It is widely percieved that the Koran is authentic because it is one document that can trace itself back to the prophet Muhammad himself. I did a bit of research on this and found that the Koran has as many authenticity problems as does the bible.
Historical background:
For the Koran, there was no single document collecting all the revelations, after Muhammad’s death in 632 C.E. Many of his followers tried to gather all the known revelations and write them down in codex form. Soon there were the codices of several scholars such as Ibn Masud, Uba ibn Ka’b, ‘Ali, Abu Bakr, al-Aswad, and others (fifteen primary codices, and a large number of secondary ones).
As Islam spread, there developed the metropolitan codices in the centers of Mecca, Medina, Damascus, Kufa, and Basra. Each were different so as to cause considerable unrest. A Step was taken by the Caliph Uthman (644-656) to prepare an official document. The caliph chose Zayd ibn Thabit to prepare the official text. Three noble families of Mecca assisted in revising the Koran. Copies of the new version were were sent to Kufa, Basra, Damascus, and perhaps Mecca, and one was, of course, kept in Medina. All other versions were ordered to be destroyed.
Conclusion:
You can see the same issues that confronted the Christian church in terms of multiple versions floating around and the similar actions being taken to define which documents were 'authentic'. Neither the Koran nor the Bible can be proved to be authentic based on original text.