In this paper, we suggest a new architecture of a computational grid that involves resources of BOINC-based volunteer computing projects and idle resources of computational clusters. We constructed a computational grid of the proposed kind, based on several computational clusters and the volunteer computing project SAT@home. This project, launched and maintained by us, is aimed at solving hard computational problems, which can be effectively reduced to Boolean satisfiability problem. In the constructed grid several new combinatorial designs based on diagonal Latin squares of order 10 were found, and also several weakened cryptanalysis problems for the Bivium cipher were solved.
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