Combinatorial Solutions Providing Improved Security for the Generalized Russian Cards Problem

We present the first formal mathematical presentation of the generalized Russian cards problem, and provide rigorous security definitions that capture both basic and extended versions of weak and perfect security notions. In the generalized Russian cards problem, three players, Alice, Bob, and Cathy, are dealt a deck of $n$ cards, each given $a$, $b$, and $c$ cards, respectively. The goal is for Alice and Bob to learn each other's hands via public communication, without Cathy learning the fate of any particular card. The basic idea is that Alice announces a set of possible hands she might hold, and Bob, using knowledge of his own hand, should be able to learn Alice's cards from this announcement, but Cathy should not. Using a combinatorial approach, we are able to give a nice characterization of informative strategies (i.e., strategies allowing Bob to learn Alice's hand), having optimal communication complexity, namely the set of possible hands Alice announces must be equivalent to a large set of $t-(n, a, 1)$-designs, where $t=a-c$. We also provide some interesting necessary conditions for certain types of deals to be simultaneously informative and secure. That is, for deals satisfying $c = a-d$ for some $d \geq 2$, where $b \geq d-1$ and the strategy is assumed to satisfy a strong version of security (namely perfect $(d-1)$-security), we show that $a = d+1$ and hence $c=1$. We also give a precise characterization of informative and perfectly $(d-1)$-secure deals of the form $(d+1, b, 1)$ satisfying $b \geq d-1$ involving $d-(n, d+1, 1)$-designs

Extended Combinatorial Constructions for Peer-to-peer User-Private Information Retrieval

We consider user-private information retrieval (UPIR), an interesting alternative to private information retrieval (PIR) introduced by Domingo-Ferrer et al. In UPIR, the database knows which records have been retrieved, but does not know the identity of the query issuer. The goal of UPIR is to disguise user profiles from the database. Domingo-Ferrer et al.\ focus on using a peer-to-peer community to construct a UPIR scheme, which we term P2P UPIR. In this paper, we establish a strengthened model for P2P UPIR and clarify the privacy goals of such schemes using standard terminology from the field of privacy research. In particular, we argue that any solution providing privacy against the database should attempt to minimize any corresponding loss of privacy against other users. We give an analysis of existing schemes, including a new attack by the database. Finally, we introduce and analyze two new protocols. Whereas previous work focuses on a special type of combinatorial design known as a configuration, our protocols make use of more general designs. This allows for flexibility in protocol set-up, allowing for a choice between having a dynamic scheme (in which users are permitted to enter and leave the system), or providing increased privacy against other users.Comment: Updated version, which reflects reviewer comments and includes expanded explanations throughout. Paper is accepted for publication by Advances in Mathematics of Communication

A classical reactive potential for molecular clusters of sulphuric acid and water

We present a two-state empirical valence bond (EVB) potential describing interactions between sulphuric acid and water molecules and designed to model proton transfer between them within a classical dynamical framework. The potential has been developed in order to study the properties of molecular clusters of these species, which are thought to be relevant to atmospheric aerosol nucleation. The particle swarm optimisation method has been used to fit the parameters of the EVB model to density functional theory (DFT) calculations. Features of the parametrised model and DFT data are compared and found to be in satisfactory agreement. In particular, it is found that a single sulphuric acid molecule will donate a proton when clustered with four water molecules at 300 K and that this threshold is temperature dependent

Research Brief One-Sheet No.8: The Impact of Police Crime on LGBTQ+ People

This research brief provides a summary of a research presentation at the Forum on 21st Century Policing: Protecting the Rights of LGBTQ+ People held by the Office of Community Oriented Policing Services at the U.S. Department of Justice, on July 21, 2016, in Washington, DC

Pesach N. Rubenstein Cheats the Hangman: A Case Study of Punishment and the Death Penalty at Brooklyn’s Raymond Street Jail

This paper tells the story of Pesach Rubenstein and how he cheated the hangman in 1876. Rubenstein was charged, tried, and convicted in Kings County, New York, for the 1875 murder of his 19 year-old cousin, Sarah Alexander. The Rubenstein case is noteworthy in that it received unprecedented media attention in the 1870s, involved the use of rudimentary forensic evidence at the trial, and divided the community on issues of religion, ethnicity, immigration (the victim and defendant were recent Jewish immigrants from Poland), and imposition of the death penalty. Using a case study approach to analyze the trial transcript, newspaper articles, and historical accounts of the murder investigation, Rubenstein’s trial, and his incarceration at Brooklyn’s Raymond Street Jail, this article offers a glimpse into the operations of an urban jail in an earlier era when our criminal justice system was in its infancy

Preemptive Dicta: The Problem Created by Judicial Efficiency

Judges regularly espouse dicta. Traditional obiter dicta, remarks that are clearly asides and not about issues considered in the case, can be easily ignored by subsequent courts. But one particular form of dicta is especially problematic because it is more difficult to ignore. Judicial efficiency dicta are statements in judicial opinions about issues involved in the case and likely to present themselves again, but not necessary for the outcome of the case. While those statements are often about issues actually considered and may contribute to judicial efficiency by saving courts time when reconsidering issues already litigated, just like obiter dicta, judicial efficiency dicta exceed courts’ authority and are more likely than actual case holdings to be incorrect. Unlike obiter dicta, however, judicial efficiency dicta are difficult to identify. And most significantly, this particular form of dicta is more likely to be followed by subsequent courts, essentially being elevated to the position of holdings. Because it is more likely to become binding and cut off the natural development of the law, this “preemptive dicta” presents a significant concern