Even a 768-bit key requires vast resources to break. Add one bit, to make it 769 bits long, and the number of possible keys doubles, the problem becomes much more difficult. A 770-bit key is that much more difficult yet, and so on. By using 768-bit keys, Randy and Avi could keep their communications secret from nearly every entity in the world for at least the next several years. A 1024-bit key would be vastly, astronomically more difficult to break.