On inversions and Doob hh-transforms of linear diffusions

Let $X$ be a regular linear diffusion whose state space is an open interval $E\subseteq\mathbb{R}$. We consider a diffusion $X^*$ which probability law is obtained as a Doob $h$-transform of the law of $X$, where $h$ is a positive harmonic function for the infinitesimal generator of $X$ on $E$. This is the dual of $X$ with respect to $h(x)m(dx)$ where $m(dx)$ is the speed measure of $X$. Examples include the case where $X^*$ is $X$ conditioned to stay above some fixed level. We provide a construction of $X^*$ as a deterministic inversion of $X$, time changed with some random clock. The study involves the construction of some inversions which generalize the Euclidean inversions. Brownian motion with drift and Bessel processes are considered in details.Comment: 19 page

On the Use of the Negation Map in the Pollard Rho Method

The negation map can be used to speed up the Pollard rho method to compute discrete logarithms in groups of elliptic curves over finite fields. It is well known that the random walks used by Pollard rho when combined with the negation map get trapped in fruitless cycles. We show that previously published approaches to deal with this problem are plagued by recurring cycles, and we propose effective alternative countermeasures. As a result, fruitless cycles can be resolved, but the best speedup we managed to achieve is by a factor of only 1.29. Although this is less than the speedup factor of root 2 generally reported in the literature, it is supported by practical evidence

The ‘Great Decarceration’: Historical Trends and Future Possibilities

During the 19th Century, hundreds of thousands of people were caught up in what Foucault famously referred to as the ‘great confinement’, or ‘great incarceration’, spanning reformatories, prisons, asylums, and more. Levels of institutional incarceration increased dramatically across many parts of Europe and the wider world through the expansion of provision for those defined as socially marginal, deviant, or destitute. While this trend has been the focus of many historical studies, much less attention has been paid to the dynamics of ‘the great decarceration’ that followed for much of the early‐ to mid‐20th Century. This article opens with an overview of these early decarceration trends in the English adult and youth justice systems and suggests why these came to an end from the 1940s onwards. It then explores parallels with marked decarceration trends today, notably in youth justice, and suggests how these might be expedited, extended, and protected

Elliptic and Hyperelliptic Curves: A Practical Security Analysis

Motivated by the advantages of using elliptic curves for discrete logarithm-based public-key cryptography, there is an active research area investigating the potential of using hyperelliptic curves of genus 2. For both types of curves, the best known algorithms to solve the discrete logarithm problem are generic attacks such as Pollard rho, for which it is well-known that the algorithm can be sped up when the target curve comes equipped with an efficiently computable automorphism. In this paper we incorporate all of the known optimizations (including those relating to the automorphism group) in order to perform a systematic security assessment of two elliptic curves and two hyperelliptic curves of genus 2. We use our software framework to give concrete estimates on the number of core years required to solve the discrete logarithm problem on four curves that target the 128-bit security level: on the standardized NIST CurveP-256, on a popular curve from the Barreto-Naehrig family, and on their respective analogues in genus 2. © 2014 Springer-Verlag Berlin Heidelberg

Conversations in a Crowded Room: An Assessment of the Contribution of Historical Research to Criminology

The relationship between history and social science generally, as well as history and criminology specifically, has long been considered problematic. But, since the likes of Burke (1992) and King (1999) spoke of a ‘dialogue of the deaf’, crime history has rapidly expanded and, more latterly, historical criminology has begun to emerge. This article reappraises the relationship of the subject areas by considering the impact that historical research has had on criminology. Although the impact is found to be somewhat patchy, the article identifies positive signs within the two fields that might point towards a more mutually‐enriching future

On the Static Diffie-Hellman Problem on Elliptic Curves over Extension Fields

We show that for any elliptic curve E(Fqn ), if an adversary has access to a Static Diffie-Hellman Problem (Static DHP) oracle, then by making O(q1− 1/n+1) Static DHP oracle queries during an initial learning phase, for fixed n > 1 and q → ∞ the adversary can solve any further instance of the Static DHP in heuristic time O˜(q1− 1/n+1). Our proposal also solves the Delayed Target DHP as defined by Freeman, and naturally extends to provide algorithms for solving the Delayed Target DLP, the One-More DHP and One-More DLP, as studied by Koblitz and Menezes in the context of Jacobians of hyperelliptic curves of small genus. We also argue that for any group in which index calculus can be effectively applied, the above problems have a natural relationship, and will always be easier than the DLP. While practical only for very small n, our algorithm reduces the security provided by the elliptic curves defined over Fp2 and Fp4 proposed by Galbraith, Lin and Scott at EUROCRYPT 2009, should they be used in any protocol where a user can be made to act as a proxy Static DHP oracle, or if used in protocols whose security is related to any of the above problems

Physical Processes in Star Formation

© 2020 Springer-Verlag. The final publication is available at Springer via https://doi.org/10.1007/s11214-020-00693-8.Star formation is a complex multi-scale phenomenon that is of significant importance for astrophysics in general. Stars and star formation are key pillars in observational astronomy from local star forming regions in the Milky Way up to high-redshift galaxies. From a theoretical perspective, star formation and feedback processes (radiation, winds, and supernovae) play a pivotal role in advancing our understanding of the physical processes at work, both individually and of their interactions. In this review we will give an overview of the main processes that are important for the understanding of star formation. We start with an observationally motivated view on star formation from a global perspective and outline the general paradigm of the life-cycle of molecular clouds, in which star formation is the key process to close the cycle. After that we focus on the thermal and chemical aspects in star forming regions, discuss turbulence and magnetic fields as well as gravitational forces. Finally, we review the most important stellar feedback mechanisms.Peer reviewedFinal Accepted Versio

A simple publicly verifiable secret sharing scheme and its application to electronic voting

A publicly verifiable secret sharing (PVSS) scheme is a verifiable secret sharing scheme with the property that the validity of the shares distributed by the dealer can be verified by any party; hence verification is not limited to the respective participants receiving the shares. We present a new construction for PVSS schemes, which compared to previous solutions by Stadler and later by Fujisaki and Okamoto, achieves improvements both in efficiency and in the type of intractability assumptions. The running time is O(nk), where k is a security parameter, and n is the number of participants, hence essentially optimal. The intractability assumptions are the standard Diffie-Hellman assumption and its decisional variant. We present several applications of our PVSS scheme, among which is a new type of universally verifiable election scheme based on PVSS. The election scheme becomes quite practical and combines several advantages of related electronic voting schemes, which makes it of interest in its own right