A key mechanism in this process is the introduction of a share_log_window, which essentially acts as a recorded snapshot of valid signatures eligible for redemption. Upon creation, this share_log_window delineates the boundaries for valid ecash transactions, specifying which signatures can be redeemed.

At the heart of the proposal is a unique redemption method that allows for the swapping of an eHash token within the designated share_log_window. This swap not only facilitates the exchange of one eHash for another but also introduces the option of utilizing different redemption methods. A critical aspect of this system is the update mechanism for the share log, where a new blinded signature replaces the old one upon redemption. This method ensures ongoing validity and security of transactions within the system.

The proposal briefly evaluates the viability of allowing each blinded signature to be redeemed more than once. However, it dismisses this possibility due to practical concerns. Once a redemption occurs, the mint or pool becomes privy to certain secrets (denoted as x and C), compromising the security and integrity of subsequent transactions involving the same signature. This insight underscores the importance of maintaining a secure, one-time redemption process for each blinded signature, ensuring the robustness and trustworthiness of the ecash system.