The REsearch centre on Privacy, Harm Reduction and Adversarial INfluence online (REPHRAIN) will bring together the UK's substantial academic, industry, policy and third sector capabilities to address the current tensions and imbalances between the substantial benefits to be gained by full participation in the digital economy and the potential for harm through loss of privacy, insecurity, disinformation and a myriad of other online harms. Combining world-leading experts from the Universities of Bristol, Edinburgh, Bath, King's and UCL, the REPHRAIN Centre will use an interdisciplinary approach - alongside principles of responsible innovation and creative engagement - to develop new insights that allow the socio-economic benefits of a digital economy to be maximised whilst minimising the online harms that emerge from this. REPHRAIN's leadership team will drive these insights in technical, social, behavioural, policy and regulatory research on privacy, privacy enhancing technologies and online harms, through an initial scoping phase and 25 inaugural projects. The work of REPHRAIN will be focused around three core missions and four engagement and impact objectives. Mission 1 emphasises the requirement to deliver privacy at scale whilst mitigating its misuse to inflict harms. This will focus on reconciling the tension between data privacy and lawful expectations of transparency by not only drawing heavily on advances in privacy-enhancing technologies (PETs), but also leveraging the full range of socio-technical approaches to rethink how we can best address potential trade-offs. Mission 2 emphasises the need to minimise harms whilst maximising the benefits from a sharing-driven digital economy, redressing citizens' rights in transactions in the data-driven economic model by transforming the narrative from privacy as confidentiality only to also include agency, control, transparency and ethical and social values. Finally, Mission 3 focuses on addressing the balance between individual agency and social good, developing a rigorous understanding of what privacy represents for different sectors and groups in society (including those hard to reach), the different online harms to which they may be exposed, and the cultural and societal nuances impacting effectiveness of harm-reduction approaches in practice. These missions are supported by four engagement and impact objectives that represent core pillars of REPHRAIN's approach: (1) design and engagement; (2) adoption and adoptability; (3) responsible, inclusive and ethical innovation; and (4) policy and regulation. Combined, these objectives will deliver co-production, co-creation and impact at scale across academia, industry, policy and the third sector. These activities will be complemented by a capability fund, which will ensure that REPHRAIN activities remain flexible and responsive to current issues, addressing emerging capability gaps, maximising impact and cultivating a public space for collaboration. REPHRAIN will be managed by a Strategic Board and supported by an External Advisory Group, the REPHRAIN Ethics Board, and will work with multiple external stakeholders across industry, public, and the third sector. Outcomes from the centre will be synthesised into the REPHRAIN Toolbox - a one-stop resource for researchers, practitioners, policy-makers, regulators and citizens - which will contribute to developing a culture of continuous learning, collaboration and open engagement and reflection within the area of online harm reduction. Overall, REPHRAIN focuses on interdisciplinary leadership provided by a highly experienced team and supported by state-of-the-art facilities, to develop and apply scientific expertise to ensure that the benefits of a digital society can be enjoyed safely and securely by all.

