We live in a modern age, but what does `modern' mean and how can a reflection on `modernity' help us to understand the world today? These are the questions that Peter Wagner sets out to answer in this concise and accessible book.

Wagner begins by returning to the question of modernity's western origins and its claims to open up a new and better era in the history of humanity. Modernity's claims and expectations have become more prevalent and widely shared, but in the course of their realization and diffusion they have also been radically transformed. In an acute and engaging analysis, Wagner examines, among others, the following key issues:

* Modernity was based on the hope for freedom and reason, but it created the institutions of contemporary capitalism and democracy. How does the freedom of the citizen relate to the freedom of the buyer and seller today? And what does disaffection with capitalism and democracy entail for the sustainability of modernity?

* Rather than a single model of modernity, there is now a plurality of forms of modern socio-political organization. What does this entail for our idea of progress and our hope that the future world can be better than the present one?

* All nuance and broadening notwithstanding, our concept of modernity is in some way inextricably tied to the history of Europe and the West. How can we compare different forms of modernity in a `symmetric', non-biased or non-Eurocentric way? How can we develop a world-sociology of modernity?

This book is the first major publication from the European Research Council-funded research project "Trajectories of modernity: comparing non-European and European varieties" (TRAMOD), which is based in the Department of Sociological Theory, Philosophy of Law and Methodology of the Social Sciences at the University of Barcelona and of which Peter Wagner is the Principal Investigator. The project TRAMOD aims at advancing the analysis of the contemporary plurality of self-understandings and related institutional structures of societies and polities in the current global context. It analyzes these self-understandings against the background of the historical trajectories of those societies. The analysis of the existing multiple forms of modernity is the major challenge to current social and political theory and comparative-historical and political sociology. It requires a conceptual and empirical analysis of that which is common to different forms of modernity and that which varies between them.

A central problem in cryptography is the distribution among distant users of secret keys, which can be used for the secure encryption of messages. This task is impossible in classical cryptography unless assumptions are made on the computational power of the eavesdropper. Quantum key distribution (QKD), on the other hand, offers security against adversaries with unbounded computing power. The ultimate level of security provided by QKD was made possible thanks to a change of paradigm. While in classical cryptography security relies on the hardness of certain mathematical problems, in QKD it relies on the fundamental laws of quantum physics. A side-effect of this change of paradigm, however, is that whereas the security of classical cryptography is based on the mathematical properties of the key itself, in QKD, the security crucially depends on the physical properties of the key generation process. But then, how can one assess the level of security provided by a real-life implementation of QKD, which inevitably differs in inconspicuous ways from the idealized, theoretical description? In fact, technological imperfections have recently been exploited to hack QKD commercial products.

Device-independent QKD (DIQKD) aims at closing the gap between theoretical analyses and practical realizations of QKD by designing protocols whose security does not require a detailed characterization of the devices used to generate the secret key. These devices are just seen as quantum black-boxes, see the Figure, generating outputs given some inputs. This stronger form of cryptography is possible if it is based on the observation of non-local quantum correlations. In some sense, DIQKD combines the advantages of classical and quantum cryptography: security against unbounded adversaries based on the law of quantum physics but which does not rely on the physical details of the generation process.

In our work, we provide a general formalism for proving the security of DIQKD protocols. The DIQKD model that we consider, however, is partly restricted as it supposes that the measurement processes generating the different bits of the raw key are causally independent of each other. This independence condition may be hard to meet in practice, but it is assumed in any of the existing security proofs, including those for standard QKD. Our analysis therefore shows that secure QKD is in principle possible independently of the internal working of the devices used in the protocol.