Traditional methods require a token for each satoshi of value, leading to impractical amounts of data for significant transactions. To address this, mints can issue tokens in various denominations using the BDHKE scheme, allowing for more efficient transfers by reducing the number of tokens needed through a mechanism that supports splitting and combining tokens. However, this approach introduces its own set of challenges, notably diminishing the anonymity set as each denomination requires a unique minting key, making each denomination essentially its own token.

An alternative solution is found in anonymous credential schemes, which allow for better privacy and interoperability among denominations. Unlike BDHKE, where each token represents a fixed amount, anonymous credentials can commit to variable values, offering a more flexible approach to represent transaction amounts. The use of Pedersen commitments within these schemes, as exemplified by WabiSabi, enables the concealment of individual amounts while ensuring that transactions remain verifiable through the public confirmation that the sum of inputs equals the sum of outputs plus any delta blinding factors. This method achieves fungibility across different denominations by treating them interchangeably, addressing the limitations posed by the BDHKE scheme.

Despite these advancements, ecash systems inherently possess a "rugpull" capability due to the control mints have over the issuance of tokens or credentials. Mints can unilaterally create tokens with values not backed by actual deposits, potentially undermining the system’s integrity. Although proof-of-reserves mechanisms can offer some level of assurance, the anonymized nature of such systems complicates the verification process, especially in multi-denomination contexts where privacy concerns are heightened. This presents a fundamental security risk, highlighting the delicate balance between privacy, fungibility, and trust in digital currency systems.

The discussion underscores the complexities and trade-offs involved in designing ecash systems that aim to provide both privacy and practicality. While advancements like anonymous credential schemes present promising solutions to enhance fungibility and privacy, the inherent risks associated with the mint's power to issue unbacked tokens highlight the ongoing challenges in achieving a secure and efficient digital cash system.