Blockchain hype has pervaded mainstream consciousness, largely owing to the capital growth of cryptocurrencies inspired by Bitcoin. This has been further driven by the increased adoption of cryptocurrencies by institutional investors and corporations. However, cryptocurrencies are just one of the many applications of blockchain technology; other areas include smart contracts, e-voting, and the Internet of Things (IoT). The attractiveness of blockchain technology lies in its ability to allow transactions to be carried out securely and immutably, without the need to establish trust in a central authority. Yet, this is only made possible by modern cryptographic protocols (hence the 'crypto' in cryptocurrency) that enable nodes to transact with each other securely, for example, through the usage of digital signatures for authentication, and cryptographic hash functions to establish peer-to-peer consensus. However, the advent of quantum computing presents an immense security risk to current classical cryptographic protocols, such as the Elliptical Curve Digital Signature Algorithm (ECDSA) which is widely used in the generation of digital signatures, rendering these cryptographic schemes non-quantum-secure in the face of a quantum adversary. In lieu of this potential adversary, post-quantum schemes are being developed to future-proof modern cryptography. The National Institute of Standards and Technology (NIST) has standardised three lattice-based PQC protocols. The NIST process of standardisation marks the beginning, not the end, of a paradigm shift to post-quantum cryptography. In this project, we will apply one such lattice-based post-quantum digital signature scheme, FALCON (Fast-Fourier Lattice-based Compact Signatures over NTRU), and implement with modifying its existing trapdoor sampler with Monte-Carlo Markov Chain (MCMC) sampling. Moreover, we will also procure an example of blockchain implementation which incorporates this FALCON++ signature scheme, in order to compare classical and post-quantum digital signatures in the context of blockchains.