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.

Lattices play an important role in various areas of engineering and computer science. In coding theory, lattice codes bring significant advantages such as concrete implementation and complexity reduction, thus overcoming the limitation of random codes in practical applications. More recently, it became widely appreciated that algebraic structures of lattice codes greatly facilitate coordination among multiple users in wireless networks. In a world where quantum computers exist, current public key cryptographic schemes will become vulnerable to attacks that exploit the nature of quantum mechanics. This is a central concern to our modern data-driven society, which has been extensively considered by governments, companies and research institutions. For instance, the National Institute of Standards and Technology (NIST, USA) launched in 2016 a call for the standardisation of quantum-resistant cryptography. Among the prospective methods which are expected to be implemented for post-quantum cryptography, lattice-based cryptography figures as a front runner. This form of cryptography explores the theory of lattices and the hardness of lattice-related problems to build primitives such as encryption schemes, one-way functions, digital signatures and fully-homomorphic encryption. While both lattice coding and lattice cryptography are concerned with the same mathematical objects --- lattices --- they consider these objects from disparate vantage points. Coding theory uses lattices to protect correctness against noise, whereas cryptography adds noise to protect security. As a consequence, both fields ask different questions of lattices: coding theory is mainly concerned with lattices that are easy to decode, whereas cryptography is focused on lattices that are hard. Despite these different perspectives, lattice coding has a lot to contribute to lattice cryptography. Firstly, in order to encrypt messages we need to encode them and the more efficient our coding schemes, the smaller will be our ciphertexts. This is particularly relevant since the size of ciphertexts is one of the key drawbacks of lattice-based cryptography. That is, these schemes are typically very fast but produce large ciphertexts. Secondly, lattice coding has and can be used to improve the security analysis of lattice-based cryptography. In this area, we study algorithms for breaking cryptographic schemes so that we can pick parameters in such a way to avoid such attacks.

The 2015 UK National Security Strategy identifies cyber security as one of the top four UK national security priorities. The UK National Cyber Security Strategy 2016-2021 (NCSS) has an underlying vision to make the UK secure and resilient to cyber threats, prosperous and confident in the digital world. It is widely recognised that the UK, indeed the world, is short of cyber security specialists. Cyber security is genuinely cross-disciplinary. It's about technology, and the networks and systems within which technology is deployed. But it's also about society and how it engages with technology. Researching the right questions requires researchers to fully understand the integrated nature of the cyber security landscape. A CDT provides the perfect vehicle within which suitably broad training can be provided. The establishment of a cohort of researchers with different backgrounds and experience allows this knowledge to be cultivated within a rich environment, where the facts of hard science can be blended with the perspectives and nuances of more social dimensions. While society has made progress in developing the technology that underpins security, privacy and trust in cyberspace, we lag behind in our understanding of how society engages with this technology. Much more fundamentally, we don't even really understand how society engages with the concepts of security, privacy and trust in the first place. We will host a CDT in Cyber Security for the Everyday, which signals that research in our CDT will focus on the technologies deployed in everyday digital systems, as well as the everyday societal experience of security. Research in our CDT will investigate the security of emerging technologies. As cyberspace continues to evolve, so, too, do the technologies required to secure its future. Research topics include the cryptographic tools that underpin all security technologies, the security of the systems within which these tools are deployed, the use of artificial intelligence to aid discovery of system vulnerabilities, and security and privacy of everyday objects which are becoming embedded in cyberspace. Our CDT will also research how to secure cyber societies. Securing increasingly networked, automated, and autonomous societies requires an integrated research approach which engages the social, technological, cultural, legal, social-psychological and political on equal terms. Research topics include exploring state, institutional and corporate responsibility over how information is gathered and used, investigating how cyber security is perceived, understood and practiced by different communities, and researching how social differences and societal inequalities affect notions of, and issues relating to, cyber security. Our training programme will be based around a suite of relevant masters programmes at Royal Holloway, including in Information Security, Geopolitics and Security, and Data Science. This will be supplemented by workshops, practice labs, and a comprehensive generic skills programme. Students will work closely with the wider cyber security community through a series of industry engagement sessions and visits, summer projects, and three-month internships. Peer-to-peer learning will be fostered through group challenges, workshop design and delivery, reading groups and a social programme.