I went on Wikipedia for this and found this tid-bit:
"In chapter 58 (Padding Footsteps of Destruction), Roy is said to have learned his elementary alchemy from Riza's father. In a flashback conversation, Roy is revealed to have become a State Alchemist in order to help the common people, despite the objection of his teacher. Upon hearing Roy's desire for power, his teacher states that he would pass his greatest and most powerful alchemy to Roy under the condition he would use it on the course of good. However, before he could elaborate, Roy's teacher began to choke from coughing up blood and manages only to reveal that he had passed all his secrets on to his daughter, and asked of Roy to look after her. The strange markings on Hawkeye's back is the method chosen by her father to pass these secrets on."