The Colonial Ministry of Defense was the branch of the Colonial Government based primarily on Caprica, whose function was to research improvements 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 the Command Navigation Program which became an integral part of much of the Colonial Defense Force's systems. While Natasi (Number Six) did not work at the Ministry, Six worked as a contractor and Baltar implied that she would get an advantage in future work for the Ministry in exchange for her help. Thus she was allowed to tag along with Baltar as a guest while assisting him with creating the CNP, accessing the Colonial Defense Mainframe located in their main building.
Six not only involved herself in his work by fixing over half of Baltar's CNP programming algorithms, she secretly added backdoors into the program that would cripple the bulk of the Colonial Defense Force and spell the doom of the Twelve Colonies. (Mini-Series).
Dr. Amorak also worked at the Ministry and was a colleague of Baltar, and was presumably killed when the Olympic Carrier was destroyed after being commandeered by Cylons. When a copy of Number Six appeared on Galactica under the alias of Shelly Godfrey, she pretended to be a systems analyst at the Ministry and the lover of Dr. Amorak (Six Degrees of Separation).