details and proofs of concept are documented extensively in the research paper titled "QCAP: A Quantum Canary Address Generation Protocol," available here, and further practical demonstrations are accessible through their GitHub repository.

Despite the promising framework of QCAP, there remain several challenges and areas requiring further development before it can be fully integrated and operational on the Bitcoin mainnet. These include improving decentralized coordination among participants, enhancing network protocols to handle potential disruptions or attacks by malicious coordinators, and increasing community engagement in protocol implementation.