Initialisation flaws in the A5-GMR-1 satphone encryption algorithm

A5-GMR-1 is a synchronous stream cipher used to provide confidentiality for communications between satellite phones and satellites. The keystream generator may be considered as a finite state machine, with an internal state of 81 bits. The design is based on four linear feedback shift registers, three of which are irregularly clocked. The keystream generator takes a 64-bit secret key and 19-bit frame number as inputs, and produces an output keystream of length between $2^8$ and $2^{10}$ bits. Analysis of the initialisation process for the keystream generator reveals serious flaws which significantly reduce the number of distinct keystreams that the generator can produce. Multiple (key, frame number) pairs produce the same keystream, and the relationship between the various pairs is easy to determine. Additionally, many of the keystream sequences produced are phase shifted versions of each other, for very small phase shifts. These features increase the effectiveness of generic time-memory tradeoff attacks on the cipher, making such attacks feasible.

High body mass index is not a barrier to physical activity: Analysis of international rugby players' anthropometric data

Recent data indicate that levels of overweight and obesity are increasing at an alarming rate throughout the world. At a population level (and commonly to assess individual health risk), the prevalence of overweight and obesity is calculated using cut-offs of the Body Mass Index (BMI) derived from height and weight. Similarly, the BMI is also used to classify individuals and to provide a notional indication of potential health risk. It is likely that epidemiologic surveys that are reliant on BMI as a measure of adiposity will overestimate the number of individuals in the overweight (and slightly obese) categories. This tendency to misclassify individuals may be more pronounced in athletic populations or groups in which the proportion of more active individuals is higher. This differential is most pronounced in sports where it is advantageous to have a high BMI (but not necessarily high fatness). To illustrate this point we calculated the BMIs of international professional rugby players from the four teams involved in the semi-finals of the 2003 Rugby Union World Cup. According to the World Health Organisation (WHO) cut-offs for BMI, approximately 65% of the players were classified as overweight and approximately 25% as obese. These findings demonstrate that a high BMI is commonplace (and a potentially desirable attribute for sport performance) in professional rugby players. An unanswered question is what proportion of the wider population, classified as overweight (or obese) according to the BMI, is misclassified according to both fatness and health risk? It is evident that being overweight should not be an obstacle to a physically active lifestyle. Similarly, a reliance on BMI alone may misclassify a number of individuals who might otherwise have been automatically considered fat and/or unfit.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.