Post-Quantum Blockchains Based on FALCON++

区块链炒作已经渗透到主流意识中，这主要是由于比特币激发的加密货币的资本增长。机构投资者和企业越来越多地采用加密货币进一步推动了这一趋势。然而，加密货币只是区块链技术的众多应用之一;其他领域包括智能合约，电子投票和物联网（IoT）。区块链技术的吸引力在于它能够安全且不可更改地进行交易，而无需建立对中央权威机构的信任。然而，这只有通过现代密码协议才有可能实现（因此，加密货币中的“加密”），其使得节点能够安全地彼此交易，例如，通过使用数字签名进行认证，以及加密散列函数来建立对等共识。然而，量子计算的出现对当前经典加密协议提出了巨大的安全风险，例如椭圆曲线数字签名算法（ECDSA），其广泛用于生成数字签名，使得这些密码方案在面对量子对手时是非量子安全的。为了取代这种潜在的对手，后量子方案正在开发，以适应未来的现代密码学。美国国家标准与技术研究所（NIST）已经标准化了三种基于格的PQC协议。NIST的标准化过程标志着后量子密码学范式转变的开始，而不是结束。在这个项目中，我们将应用一个这样的基于格的后量子数字签名方案，快速傅立叶格基紧凑签名NTRU（Fast-Fourier Lattice-based Compact Signatures over NTRU），并实现修改其现有的陷门采样器与蒙特-卡罗马尔可夫链（MCMC）采样。此外，我们还将获得一个区块链实现的例子，其中包含了这个ESTCON ++签名方案，以便在区块链的背景下比较经典和后量子数字签名。

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.