OP_CAT and Bitcoin’s Path to Quantum Resistance

The discussion revolves around the feasibility and practicality of using a quantum computer to derive a private key from its corresponding public key, specifically focusing on the secp256k1 elliptic curve used in Bitcoin transactions. The primary concerns raised include the time it would take to initiate a quantum computer and prepare it for such a task, the duration required to actually compute the private key, the associated costs of these processes, and the likelihood of completing this operation while a transaction is still pending in the mempool, allowing for the possibility of altering the transaction with the newly discovered private key.

Quantum computing's potential to break cryptographic algorithms underpins the theoretical capability to derive private keys from public ones. However, the practicality of such an endeavor is questioned, especially in the context of small-scale Bitcoin transactions. The example mentioned involves a $25 Bitcoin purchase made five years prior, highlighting the concern that by the time a quantum computer is ready to decipher the private key from the public key exposed during a transaction broadcast, the transaction could already be confirmed and added to a block. This scenario suggests that the effort and resources required to exploit quantum computing in this manner may not justify the potential gains from small transactions, particularly those that do not reuse addresses and thus present a moving target.

Furthermore, the discussion touches upon the current state of Bitcoin scripting capabilities, with a nod to the anticipation of OP_CAT's return to the mainnet. In the meantime, it points out the opportunity to experiment with OP_CAT on the signet testing network by running a Bitcoin Inquisition node with signet enabled. This mention underlines ongoing developments within the Bitcoin protocol and the community's efforts to explore and expand its scripting functionalities.