In 1932, Cockcroft and Walton performed the alchemist's dream of transforming one chemical element into another when they bombarded lithium with low energy protons from their prototype accelerator, disintegrating it into two helium nuclei. Despite the passage of 70 years from this pioneering work, our understanding of nuclear physics is still largely dictated by what can be achieved by inducing nuclear reactions between stable nuclei i.e. those isotopes which are found in Nature. This has mainly restricted precision studies to nuclei which are close to the line of stability. Our knowledge of nuclear forces and how nuclei behave can only be advanced by studying nuclei with very different numbers of protons and neutrons those of stable isotopes (which are comparatively few in number). A better understanding of the underlying mechanism of nuclei is the goal of our research, but it also has consequences beyond nuclear physics. For example it can help our understanding of the processes in supernova explosions where most of the heavy elements found in Nature are thought to be synthesised. At the ISOLDE facility, part of the international CERN Laboratory in Geneva, Switzerland, radioactive nuclei are produced with high intensities in the so-called isotope separation on-line (ISOL) technique where a primary target is bombarded with an intense, high energy proton beam. Using different primary targets, ISOLDE can produce beams of varying intensity of over 700 isotopes of 70 different chemical elements. This facility is unique worldwide in the diversity of available beams which it can produce. A recent advance at ISOLDE has been the so-called REX-ISOLDE facility which accelerates these radioactive nuclei to energies where they start to resist the Coulomb repulsion between the positively charge protons when they come into contact with other nuclei in a fixed target. At such energies, interactions take place which allow us to probe the structure of these exotic radioactive nuclei with high precision. Two of these mechanisms are the focus of this grant application. The first, known as Coulomb excitation, is where some of the energy of the interaction goes into exciting the nucleus into higher energy states. The ease with which this takes place reflects the nuclear collectivity, a property which is generally largest for nuclei which are deformed, typically having a non-spherical shape such as a rugby-ball shape, known as prolate deformation. Coulomb-excitation measurements therefore allow us to study the nuclear shape, in particular, a certain special class of nuclei which exhibit shape coexistence. This phenomenon occurs when different states in a particular isotope have different distinct shapes. The second mechanism we aim to employ is known as light-ion transfer. In this interaction between the accelerated beam nucleus and the target nucleus, particles such as protons and neutrons are exchanged. The transferred particle will then occupy one of a number of allowed energy states in the nucleus to which it has been added / there are only a small set of allowed states due to the importance of quantum mechanics in determining the properties of the nucleus. By measuring the ease with which a particle is transferred in such a reaction, we can infer details about the energy states in the nucleus which it has been transferred onto, with high precision. This is especially interesting for the very neutron-rich nuclei since these states are expected to shift around relative to their location in the less exotic nuclei we have studied in the past. It is suggested that this behaviour could very sensitively affect how much of various heavy elements is produced in supernova explosions. Since we know the relative proportions of heavy elements existing in the Solar System, we have a strong constraint on the changes possible in the nuclear physics and a strong motivation for making such studies.

Public key cryptography (PKC) depends on the existence of computational problems that are incredibly hard - but not impossible - to solve. Classical examples that were fundamental to the origins of PKC in the 1970s (and indeed were prominent centuries earlier) are the integer factorisation problem and the discrete logarithm problem (DLP). While there are no known efficient, i.e., polynomial-time algorithms for solving these problems that run on classical computers, thanks to Shor's astounding breakthrough ideas in 1994, both can be solved efficiently on a quantum computer of sufficient size. Intense research in the areas of quantum computation, quantum information theory and quantum algorithms ensued, and replacement post-quantum (PQ) cryptosystems have been studied in earnest for the past 15 years or so, with standardisation efforts in process by both NIST and ETSI. PQ cryptosystems must be secure against both classical and quantum computers and therefore their underlying hardness assumptions must be studied intensely before they can be fully trusted to replace our existing PKC hardness assumptions. Until these standards have been established and cryptographic practice migrates entirely to PQ cryptography, it is also essential that the study of classical hardness assumptions persists, particularly as sporadic and sometimes spectacular progress can occur: for instance, for a special but large family of finite fields the DLP can be solved on a classical computer in quasi-polynomial time, i.e., `very nearly' efficiently, thanks to a series of results due to Dr. Granger and his collaborators, and Joux and his collaborators. In this project we will research and develop algorithms for solving computational problems that are foundational to the security of PKC, both now and in the future. In particular, we will study: the DLP in the aforementioned special family of finite fields, for which an efficient classical algorithm is potentially on the horizon; the security of the Legendre pseudo-random function, which is extremely well suited for multi-party computation and has been proposed for use in the next iteration of Ethereum - the de facto standard blockchain platform - but is not so well-studied; and finally the security of supersingular isogeny-based PQ cryptography, which although a relatively young field offers many very promising applications. Due to their nature, any cryptographic assumptions based on mathematical constructions are potentially weaker than currently believed, and we will deepen our understanding and assess the hardness of these natural and fundamental problems, thus providing security assurances to the cryptography community and more generally all users of cryptography.