Over the last decade, there have been significant efforts in developing efficient XOR-enabled SAT solvers for cryptographic appli- cations. In [22] we proposed a solver specialised to cryptographic problems. This solver is dedicated to instances arising from the index calculus attack on the discrete logarithm problem for elliptic curve-based cryptosystems and its most prominent feature is the module that performs an enhanced version of the Gaussian Elimination. [22] is concentrated on the theoretical aspects of the new tool, but the running time-per-conflict results suggest that this module uses efficient implementation techniques as well. Thus, the first goal of this paper is to give a comprehensive ex- position of the implementation details of WDSat. In addition, we show that the WDSat approach can be extended to other cryptographic applications, mainly all attacks that involve solving dense Boolean polynomial systems. We give complexity analysis for such systems and we compare different state-of-the-art SAT solvers experimentally, concluding that WDSat gives the best results. As a second contribution, we provide an original and economical implementation of a module for handling OR-clauses of any size, as WDSat currently handles OR-clauses comprised of up to four literals. We finally provide experimental results showing that this new approach does not impair the performance of the solver.