Quantum Algorithm for the Collision Problem

In this note, we give a quantum algorithm that finds collisions in arbitrary r-to-one functions after only O((N/r)^(1/3)) expected evaluations of the function. Assuming the function is given by a black box, this is more efficient than the best possible classical algorithm, even allowing probabilism. We also give a similar algorithm for finding claws in pairs of functions. Furthermore, we exhibit a space-time tradeoff for our technique. Our approach uses Grover's quantum searching algorithm in a novel way.Comment: 8 pages, LaTeX2

A Protocol for Generating Random Elements with their Probabilities

We give an AM protocol that allows the verifier to sample elements x from a probability distribution P, which is held by the prover. If the prover is honest, the verifier outputs (x, P(x)) with probability close to P(x). In case the prover is dishonest, one may hope for the following guarantee: if the verifier outputs (x, p), then the probability that the verifier outputs x is close to p. Simple examples show that this cannot be achieved. Instead, we show that the following weaker condition holds (in a well defined sense) on average: If (x, p) is output, then p is an upper bound on the probability that x is output. Our protocol yields a new transformation to turn interactive proofs where the verifier uses private random coins into proofs with public coins. The verifier has better running time compared to the well-known Goldwasser-Sipser transformation (STOC, 1986). For constant-round protocols, we only lose an arbitrarily small constant in soundness and completeness, while our public-coin verifier calls the private-coin verifier only once

Quantum Interactive Proofs with Competing Provers

This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that every language having an ordinary quantum interactive proof system also has a quantum refereed game in which the verifier exchanges just one round of messages with each prover. A key part of our proof is the fact that there exists a single quantum measurement that reliably distinguishes between mixed states chosen arbitrarily from disjoint convex sets having large minimal trace distance from one another. We also show how to reduce the probability of error for some classes of quantum refereed games.Comment: 13 pages, to appear in STACS 200

Making Classical Ground State Spin Computing Fault-Tolerant

We examine a model of classical deterministic computing in which the ground state of the classical system is a spatial history of the computation. This model is relevant to quantum dot cellular automata as well as to recent universal adiabatic quantum computing constructions. In its most primitive form, systems constructed in this model cannot compute in an error free manner when working at non-zero temperature. However, by exploiting a mapping between the partition function for this model and probabilistic classical circuits we are able to show that it is possible to make this model effectively error free. We achieve this by using techniques in fault-tolerant classical computing and the result is that the system can compute effectively error free if the temperature is below a critical temperature. We further link this model to computational complexity and show that a certain problem concerning finite temperature classical spin systems is complete for the complexity class Merlin-Arthur. This provides an interesting connection between the physical behavior of certain many-body spin systems and computational complexity.Comment: 24 pages, 1 figur

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation

Comparison of the estimated incidence of acute leptospirosis in the Kilimanjaro Region of Tanzania between 2007-08 and 2012-14

Background: The sole report of annual leptospirosis incidence in continental Africa of 75–102 cases per 100,000 population is from a study performed in August 2007 through September 2008 in the Kilimanjaro Region of Tanzania. To evaluate the stability of this estimate over time, we estimated the incidence of acute leptospirosis in Kilimanjaro Region, northern Tanzania for the time period 2012–2014. Methodology and Principal Findings: Leptospirosis cases were identified among febrile patients at two sentinel hospitals in the Kilimanjaro Region. Leptospirosis was diagnosed by serum microscopic agglutination testing using a panel of 20 Leptospira serovars belonging to 17 separate serogroups. Serum was taken at enrolment and patients were asked to return 4–6 weeks later to provide convalescent serum. Confirmed cases required a 4-fold rise in titre and probable cases required a single titre of ≥800. Findings from a healthcare utilisation survey were used to estimate multipliers to adjust for cases not seen at sentinel hospitals. We identified 19 (1.7%) confirmed or probable cases among 1,115 patients who presented with a febrile illness. Of cases, the predominant reactive serogroups were Australis 8 (42.1%), Sejroe 3 (15.8%), Grippotyphosa 2 (10.5%), Icterohaemorrhagiae 2 (10.5%), Pyrogenes 2 (10.5%), Djasiman 1 (5.3%), Tarassovi 1 (5.3%). We estimated that the annual incidence of leptospirosis was 11–18 cases per 100,000 population. This was a significantly lower incidence than 2007–08 (p<0.001). Conclusions: We estimated a much lower incidence of acute leptospirosis than previously, with a notable absence of cases due to the previously predominant serogroup Mini. Our findings indicate a dynamic epidemiology of leptospirosis in this area and highlight the value of multi-year surveillance to understand leptospirosis epidemiology

Risk factors for human acute leptospirosis in northern Tanzania

Introduction: Leptospirosis is a major cause of febrile illness in Africa but little is known about risk factors for human infection. We conducted a cross-sectional study to investigate risk factors for acute leptospirosis and Leptospira seropositivity among patients with fever attending referral hospitals in northern Tanzania. Methods: We enrolled patients with fever from two referral hospitals in Moshi, Tanzania, 2012–2014, and performed Leptospira microscopic agglutination testing on acute and convalescent serum. Cases of acute leptospirosis were participants with a four-fold rise in antibody titers, or a single reciprocal titer ≥800. Seropositive participants required a single titer ≥100, and controls had titers <100 in both acute and convalescent samples. We administered a questionnaire to assess risk behaviors over the preceding 30 days. We created cumulative scales of exposure to livestock urine, rodents, and surface water, and calculated odds ratios (OR) for individual behaviors and for cumulative exposure variables. Results: We identified 24 acute cases, 252 seropositive participants, and 592 controls. Rice farming (OR 14.6), cleaning cattle waste (OR 4.3), feeding cattle (OR 3.9), farm work (OR 3.3), and an increasing cattle urine exposure score (OR 1.2 per point) were associated with acute leptospirosis. Conclusions: In our population, exposure to cattle and rice farming were risk factors for acute leptospirosis. Although further data is needed, these results suggest that cattle may be an important source of human leptospirosis. Further investigation is needed to explore the potential for control of livestock Leptospira infection to reduce human disease

Experimental quantum tossing of a single coin

The cryptographic protocol of coin tossing consists of two parties, Alice and Bob, that do not trust each other, but want to generate a random bit. If the parties use a classical communication channel and have unlimited computational resources, one of them can always cheat perfectly. Here we analyze in detail how the performance of a quantum coin tossing experiment should be compared to classical protocols, taking into account the inevitable experimental imperfections. We then report an all-optical fiber experiment in which a single coin is tossed whose randomness is higher than achievable by any classical protocol and present some easily realisable cheating strategies by Alice and Bob.Comment: 13 page

Formal Verification of Security Protocol Implementations: A Survey

Automated formal verification of security protocols has been mostly focused on analyzing high-level abstract models which, however, are significantly different from real protocol implementations written in programming languages. Recently, some researchers have started investigating techniques that bring automated formal proofs closer to real implementations. This paper surveys these attempts, focusing on approaches that target the application code that implements protocol logic, rather than the libraries that implement cryptography. According to these approaches, libraries are assumed to correctly implement some models. The aim is to derive formal proofs that, under this assumption, give assurance about the application code that implements the protocol logic. The two main approaches of model extraction and code generation are presented, along with the main techniques adopted for each approac