The Space–Air–Ground Integrated Network (SAGIN) expands cyberspace greatly. Dynamic network architecture, complex communication links, limited resources, and diverse environments make SAGIN’s authentication and key distribution much more difficult. Public key cryptography is a better choice for terminals to access SAGIN dynamically, but it is time-consuming. The semiconductor superlattice (SSL) is a strong Physical Unclonable Function (PUF) to be the hardware root of security, and the matched SSL pairs can achieve full entropy key distribution through an insecure public channel. Thus, an access authentication and key distribution scheme is proposed. The inherent security of SSL makes the authentication and key distribution spontaneously achieved without a key management burden and solves the assumption that excellent performance is based on pre-shared symmetric keys. The proposed scheme achieves the intended authentication, confidentiality, integrity, and forward security, which can defend against masquerade attacks, replay attacks, and man-in-the-middle attacks. The formal security analysis substantiates the security goal. The performance evaluation results confirm that the proposed protocols have an obvious advantage over the elliptic curve or bilinear pairings-based protocols. Compared with the protocols based on the pre-distributed symmetric key, our scheme shows unconditional security and dynamic key management with the same level performance.