On (in)ability to embed data into Schnorr

In the exploration of embedding data within blockchain transactions, particularly through the manipulation of private keys and signatures, a method is revealed that allows for a certain degree of control over the encoded information. This technique hinges on the understanding and manipulation of three critical components: P, R, and s values, which are part of the digital signature process in blockchain technology. By directly influencing P and R with specific data inputs, one can achieve around 66% control over the outcome. However, to push this figure beyond 70%, a finer manipulation or "grinding" of the s-value is required, though this approach demands additional computational effort.

The effectiveness of hiding data in this manner varies significantly based on the nature of the data itself. For instance, encoding ASCII text, especially when it comprises common English words or predictable patterns, significantly lowers the entropy of the data, making it potentially easier for attackers to exploit using methods akin to those used in attacking brainwallets. Such vulnerabilities underscore the inherent risks in storing valuable data within the blockchain in a manner that does not sufficiently obfuscate it.

Despite these challenges, the technique offers intriguing possibilities for applications like NFT minting and transfer. The key to its utility lies in the balance between encoding efficiency and security. While fully random data poses a substantial challenge for unauthorized decoding, structured or patterned data offers less resistance. Thus, the approach presents a spectrum of application potential, from relatively insecure but efficient encoding methods to more secure, albeit less efficient, ones. The notion of encoding data into private keys and signatures without immediate disclosure provides a tactical advantage, allowing for the confirmation of funds or data prior to revealing the means of its encoding. This strategy has particular relevance for use cases involving content storage on the blockchain, where space efficiency and security are paramount.

This nuanced method also holds implications for combating spam on the blockchain by enabling a verifiable yet concealed data transfer mechanism. It suggests a future where blockchain's capacity for data storage and verification can be leveraged in novel ways, albeit with considerations for the trade-offs between data density, security, and the potential for misuse.