Verifying the authenticity of the source of network traffic and the path that this traffic has traversed is an important building block for secure network protocols and defense mechanisms. We investigate these problems of in-network source authentication and path validation. Existing approaches are either unable to satisfy security requirements or need significant computational resources due to cryptographic operations, thus limiting their suitability in practice where potentially every packet needs to be checked at line rate. We present Orthogonal Sequence Verification (OSV), a lightweight and scalable technique to address this problem. OSV uses orthogonal capabilities to enable source authentication and path verification simultaneously. The verification of these orthogonal capabilities is based on inner product computations, which can be easily realized by basic bitwise operations in a processor. Therefore, OSV significantly reduces computational cost, while achieving the necessary security properties. We present evaluation results which show that OSV is three orders of magnitude faster than the current approaches based on cryptographic operations. Therefore, we believe that our work presents an important contribution toward realizing high-performance, secure network protocols and network attack defenses in practice.