OP_CAT Enables Winternitz Signatures

The ongoing discussions among Bitcoin developers emphasize the need for a smaller signature scheme in a post-quantum bitcoin network to maintain or improve transaction per second (TPS) rates without increasing blocksize. Lattice-based cryptography is highlighted as a promising avenue for achieving quantum resistance while keeping signature sizes manageable. However, current hash-based signature alternatives like Lamport, WOTS, or SPHINCS, though operational, are not ideal due to their large size, which could negatively impact network efficiency. These methods are considered more of a temporary solution or an "emergency quantum-resistant escape hatch" in scenarios where consensus on a more efficient, compact signature scheme is not reached, or if a newly adopted scheme is found to be insecure.

The aspiration within the community is to eventually discover or invent a quantum-resistant signature scheme that significantly reduces the signature size to around 64 bytes. This would necessitate introducing new opcodes or address formats to facilitate widespread adoption. The emphasis is on diversification and not relying solely on a single cryptographic method to safeguard the network against quantum threats.

Further to this discussion, there's mention of a specific proposal that aims to improve upon existing script constructions for quantum resistance. This proposal claims advancements over previous work by requiring only Conditional Array Transfer (CAT) instead of General Script Reduction (GSR) for operation, potentially reducing the necessary script size if additional opcodes were available (notably OP_LSHIFT). Additionally, it highlights a significant reduction in witness sizes from 24kb to 8kb compared to prior models, although it specifies that this was achieved using a basic version of WOTS with checksum compression due to limitations in implementing XOR operations without access to an OP_XOR opcode. This conversation reflects an active exploration and innovation within the Bitcoin development community to address the challenges posed by quantum computing.