K is a contact of Professor Karl von Toten. His or her name is unknown, K is a nickname used by von Toten in his diary.
K seems to be a German contact of von Toten's, who he shared ideas of his work with. K would seem to have some connection to the emperor, since the German word for Emperor is Kaiser. He also seems to have power over von Toten his work. That makes it more likely that he is the Emperor.
K's identity is not revealed. However, it might be that he is the emperor himself. Then K would be short of Kaiser. Then again, K and emperor were mentioned in the same sentence.
Another possibility is Katia von Bonen, who is a friend of Toten's, and maybe his wife. However, Karl von Toten seemed to be explaining his work to her as a new matter. This was risky, since he sends classified information via the mail.