The function of the Torah of Adam was to correct the snake because there was not yet corruption in creation. After his sin there was a spreading of foulness in his body, in creation, and in the various different activities or areas of human experience, which meant that there were more mitzvos. It went from one mitzvah to seven mitzvos. The Torah of Noach until the time of Moshe was fundamentally concerned with the correction of foulness and the fixing of the snake as well. By the time of the giving of the Torah, the sitra achra had been spreading in 613 areas of human experience, thus the 613 mitzvos to be correct the entire situation.