Major Emmanuel Chirchir confirmed that the attackers are Abu Baara al-Sudani, Omar Nabhan, Khattab al-Kene and Umayr.
He told The Associated Press: "I confirm those are the names of the terrorist."
Little is known about their identity.
Matt Bryden, the former head of the United Nations Monitoring Group on Somalia, said via email that al-Kene and Umayr are known members of al-Hijra, a Kenyan extremist group affiliated with al-Shabab. He added that Nabhan may be a relative of Saleh Ali Saleh Nabhan, who was the most-wanted al-Qaida operative in the region until he was killed in a 2009 strike led by Navy Seals.