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.

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.

Today we use many objects not normally associated with computers or the internet. These include gas meters and lights in our homes, healthcare devices, water distribution systems and cars. Increasingly, such objects are digitally connected and some are transitioning from cellular network connections (M2M) to using the internet: e.g. smart meters and cars - ultimately self-driving cars may revolutionise transport. This trend is driven by numerous forces. The connection of objects and use of their data can cut costs (e.g. allowing remote control of processes) creates new business opportunities (e.g. tailored consumer offerings), and can lead to new services (e.g. keeping older people safe in their homes). This vision of interconnected physical objects is commonly referred to as the Internet of Things. The examples above not only illustrate the vast potential of such technology for economic and societal benefit, they also hint that such a vision comes with serious challenges and threats. For example, information from a smart meter can be used to infer when people are at home, and an autonomous car must make quick decisions of moral dimensions when faced with a child running across on a busy road. This means the Internet of Things needs to evolve in a trustworthy manner that individuals can understand and be comfortable with. It also suggests that the Internet of Things needs to be resilient against active attacks from organised crime, terror organisations or state-sponsored aggressors. Therefore, this project creates a Hub for research, development, and translation for the Internet of Things, focussing on privacy, ethics, trust, reliability, acceptability, and security/safety: PETRAS, (also suggesting rock-solid foundations) for the Internet of Things. The Hub will be designed and run as a 'social and technological platform'. It will bring together UK academic institutions that are recognised international research leaders in this area, with users and partners from various industrial sectors, government agencies, and NGOs such as charities, to get a thorough understanding of these issues in terms of the potentially conflicting interests of private individuals, companies, and political institutions; and to become a world-leading centre for research, development, and innovation in this problem space. Central to the Hub approach is the flexibility during the research programme to create projects that explore issues through impactful co-design with technical and social science experts and stakeholders, and to engage more widely with centres of excellence in the UK and overseas. Research themes will cut across all projects: Privacy and Trust; Safety and Security; Adoption and Acceptability; Standards, Governance, and Policy; and Harnessing Economic Value. Properly understanding the interaction of these themes is vital, and a great social, moral, and economic responsibility of the Hub in influencing tomorrow's Internet of Things. For example, a secure system that does not adequately respect privacy, or where there is the mere hint of such inadequacy, is unlikely to prove acceptable. Demonstrators, like wearable sensors in health care, will be used to explore and evaluate these research themes and their tension. New solutions are expected to come out of the majority of projects and demonstrators, many solutions will be generalisable to problems in other sectors, and all projects will produce valuable insights. A robust governance and management structure will ensure good management of the research portfolio, excellent user engagement and focussed coordination of impact from deliverables. The Hub will further draw on the expertise, networks, and on-going projects of its members to create a cross-disciplinary language for sharing problems and solutions across research domains, industrial sectors, and government departments. This common language will enhance the outreach, development, and training activities of the Hub.

How liquids wet solid surfaces is of fundamental importance to a wide-range of scientific disciplines and technological applications from creating thin films on semiconductor wafers, through adhesion and coating of surfaces, to effective droplet deposition and mixing on DNA microarrays. Electrostatic fields can alter how effectively a liquid wets a solid surface. In recent years uniform electric fields have been used to control and manipulate droplets of conducting (ion containing) liquids, typically a salt solution, by using the liquid-solid contact area as one electrode in a capacitive structure - so called electrowetting. This has led to new voltage controlled variable focus liquid lenses, liquid-based electronic paper and droplet-based microfluidic systems. The key to electrowetting is the ability of an applied voltage to reversibly increase the effective hydrophilicity of a solid surface and reduce the contact angle of the droplet without altering the surface chemistry. However, many liquids of interest are not conducting and the need for a sandwich-style capacitive structure and direct physical contact to the liquid limits its range of applicability. In this project we create a new method of controlling hydrophilicity and oleophilicity of materials by using the dielectric properties of liquids, but with the effects localized to an interface. Unllike electrowetting which focuses on the ions, our method focuses on the dipoles in a liquid. Using a non-uniform electric field generates unequal forces on the two ends of the dipole. The resulting dielectrophoretic force can result in movement and redistribution of the liquid into the areas of highest field gradient. The basis of our project is the understanding that when the liquid has solid-liquid, liquid-vapor or liquid-liquid interfaces, dielectric energy changes can be coupled to surface free energy changes. With a suitable decaying electric field, the effects of liquid dielectrophoresis can be confined to either the solid-liquid interface or to the liquid-vapor (or liquid-liquid) interface and can be used with a non-conducting liquid. By using microfabricated interdigitated electrodes a decaying, and hence non uniform, electric field can be created above a solid surface. For a droplet thicker than the decay length of the electric field, the major change of the surface energy compensating liquid dielectrophoretic energy changes is via a change in the contact area with a solid and so this can be a method of reversibly controlling the contact angle and, hence, the hydro- and oleo- philicity of a surface. For a thin liquid film the major change of the surface energy compensating liquid dielectrophoretic energy changes is via a change in the shape of the liquid-vapor (or liquid-liquid) interface and so, in this case, it becomes a method for shaping a liquid surface. In this method of localizing the effects of liquid dielectrophoresis to an interface the contrast to electrowetting is that, 1. the electric fields are non-uniform; 2. the electric fields are generated by surface microfabricated co-planar rather than sandwich electrode structures; 3. the forces act upon the dipoles in the liquids, which can therefore be non-conducting (or conducting), rather than upon ions of conducting liquids; 4. the method does not suffer from saturation of the contact angle and so can be used to produce liquid films. The research in this project seeks to establish an approach to wetting that allows conducting and non-conducting liquids to be manipulated using electric fields in a manner complementary to electrowetting. The project will provide the understanding needed to allow future development of novel droplet microfluidic, liquid microactuation, liquid-based optics and displays. The project includes industrial partners who have expertise in the development and commercialisation of microfluidic liquid handling, lab-on-chip devices, display devices and optofluidic systems.