A simple backup scheme for wallet accounts

Understanding the relationship between individual secrets, denoted as Ci, and the shared secret S in the context of decrypting a ciphertext payload presents a nuanced challenge. The inquiry revolves around the mathematical operation XOR (exclusive or) applied to these secrets within a cryptographic framework. Specifically, the question delves into how XOR operations on individual secrets contribute to revealing or constructing the shared secret necessary for decryption tasks.

When considering a scenario with two public keys (xpubs) in a descriptor, an initial assumption might be that the XOR result of both Ci values directly yields the shared secret S. This perspective stems from the basic properties of XOR operations where combining two unique inputs produces a distinct output, which in this case, is misconceived as the shared secret. However, the complexity increases with the introduction of additional xpubs, particularly when dealing with an even number of them. The notion here explores whether the aggregate XOR of all Ci values, given each individual secret undergoes XOR operations an odd number of times and is subsequently revealed, equates to the shared secret.

The exploration further extends to alternative cryptographic schemes where each Ci could potentially be a piece of ciphertext decrypted by its corresponding public key (pubkey), thus revealing the shared secret in a different manner than through XOR subtraction from the shared secret. This theoretical approach suggests a more direct relationship between individual secrets and the shared secret without relying on the intermediary XOR operations.

Despite the initial hypotheses and logical deductions about isolating individual secrets or manipulating subsets of Ci values to deduce the shared secret, practical experimentation leads to the conclusion that achieving a definitive XOR result necessitates at least two unknowns. This outcome highlights the inherent complexity and security measures embedded in cryptographic protocols designed to safeguard shared secrets. Through engaging with these cryptographic concepts, it becomes evident that straightforward isolation or deduction of the shared secret through simple XOR operations among individual secrets is not feasible given the structured constraints and intended security outcomes of such cryptographic frameworks.