The aim of Analysis of Algorithms, a term coined by Donald Knuth, is to precisely analyse various algorithms in an asymptotic and probabilistic sense. Apart from the average behaviour for large values of the parameter, limiting distributions of quantities describing the algorithms are also of interest. Specifically, we focus on the design and the analysis of algorithms (1) for efficient computations in Abelian groups, e.g. in public key cryptography and (2) for efficient generation of combinatorial structures, e.g. Boltzmann Sampler.