The digital signature scheme, which underpins most of the existing distributed ledgers, is generally based on non-quantum-resilient algorithms (e.g. elliptic curve digital signature algorithm). This highlights the need for quantum-secure signature schemes in future distributed ledgers (and other products). Therefore, in this paper, we propose a novel quantum-secure digital signature scheme designed specifically for cryptocurrencies. Our proposed scheme is a hash-based signature scheme, which is a variant of Winternitz-one time signature scheme. A comparison of the proposed scheme and two other competing quantum-secure cryptocurrencies (IoTA and QRL) reveals that our scheme respectively achieves 59% and 24% reductions in signature lengths without compromising the level of security. A salient feature of the proposed approach is that, unlike the previously proposed variants of Winternitz scheme, we avoid the need for any expensive computation. In addition, we formally model the classical cryptocurrency and the proposed quantum-secure cryptocurrency using high-level Petri-nets, which allows the implementer to understand their workings in the presence of a quantum attacker. Furthermore, we also provide formal security proof in the random oracle model.