A 22-year-old man suffered bruises to his face and torn ankle ligaments when he was assaulted in Rustington on Sunday March 2.
He was walking near Sainsbury's in New Road at 9.45am when a male passenger of a car got out and punched him in the face, knocking him to the ground. The victim was then kicked in the head.
His attacker, who left the scene in a small three-door car, is described as white, 6ft, and wearing a white T-shirt and jeans.
A police spokesman said: "This was an unprovoked attack. The victim has been left in a lot pain and we are keen to trace this man.
"We believe there were witnesses to the attack and would ask them or anyone with information to contact police on 0845 6070999.
The attack is one of a series of crimes police are investigating in Arundel, Rustington and Worthing.
In Worthing, two youths talked their way into the home of a vulnerable man in Meadow Road, Worthing, and stole his wallet, which contained £15.
The youths, aged about 15, knocked on his door and said they were visiting on behalf of the police. The victim allowed them in and later discovered his wallet was missing.
One of the youths was described as wearing a dark coat.
A police spokesman said: "Official visitors will usually arrange an appointment with you beforehand.
"If you are not expecting them and you are alone, then ask them to call back when you have someone with you.
"Genuine callers will always be happy to make an appointment and will carry an identity card with a photograph. They won't mind waiting if you want to phone and confirm their identity.
"If someone official calls at your door, then you should always check your back door is locked and then use a spy hole or the window to see who it is. Always use a security chain while you are talking to the person on your doorstep."
In Arundel, a large amount of outdoor clothing was stolen when burglars broke the front window of Peglars in the High Street at 3.20am. The burglars put the clothes in black bin bags and ran off along Tarrant Street.
Jewellery and credit cards were stolen from a house in Fourth Avenue, Worthing, while the occupants were outside gardening.
A police spokesman warned: "Now we are starting to enjoy finer weather, we would advise people to be vigilant about their home security.
"Thefts often occur when house owners are enjoying the sunshine in their gardens and the burglar enters an open door or window.
"People may only be away from the house for a few seconds but that is all the time a thief needs.
"If you are in your garden, then you should lock the doors or be in a position where you can see them. Do not leave windows open when you are popping out for a few minutes."
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