On (in)ability to embed data into Schnorr

In a detailed discussion focusing on the specifics of cryptographic grinding in Bitcoin transactions, the conversation delves into the efficiency and practical implications of such methods. The debate scrutinizes the statistical occurrence of direct key leakage compared to the rate achieved through grinding techniques. It's highlighted that in a particular instance, the success rate of deriving keys through grinding stands at approximately 8 out of 96 scenarios. This figure starkly contrasts with the outcomes from direct key leakages, presenting a significantly diminished efficacy, roughly marking a quarter of the rate observed in the latter scenario.

Furthermore, the discourse raises considerations regarding the computational effort required for grinding. This aspect is deemed potentially impactful, especially when operations are conducted at a larger scale. The conversation also questions the rationale behind excluding certain variables from the efficiency measurement of grinding practices. Specifically, it challenges the exclusion of 'P' from the evaluation, arguing that even in configurations like explicit multisig transactions that do not compromise control over the output, the embedding rate could essentially double without necessitating additional work. This argument is illustrated by comparing the embedding rates of different methods: using a combination of 'P', 'R', and 's' could potentially yield a 1/6 rate, as opposed to a more labor-intensive approach of grinding all four 'P', 'R' values to achieve merely a 1/12 rate.

This exchange underscores the complexity and nuances associated with optimizing cryptographic practices within Bitcoin development. The insights shared through this dialogue contribute to a broader understanding of the challenges and considerations relevant to enhancing security and efficiency in cryptocurrency transactions.