The paper presents the results of investigating the effect of increase of observation correlations on detectability and identifiability of a single gross error, the outlier test sensitivity and also the response-based measures of internal reliability of networks. To reduce in a research a practically incomputable number of possible test options when considering all the non-diagonal elements of the correlation matrix as variables, its simplest representation was used being a matrix with all non-diagonal elements of equal values, termed uniform correlation. By raising the common correlation value incrementally, a sequence of matrix configurations could be obtained corresponding to the increasing level of observation correlations. For each of the measures characterizing the above mentioned features of network reliability the effect is presented in a diagram form as a function of the increasing level of observation correlations. The influence of observation correlations on sensitivity of the w -test for correlated observations (Förstner 1983,Teunissen 2006) is investigated in comparison with the original Baarda’s w -test designated for uncorrelated observations, to determine the character of expected sensitivity degradation of the latter when used for correlated observations. The correlation effects obtained for different reliability measures exhibit mutual consistency in a satisfactory extent. As a by-product of the analyses, a simple formula valid for any arbitrary correlation matrix is proposed for transforming the Baarda’s w -test statistics into the w -test statistics for correlated observations.

We analyze the Google-Apple exposure notification mechanism designed by the Apple-Google consortium and deployed on a large number of Corona-warn apps. At the time of designing it, the most important issue was time-to-market and strict compliance with the privacy protection rules of GDPR. This resulted in a plain but elegant scheme with a high level of privacy protection. In this paper we go into details and propose some extensions of the original design addressing practical issues. Firstly, we point to the danger of a malicious cryptographic random number generator (CRNG) and resulting possibility of unrestricted user tracing. We propose an update that enables verification of unlinkability of pseudonymous identifiers directly by the user. Secondly, we show how to solve the problem of verifying the “same household” situation justifying exempts from distancing rules. We present a solution with MIN-sketches based on rolling proximity identifiers from the Apple-Google scheme. Thirdly, we examine the strategies for revealing temporary exposure keys. We have detected some unexpected phenomena regarding the number of keys for unbalanced binary trees of a small size. These observations may be used in case that the size of the lists of diagnosis keys has to be optimized.