A Theory of Secure and Efficient Implementation of Electronic Money

Abstract

Scalable and secure implementation of central bank digital currencies (CBDC) has been a challenge. Blockchains provide high operator-independent security and enable central banks to outsource CBDC operations while retaining control over the amount of circulating money. Scalability of blockchain depends on the possibility of decomposing the blockchain. We study how the choice of money scheme: accounts, bills, or unspent transaction outputs (UTXOs) influences the existence of secure and decomposable blockchain implementations of CBDC. We give formal definitions to money schemes, their decompositions, atomic decompositions inspired from the properties of blockchain implementations. For our formalism, we use tools from universal algebra and category theory. We present a general decomposition theory and conditions under which money schemes have atomic decompositions. Bill money schemes meet these conditions but account and UTXO schemes do not. Bill schemes enable scalable and secure implementations of CBDC while the more traditional schemes have some issues.