On (in)ability to embed data into Schnorr

In the discussion regarding the potential for embedding data within Bitcoin's unspent transaction output (UTXO) set through innovative cryptographic techniques, several key ideas were explored. The conversation began with a consideration of using scriptPubKeys with spending conditions reminiscent of HTLC/atomic swaps, which could either involve setting a block height far into the future or choosing a number with no known preimage to facilitate certain transactions. This approach was critiqued for potentially abandoning the NUMS (Nothing-Up-My-Sleeve) variant of Taproot, highlighting the importance of maintaining flexibility in transaction scripting without compromising security.

The discourse then shifted towards more nuanced cryptographic strategies, such as embedding data in signatures without leading to key reuse or loss of control over outputs. One proposed method involves creating a series of transactions that encode data within their signatures, using a chain of public keys generated from initial secret keys and subsequent hash operations. This process allows for data to be securely published in the blockchain while ensuring that private keys remain secure until specific conditions are met.

Furthermore, the discussion touched upon the practical limitations and considerations of such methods, including the impact on the UTXO set size and the detectability of embedded data. The feasibility of these techniques under current Bitcoin network policies and standardness constraints was also examined, suggesting that while less efficient than some existing methods like OP_RETURN, these approaches offer a more discreet alternative for data embedding.

Finally, the exchange underscored the theoretical and practical complexities of achieving data embedding within Bitcoin transactions. It highlighted the balance between innovation in cryptographic techniques and adherence to the principles of security, privacy, and network efficiency. The conversation reflects ongoing efforts to explore the boundaries of what is possible within Bitcoin's scripting system, acknowledging both the potential and the challenges of integrating advanced cryptographic solutions into the blockchain space.