To get weighted residuals, the difference between the measured and the predicted value is divided by an estimate of its root mean square value. To estimate the spatial standard deviation of the isotopic ratio, we equate the sum of the squared weighted residuals to its approximate expected value. The approximate expected value is obtained by a bootstrap resampling method. Based on the estimated null distribution of the estimated spatial standard deviation, we test the hypothesis that the isotopic ratio is constant throughout the sample. To check the validity of our methods, we analyze SIMS data collected from a homogeneous chromium sample.
Results are consistent with the hypothesis of homogeneity.
Further, the expected value of the estimated standard deviation closely tracks the actual standard deviation. While these new features are useful, as with any other security critical application, new features can open the door for new types of attacks. In this paper, we will concentrate on those attacks against a PKI which allow an attacker to take advantage of a compromised private key. In particular, we will look at types of attacks that may allow an attacker, who has compromised someone else's private key, to either circumvent or exploit the mechanisms designed to deal with key compromise. The paper includes descriptions of several such attacks as well as suggestions to either prevent these attacks or to mitigate the damage that they can cause.