On (in)ability to embed data into Schnorr

Embedding data into a valid signature presents an intriguing concept that hinges on the balance between secrecy and the potential risk of compromising private keys. By utilizing components of the signature, such as R and P values derived from specific chunks of data, it becomes possible to encode information within these signatures. This method, while innovative, introduces weaknesses akin to those found in systems vulnerable to known plaintext attacks. The essence of this technique lies in its reliance on the obscurity of the data being embedded; only the person possessing this data can fully understand the encoding, aiming for an efficiency rate of around 70%. This is achieved through meticulous manipulation of SHA-256 hashes.

The approach discussed involves a delicate trade-off between data obfuscation and the computational effort required to decode or break the encryption. The efficiency of encoding, hovering at approximately 70%, indicates that a significant portion of the data can be secured effectively against unintended decryption attempts. Nevertheless, the strategy also acknowledges the possibility of gradually reducing the strength of the encoded bits to adjust the level of security or computational challenge presented to an attacker. For instance, by tweaking the number of bits at risk of exposure, one could theoretically determine the feasibility of a lattice attack breaking the code.

This exploration into cryptographic techniques underlines a fundamental interest in balancing encryption strength with the practicality of decoding efforts, particularly in contexts where the confidentiality of the encoded information is paramount. Moreover, it reflects ongoing discussions within technological communities about enhancing security measures without overly compromising on efficiency or introducing excessive vulnerabilities.