The Colonial Ministry of Defense was the branch of the Colonial Government whose function was to research improvments in technology that can more effectively defend the Twelve Colonies from the Cylon threat if they ever decide to return.
Dr. Gaius Baltar was a consultant for the Ministry and worked on the development of Command Navigation Program which became an integral part of much of the Colonial Defense Force's systems. 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 Number 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.