## 2 Related Work  
In recent years, researchers have made many contributions to the access authentication of SGINs. [PERSON] et al. [2] provided a systematic overview of 6G security and privacy issues. They analyzed the security architecture of 6G and considered the new open authentication protocols (e.g., satellite, sea area) for non-3 GPP networks, as one of the priorities for 6G network access security. [PERSON] et al. [16] made use of the broadcasting function of satellites to propose an efficient and lightweight access authentication scheme, to prevent the burden of \"message storms\" on satellite authentication. [PERSON] et al. [17] proposed an authentication scheme for heterogeneous B5G networks (including satellite networks) and proposed a user detection scheme based on trust evaluation. [PERSON] et al. [18] proposed an anonymous mutual authentication scheme based on RLWE, which can resist attacks based on quantum computing and guarantee efficiency and security in the post-quantum era. [PERSON] et al. [19] proposed a mutual authentication protocol named IMAS, which introduced group management forms to the satellite, to accomplish the multicast authentication between UE and satellites. [PERSON] et al. [20] proposed an access authentication protocol based on elliptic curve cryptography (ECC), which included three entities: the UE, satellite, and ground station. In addition, the scheme designed a batch handover scheme to reduce overheads. In the face of the high privacy requirements of users of 6G, anonymous authentication based on aliases or group signature authentication can be used. Although the alias mechanism [21] has good performance in information transmission and privacy protection, users need to store a large number of certificates, which leads to a large amount of overheads [22]. The traditional group signature message will bring some transmission overheads. [PERSON] et al. [23] proposed a short group signature (SGS) scheme, which allows bilinear pairing to be widely used in modern cryptography. [PERSON] and [PERSON] [12] proposed a batch authentication scheme based on SGS, so that SGS can be applied to a large number of user authentication scenarios. [PERSON] [24] proposed a scheme to transform the SGS signature algorithm into a signcryption algorithm, which ensures message integrity and confidentiality. Owing to the large number of user nodes, researchers have proposed batch authentication. [PERSON] et al. [25] proposed a fast anonymous batch authentication scheme for vehicle networking, which can verify multiple requests at a time and negotiate a session key with the vehicle through broadcast messages. Considering that a failure of batch authentication will lead to the failure of all authentication of a batch of nodes, the author also proposed to rebatch authentication to prevent possible DoS attacks. [PERSON] et al. [26] proposed a lightweight group authentication scheme for M2M networks, and the UE in their scheme can also accomplish rebatch authentication by dichotomizing. [PERSON] et al. [27] proposed ECC-based lightweight security without using a batch verification method (LSWBVM). Their method can authenticate a large number of request messages and verify messages one by one. Due to the presence of multiple SGIN operators, cross-domain roaming authentication has become a research direction. [PERSON] et al. [28] proposed a lightweight group key negotiation protocol based on \((t,\ n)\) secret sharing and proposed a cross-domain handover authentication scheme. Considering the problems of different operators in the converged network, [PERSON] et al. [29] proposed a decentralized anonymous authentication scheme applied to the cross-operator satellite service scenario, which can carry out cross-domain fast handover authentication and ensure the fairness of billing. [PERSON] et al. [30] proposed an authentication scheme based on group signatures and completed cross-domain roaming of users through advanced negotiation between ground stations and satellites. [PERSON] et al.