The Defence Ministry's job was to continue researching better and better technology that can effectively defend the Twelve Colonies from the Cylon threat if they ever decide to return. Gaius Baltar was a consultant for the Ministry and worked on the Command Navigation Program. Number Six probably also worked at the Ministry as when she fixed his algorithm for him, she put backdoors into the program and also accessed the Colonial Defense Mainframe located in their main building.
Dr. Amorak also worked at the Ministry, and when Six appeared on the Galactica under the alias of Shelly Godfrey, she pretended to be a systems analyst at the Ministry and the lover of Dr. Amorak.