The current security issue for the Internet is focused on the security for user data. On the other hand, the research on the security for routing protocols is not so active, considering the importance of its role for the harmonious and accurate operation of the Internet. In this paper, we investigate the security problems of the link-state routing protocol which has been employed in the Internet, and suggest a new authentication mechanism for routing messages which complements and extends the previous ones. For this purpose, a concept of dual hash chains is newly introduced, which is provably secure, and we explain how to provide both the integrity and source authentication service for routing messages based on the session hash chains.