In the movie "Star Trek - Into Darkness", Carol Marcus mentions that her father gave her access to his super secret work. Khan was part of this work, he designed loads of things while there, it would be quite illogical that they both worked in the exact same field of expertise but never met. Then, when they catch Khan and march him through Engineering, Carol catches a glimpse of Khan and it seems she recognizes him. Later, in Med Bay while the Vengeance chases them, Khan says they are wrong to think they're safe at warp, and it only takes one very knowing look from him to Carol to make her run to the bridge. He obviously knows who she is. But what kind of history do they have? No source even mentions them knowing each other, but their few moments together seem kind of familiar. The entire internet seems to ignore that relationship, I can't find any answer to this!
They have no history.
She finagled a transfer onto the Enterprise precisely so that she could study the super-torpedoes that her father's secret research team were working on so secretively.
“Prepped and loaded for use in the weapons bay,” he informed her. Somehow, he thought, everything that had happened since the slaughter at Starfleet Headquarters seemed to keep coming back to the new weapons system. But why? “What are they? What’s so special about them other than that they’re supposed to be undetectable when in flight?”
She looked over at him. “I don’t know. That’s why I manipulated a transfer onto your ship—to find out.” Halting abruptly, she turned to face him, plainly embarrassed. “I do apologize for that, and I am sorry. I’m Carol Marcus.”
And her concern over what Khan said was motivated by her intuition as to what her father's actually been up to...
From where he was seated, Khan lifted his gaze to meet that of the doctor. “If you think you’re cleanly away, if you think you’re safe at warp—you’re wrong.” McCoy just grunted at the prisoner’s reply, but it touched something in Carol Marcus. Having taken a break from her research, her eyes now grew wide at the prisoner’s remark. Before a curious McCoy could think to question her, she had bolted from the room.