Industrial Control Systems underpin almost all aspects of life in the UK, the power network operated by the National Grid and the rail network, which is over seen by the Rail Safety and Standards Board (RSSB) are two key examples of this. In this project we will work with the National Grid and RSSB to perform a detailed security analysis of their systems, looking for possible points of cyber attack and building an understanding of the impact of possible failures. This will lead to better security for these important systems. Based on what we learn from this analysis we will work with the company Level 3 TRL and Parsons Brinckerhoff to generalise our methods into business processes that other owners of industrial control systems can use to help ensure their systems are safe from cyber attacks.

The terahertz (THz) frequency region within the electromagnetic spectrum, covers a frequency range of about one hundred times that currently occupied by all radio, television, cellular radio, Wi-Fi, radar and other users and has proven and potential applications ranging from molecular spectroscopy through to communications, high resolution imaging (e.g. in the medical and pharmaceutical sectors) and security screening. Yet, the underpinning technology for the generation and detection of radiation in this spectral range remains severely limited, being based principally on Ti:sapphire (femtosecond) pulsed laser and photoconductive detector technology, the THz equivalent of the spark transmitter and coherer receiver for radio signals. The THz frequency range therefore does not benefit from the coherent techniques routinely used at microwave/optical frequencies. Our programme grant will address this. We have recently demonstrated optical communications technology-based techniques for the generation of high spectral purity continuous wave THz signals at UCL, together with state-of-the-art THz quantum cascade laser (QCL) technology at Cambridge/Leeds. We will bring together these internationally-leading researchers to create coherent systems across the entire THz spectrum. These will be exploited both for fundamental science (e.g. the study of nanostructured and mesoscopic electron systems) and for applications including short-range high-data-rate wireless communications, information processing, materials detection and high resolution imaging in three dimensions.

Our proposal builds on the successful start made by Cambridge Centre for Analysis (CCA), a current EPSRC Centre for Doctoral Training. We propose to develop further our activity in two important and rapidly evolving areas of analysis, namely mathematics of information and statistics of complex systems. Beginning with Newton, for whom the development of calculus and the mathematical understanding of bodies in motion were closely intertwined, the mathematics used to describe real phenomena consistently involves notions of continuity, rate of change, average value, and basic challenges such as the relationship between discrete and continuum objects. This is the domain of analysis, encompassing modelling by partial differential equations and by random processes, and the mathematical theory which guides effective computation for such models. The centrality of mathematical analysis in the relationship between mathematics and its applications has been acknowledged by successive International Reviews of Mathematics, as has the need to increase the capacity of UK PhD training in analysis. Mathematical Analysis and its Applications is an EPSRC Priority Area. Beyond the established and important uses of analysis in modelling physical phenomena, digital technology has created new areas where mathematical analysis, in guiding the extraction of knowledge from massive discrete systems, plays an essential role. These include the fields of high-dimensional statistics and the mathematics of information, including compressed sensing. In each of these, one is looking for a reliable means to interpret massive high-dimensional data. Already several CCA students are working in these areas. Big Data is one of the Eight Great Technologies championed by the Minister for Universities and Science. Statistics and Data to Knowledge are EPSRC Priority Areas. We propose a first year training programme based on our current successful model, now expanded by two further core courses, one in Statistics of Complex Systems and one in Mathematics of Information. These new courses will be paired with postgraduate level courses from the existing Cambridge Masters' (MASt), which students can use to consolidate their understanding. The core courses themselves are based on supervised student team assignments leading to student presentations. The other main components of the first year are research mini-projects (often the route to a PhD project) and an industry workshop. Years two to four are devoted mainly to the PhD thesis. First year training establishes a collaborative ethos in the cohort and, by mixing students with different prior skills, encourages cross-fertilization of ideas across the different threads of analysis. This is sustained in later years through a programme of seminars, workshops and training in transferable skills. The students appreciate that their collective understanding of a given problem using different skills will often exceed each individual's understanding. This makes cohort-based training especially valuable in analysis. We already expose all our students to the role of mathematics and the opportunities for mathematicians in industry and society, and we encourage first-hand engagement with applications through mini-projects, industrial seminars and study weeks, and, for some, PhD projects with industrial partners. The development of core skills and eventually the ability to generate new ideas is the hardest and crucial part of training as a research mathematician. This is necessarily our overriding task, in which we seek synergy and inspiration from user engagement. In the new CDT, our network of industrial connections will be further enhanced, along with our collaborations with Cambridge engineering colleagues, and our links with the Smith Institute for Industrial Mathematics.

