Handover authentication in high mobil-ity scenarios is characterized by frequent and short-term parallel execution. Moreover, the penetrationloss and Doppler frequency shift caused by high speedalso lead to the deterioration of network link qual-ity. Therefore, high mobility scenarios require han-dover schemes with less handover overhead. How-ever, some existing schemes that meet this require-ment cannot provide strong security guarantees, whilesome schemes that can provide strong security guar-antees have large handover overheads. To solve thisdilemma, we propose a privacy-preserving handoverauthentication scheme that can provide strong secu-rity guarantees with less computational cost. Based onOrthogonal Time Frequency Space (OTFS) link andKey Encapsulation Mechanism (KEM), we establishthe shared key between protocol entities in the initialauthentication phase, thereby reducing the overhead inthe handover phase. Our proposed scheme can achievemutual authentication and key agreement among theuser equipment, relay node, and authentication server.We demonstrate that our proposed scheme can achieveuser anonymity, unlinkability, perfect forward secrecy,and resistance to various attacks through security anal-ysis including the Tamarin. The performance evalua-tion results show that our scheme has a small computa-tional cost compared with other schemes and can also provide a strong guarantee of security properties