The 29-year-old woman was attacked in Papermill Wynd in Edinburgh at about 01:00 on Saturday 19 December.
Police said she had been out in the city centre with friends and was walking home when a man approached her in Queen Street.
The pair walked together until they reached Papermill Wynd, where the man assaulted her.
She contacted police after returning home and detectives said they have since been pursuing various lines of inquiry to identify the man or speak with anyone who may have witnessed the attack.
The suspect was described as being of South Asian appearance, in his late 20s, 5ft 7in of skinny build. He had short, dark hair and was wearing blue jeans and a dark waterproof jacket.
Det Sgt Jon Pleasance, of Police Scotland, said: "This was a distressing ordeal for the victim and we have been actively conducting inquiries in the area to trace the suspect.
"I would ask that anyone who remembers seeing any suspicious activity around Papermill Wynd in the early hours of 19 December contacts police immediately.
"We would also ask anyone who was returning from work or a Christmas night out in the city centre that evening and remembers seeing this male approaching and then walking with the victim to get in touch."
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