International Association
for Cryptologic Research

The interest shown by central banks in deploying Central Bank Digital Currency (CBDC) has spurred a blooming number of conceptually different proposals from central banks and academia. Yet, they share the common, transversal goal of providing citizens with an additional digital monetary instrument. Citizens, equipped with CBDC wallets, should have access to CBDC fund and defund operations that allow the distribution of CBDC from the central bank to citizens with the intermediation of commercial banks. Despite their key role in the CBDC deployment as acknowledged, e.g., by the European Central Bank, operations fund and defund have not been formally studied yet. In this state of affairs, this work strives to cryptographically define the problem of fund and defund of CBDC wallets as well as the security and privacy notions of interest. We consider a setting with three parties (citizen, commercial bank and central bank) and three ledgers: the CBDC ledger, the retail ledger (where citizens have their accounts with their commercial banks) and the wholesale ledger (where commercial banks have their accounts with the central bank). We follow a modular approach, initially defining the functionality of two types of ledgers: Basic Ledger (BL), which supports basic transactions, and Conditional Payment Ledger(CP), which additionally supports conditional transactions. We then use BL and CP to define the CBDC-Cash Environment (CCE) primitive, which captures the core functionality of operations fund and defund. We require that CCE satisfies balance security: either operation fund/defund is successful, or no honest party loses their funds. CCE also satisfies that fund/defund cannot be used to breach the privacy of the CBDC ledger. Finally, we provide two efficient and secure constructions for CCE to cover both CP and BL types of CBDC ledger. Our performance evaluation shows that our constructions impose small computation and communication overhead to the underlying ledgers. The modular design of CCE allows for the incorporation in our CCE constructions of any CBDC ledger proposal that can be proven a secure instance of CP or BL, enabling thereby a seamless method to provide CBDC fund and defund operations.