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This paper proposes a Light-Weight Secure Routing (LWSR) protocol for wireless ad hoc networks, in which a novel routing authentication mechanism with simple geometric properties of lines is employed. The LWSR protocol can prevent not only attacks from outside on the authentication of the routing packets but also attacks from inside on the revocation of the Re-Line mechanism. Using no digital signatures, our new protocol can save a considerable part of the computation cost and get rid of the need for the pre-deployed architecture supported by Public Key Infrastructure (PKI). To sum up, the new LWSR protocol can significantly minimize the computational overhead of both the authorization and verification processes, and it is also suitable for most routing protocols with certain modifications. Finally, the storage size of the security parameters is also minimized.