This paper presents a physically-secure wireless communication system utilizing orbital angular momentum (OAM) waves at 0.31THz. A trustworthy key distribution mechanism for symmetric key cryptography is proposed by exploiting random hopping among the orthogonal OAM-wave modes and phases. Keccak-f[400] based pseudorandom number generator provides randomness to phase distribution of OAM-wave modes for additional security. We assess the security vulnerabilities of using OAM modulation in a THz communication system under various physical-layer threat models as well as analyze the effectiveness of these threat models for varying attacker complexity levels under different conditions.