The attack mechanism is described without the necessity for complex mathematical manipulations. It operates by signing a transaction with two inputs that are secured by the identical private key, enabling the leakage of critical information directly to the attacker through an encrypted channel.

The detailed process outlines how specific values (k1, k2, z, s1, and s2) are calculated using the private key (x), an attacker's secret, and hash functions to ultimately reveal the 256_bit_secret. This vulnerability is particularly concerning due to its low probability nature, potentially being activated by unsuspecting activities such as "dusting" an address—a scenario where small amounts of cryptocurrency are sent to a wallet to unveil the owner's identity or other details. The technique specifically mentions leveraging a transaction ID (TXID) that adheres to a certain 32-bit checksum to trigger this secretive extraction of private data.

Furthermore, the text acknowledges the theoretical countermeasures against such attacks, mentioning the efficacy of level 2 or 3 Anti-Exfil protocols, assuming the companion application is secure and not compromised. These protective measures are designed to safeguard against the exploitation of vulnerabilities like those exploited by Dark Skippy and Dark Smoothie, yet their effectiveness hinges on the integrity of the associated software. This exposition underlines a critical scrutiny required in the security practices surrounding cryptographic transactions, emphasizing the need for rigorous testing and the implementation of advanced security protocols to mitigate such sophisticated attacks.