A New Test Statistic for Key Recovery Attacks Using Multiple Linear Approximations

The log-likelihood ratio (LLR) and the chi-squared distribution based test statistics have been proposed in the literature for performing statistical analysis of key recovery attacks on block ciphers. A limitation of the LLR test statistic is that its application requires the full knowledge of the corresponding distribution. Previous work using the chi-squared approach required {\em approximating} the distribution of the relevant test statistic by chi-squared and normal distributions. Problematic issues regarding such approximations have been reported in the literature. Perhaps more importantly, both the LLR and the chi-squared based methods are applicable only if the success probability $P_S$ is greater than 0.5. On the other hand, an attack with success probability less than $0.5$ is also of considerable interest. This work proposes a new test statistic for key recovery attacks which has the following features. Its application does not require the full knowledge of the underlying distribution; it is possible to carry out an analysis using this test statistic without using any approximations; the method applies for all values of the success probability. The statistical analysis of the new test statistic follows the hypothesis testing framework and uses Hoeffding\u27s inequalities to bound the probabilities of Type-I and Type-II errors

Assessment of myocardial function in pediatric patients with operated tetralogy of Fallot: preliminary results with 2D strain echocardiography

The global myocardial function in patients after repair of tetralogy of Fallot (TOF) can be assessed by cardiovascular magnetic resonance (CMR) and measurement of B-type natriuretic peptides. Two-dimensional echocardiography-derived strain and strain rate (2D strain) facilitate the assessment of regional myocardial function. We evaluated myocardial function in 16 children with residual severe pulmonary valve regurgitation and right ventricular (RV) volume overload after TOF repair before, 1 month after, and 6 months after pulmonary valve replacement (PVR). In 2D strain echocardiography preoperatively, the longitudinal systolic RV strain was reduced (p < 0.05). One month after PVR, longitudinal systolic RV strain decreased further (p < 0.05), while systolic and early diastolic radial left ventricular strain and strain rate increased (each p < 0.05), followed by a return toward preoperative values after 6 months. Six months after PVR, preoperatively elevated RV end-diastolic volume (p < 0.01) assessed by CMR and N-terminal pro-B-type natriuretic peptide (p < 0.05) decreased. In conclusion, the impairment of the regional myocardial after TOF repair and transient changes after PVR can be subtly analyzed by 2D strain echocardiography in addition to the established assessment of myocardial function with CMR and measurement of B-type natriuretic peptides