Biometrics authenticated schemes using smart cards have attracted much attention in multi-server environments. Several schemes of this type where proposed in the past. However, many of them were found to have some design flaws. This paper concentrates on the security weaknesses of the three-factor authentication scheme by Mishra et al. After careful analysis, we find their scheme does not really resist replay attack while failing to provide an efficient password change phase. We further propose an improvement of Mishra et al.’s scheme with the purpose of preventing the security threats of their scheme. We demonstrate the proposed scheme is given to strong authentication against several attacks including attacks shown in the original scheme. In addition, we compare the performance and functionality with other multi-server authenticated key schemes.

We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates are used to illustrate the long-time behavior of the population under investigation.

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