Digital signatures are used everywhere around us. They are well-studied and have been standardized since 1994. In 2002, Johnson et al. introduced the notion of homomorphic digital signatures, allowing one to perform computations on signed data. These signatures are especially useful for linear network coding, a technique used to improve throughput and resilience of networks, and in verifiable cloud computing. However, homomorphic signatures are not standardized and less well-studied, which creates a challenge when choosing one of the published schemes. Moreover, most schemes remain unimplemented, and it is insufficient to compare their theoretical performance for real-world applications. Those schemes that are implemented are not directly comparable since they use different instantiations of the same primitives or they are implemented in different programming languages.
In this thesis, we set out to find out how we can assess the performance of homomorphic signa- ture schemes. To this end, we have implemented eleven pairing-based linearly homomorphic signature schemes. All signature schemes have been implemented on the BLS12-381 curve to constitute a fair comparison. We assess the performance of the signature schemes based on their signing, verifying and combining performance, as well as the sizes of their keys and signatures. Furthermore, we analyse the impact that additional features such as supporting a multi-party setting have on the performance of a signature scheme. Based on our exper- imental results, we make recommendations for three types of applications: For constrained devices, the scheme Li20 is the most suitable due to its compact signing key and efficient sign- ing operation. For network coding, which requires fast verification, fast combining, and small signatures, we also recommend the scheme by Li et al. Finally, for a multi-party, privacy- preserving scheme, we recommend the scheme by Sch18 and Sch19, which preserve input privacy of homomorphically combined signatures. We find that we can assess the perfor- mance of a homomorphic signature scheme based on the speed of the signing, verifying and combining operation. Our implementation is publicly available.

Amsterdam Airport Schiphol has 5 runways, each of which can be used for take-off or landing of aeroplanes. The weather heavily influences which runway configuration air traffic control might pick. Airport Forecasting Service (AFOS) predicts which configuration of runways works most efficiently given a set of expected weather conditions and the standard deviations of wind components. These standard deviations give the system an indication of the accuracy of the weather forecasts.

Currently, the KNMI (Royal Netherlands Meteorological Institute) is the only meteorological institute that provides these standard deviations along with the weather forecast. This raises the main research question of this report: Is it possible to make accurate enough estimations of the standard deviation of wind direction and wind speed using historical data and future weather expectations. Estimating these standard deviations has been researched with two different approaches: a statistical method approach and a machine learning approach.

Statistical Methods Four fitting methods have been researched in search of the best statistical model to estimate the standard deviation of wind direction and speed: the Maximum Likelihood Method (MLM) and three Least Square Method implementations of a Weibull, Minimum Weibull and Double Weibull distribution. The performance of aggregates on the outcome of these four methods was also researched. One case takes the minimum standard deviation of the four, the other takes the mean.

MLM not only performs the best but also performs most consistently of the four fitting methods. Taking into account aggregates, MLM is more consistent than the minimum method but the minimum method outperforms it. Neither of these methods managed to meet the success criteria.

Machine Learning In regards to machine learning, the problem of estimating the standard deviations of wind direction and wind speed is a regression problem. The following machine learning models have been researched for Estimatic: MLPN, LSTM RNN, ERNN and RBFN.

LSTM RNNs outperform MLPNs, RBFNs and ERNNs for both wind direction and speed standard deviation estimation. LSTM RNN performance did not meet the success criteria.

The research concludes that it is not possible to make accurate enough estimations of the standard deviation of wind components using the historical data and future weather expectations available for Amsterdam Airport Schiphol.