The incident happened on the 20:14 service, between Keith and Elgin, on Friday 16 June at about 21:20.
The suspect - believed to be travelling with about seven other men - then got off the train at Elgin.
He was white, about 25, and 6ft tall. He was wearing a black and white top and sunglasses.
Det Con Nick Ritchie, of British Transport Police, said: "No-one has the right to treat another person like that.
"We're determined to stamp out this kind of behaviour from our rail network, so please, if you know this man, let us know."
Anyone with information can text 61016 or call 0800 40 50 40, quoting reference 682 of 16 June.

Police said a boy on the bank saw his father's boat capsize on the River Wey in Guildford at about 13:10 BST on Monday.
Insp Claire Sutherland said the boy jumped into the fast-flowing river to try to save him but members of the public shouted to come back.
Divers are trawling the river in Millmead.
Members of the public have been urged not to go into the water if they spot the missing kayaker, but to call 999 immediately.
A flood warning is in place for parts of the River Wey, following heavy rain and storms over the weekend.
A police helicopter, firefighters and ambulance crews were all at the scene on Monday.
The river from Millmead to Stoke Lock is a popular with kayakers.
Wey Valley Kayak Club, which has about 400 members, is situated about about one mile down river from where the man capsized.
It tweeted on Monday morning the Wey from Godalming Wharf to Thames Lock was not safe.

The car owner contacted the AA after the cub was seen darting under a wheel arch and up into the engine bay of the Audi SQ5.
Patrolman Jason Robertson spotted a dangling leg and was able to pull the animal - which had made its way into the gearbox - free.
The cub, now named Basset, was unhurt.
He is being looked after by staff at the Scottish SPCA's wildlife rescue centre in Fishcross.
Mr Robertson, who has worked for the AA since 2006, said: "When I saw the job come up with 'fox in engine bay' I feared the worst. I thought maybe it had been hit and I would be arriving at quite a gruesome scene, but I was pleasantly surprised to find that wasn't the case.
"The SSPCA were there but had been unable to find the fox. We tried to coax it out with cat food but when that didn't work, I jacked the car up and saw one of the cub's legs dangling down. Luckily, it was pulled out unscathed.
"I've rescued plenty of kids from locked cars, but this was definitely a first for me."
Scottish SPCA centre manager Colin Seddon said: "Basset appeared unharmed and is doing well now. We'll keep him in our care until the summer when he'll be released back into the wild with a number of other fox cubs at a carefully selected site."

Southern Water said the pipe burst in Chestnut Avenue had affected homes in the SO53 and SO16 postcodes leaving them with no water or low pressure.
The company said supplies would gradually return to normal later as the main was being repaired.
Chestnut Avenue is expected to remain closed until Friday as the burst had caused substantial damage.
Engineers have closed off the road between the Bournemouth Road junction and the Tollgate junction.
An appeal for witnesses has been made after a woman was inappropriately touched on a train travelling between Aberdeen and Inverness.
[NEXT_CONCEPT]
A search has resumed for a man missing after his kayak overturned on a river in Surrey.
[NEXT_CONCEPT]
A fox cub is recovering at an animal centre after being rescued from the gear box of a car in Aberdeen by an AA patrolman.
[NEXT_CONCEPT]
A burst water main in Eastleigh has caused flooding in a road and left about 4,000 homes without water.