Which of the following is the primary objective of a rootkit?

While a rootkit might open a port, this is a method or consequence of its presence, not its primary objective, which is concealment.

Rootkits typically exploit vulnerabilities, but creating a buffer overflow is a specific exploit technique to gain initial access, not the rootkit's ongoing primary objective.

Rootkits are designed to gain and maintain surreptitious access to a computer while hiding their presence from legitimate users and system administrators. They achieve this by modifying core operating system files, utilities, or kernel modules, replacing legitimate programs with malicious versions to obscure malicious processes, files, or network connections.

Providing an undocumented opening in a program is a description of a backdoor, which can be a component of a rootkit's functionality, but the rootkit's overarching goal is hiding.