Women in and around St Andrews, Fife, were advised not to walk alone at night after a 27-year-old was raped on Wednesday last week.
Police believe the same man may have indecently assaulted an 18-year-old student on campus the following day.
The suspect is described as 5ft 8in to 5ft 10in tall and wearing a dark puffa-style jacket, tracksuit bottoms, a grey beanie hat and possibly gloves.
Detective Chief Inspector Pauline McCallum said: "We wish to speak to the man pictured in the images in connection with our inquiries, and anyone who can assist us in tracing him is asked to come forward.
"Similarly, we would ask the man himself to get in touch and help with our investigation."
The first assault happened in the Doubledykes Road area.
A student was then targeted as she walked along a lane between the university sports hall and the David Russell Apartments. Both attacks happened in the early hours.
Anyone with information is asked to contact the Police Service of Scotland on 101 or to call Crimestoppers on 0800 555111.