The security of many cryptographic protocols in use today relies on the computational hardness of mathematical problems such as integer factorization. These problems can be solved using quantum computers, and therefore most of our security infrastructures will become completely insecure once quantum computers are built. Post-quantum cryptography aims at developing security protocols that will remain secure even after quantum computers are built. The biggest security agencies in the world including GCHQ and the NSA (the American National Security Agency) have recommended a move towards post-quantum protocols, and the new generation of cryptographic standards will aim at post-quantum security. Driven by the need to upgrade our cybersecurity infrastructures, many cryptographic algorithms have recently been developed which are claimed to offer post-quantum security. These proposals are based on a few distinct mathematical problems which are hoped to remain difficult for quantum computers, including lattice problems, multivariate polynomial system solving, coding theory problems, isogeny problems, and the security of cryptographic hash functions. Unfortunately, many of these problems, and more importantly the cryptographic algorithms that are built on top of them, have not been subject to a thorough security analysis yet, therefore leaving us with a risk to oversee major weaknesses in algorithms to be deployed in security applications. In this fellowship, we will develop breakthrough cryptanalysis techniques to analyse the security of post-quantum cryptography candidate algorithms, and determine which algorithms may or may not be further considered for digital security applications. Using the insight gained through cryptanalysis, we will then develop new post-quantum cryptographic algorithms offering better security, efficiency and functionality properties in applications.

The emergence of a global ubiquitous computing environment in which each of us routinely interacts with many thousands of interconnected computers embedded into the everyday world around us will transform the ways in which we work, travel, learn, entertain ourselves and socialise. Ubiquitous computing will be the engine that drives our future digital economy, stimulating new forms of digital business and transforming existing ones.However, ubiquitous computing also carries considerable risks in terms of societal acceptance and a lack of established models of innovation and wealth creation, so that unlocking its potential is far from straightforward. In order to ensure that the UK reaps the benefits of ubiquitous computing while avoiding its risks, we must address three fundamental challenges. First, we need to pursue a new technical research agenda for the widespread adoption of ubiquitous computing. Second, we must understand and design for an increasingly diverse population of users. Third, we need to establish new paths to innovation in digital business. Meeting these challenges requires a new generation of researchers with interdisciplinary skills in the technical and human centred aspects of ubiquitous computing and transferable skills in research, innovation and societal impact.Our doctoral training centre for Ubiquitous Computing in the Digital Economy will develop a cohort of interdisciplinary researchers who have been exposed to new research methods and paradigms within a creative and adventurous culture so as to provide the future leadership in research and knowledge transfer that is necessary to secure the transformative potential of ubiquitous computing for the UK digital economy. To achieve this we will work across traditional research boundaries; encourage students to adopt an end-to-end perspective on innovation; promote creativity and adventure in research; and place engagement with society, industry and key stakeholders at the core of our programme.Our proposal brings together a unique pool of researchers with extensive expertise in the technologies of ubiquitous and location based computing, user-centred design, societal understanding, and research and training in innovation and leadership. It also involves a wide spectrum of industry partners from across the value chain for ubiquitous computing, spanning positioning, communications, devices, middleware, databases, design, and our two driving market sectors of the creative industries and transportation.Our training programme is based on the approach of personalised pathways that develop individual students' interdisciplinary and transferable skills, and that produce a personal portfolio to showcase the skills and experience gained alongside the more traditional PhD thesis. It includes a flexible taught programme that emphasises student-led seminars, short-fat modules, training projects and e-learning as delivery mechanisms that are suited to PhD training; an industrial internship scheme under which students spend three months working at an industrial partner; and a PhD research project that builds on a proposal developed during the first year of training and that is supported by multiple supervisors from different disciplines with industry involvement. Our DTC will foster a community of researchers through a dedicated shared space, a programme of community building events, training for supervisors and well as students, funding for a student society, and an alumni programme.