  In India, post the demonetization exercise in 2016, digital payments have
become extremely popular. Among them, the volume of transactions using Paytm
wallets and UPI (Unified Payment Interface) have grown manifold. The lockdowns
due to COVID-19 Pandemic have furthered this trend. Side by side,
crypto-currencies such as bitcoin are also gaining traction. Many countries are
considering issuing a Digital Currency via their Central Banks. In this paper,
we propose a novel Decentralized Digital Currency System (DDCS) that makes use
of Merkle Hash-Trees as Authenticated Data Structures. DDCS uses a Ledger-less,
distributed, peer-to-peer architecture. We name the proposed currency
$\delta$-Money. $\delta$-Money is intended as a replacement for physical
currency and has in-built security features that rival crypto-currencies.
Transactions using $\delta$-Money happen in a disintermediated manner but with
post-facto reconciliation. In place of Central Bank-issued Digital Currency
(CBDC), we envisage a scenario where multiple Payment Banks issue digital
currencies that have stable valuations without being subject to either
volatility or perennial devaluation.
