We study the problem of decoding secret messages encrypted by the German Army with the M3 Enigma machine after September 15, 1938. We focused our attention on the algorithmization and programming of this problem. A completion and optimization of Zygalski’s sheets method were presented previously. We describe below the missing algorithm solving the problem of the plugboard settings with an algebraic justification. This method is the original idea of the authors, and we can use it for cryptanalysis together with both Zygalski’s sheets method and Rejewski’s bomb method. Next, we present a reconstruction of the cryptologic bomb. We enclose an implementation of both algorithms in Cpp language.