Which method allows sysadmins to configure devices and services for administrative logins, using cryptographic keys or passwords?

The method that allows system administrators to configure devices and services for administrative logins using cryptographic keys or passwords is SSH (Secure Shell). SSH is a protocol that provides a secure channel over an unsecured network in a client-server architecture, ensuring that data is transmitted securely. It utilizes encryption to protect credentials and prevents unauthorized access, making it a standard tool for remote administration of servers and other network devices.

In SSH, administrative logins are commonly secured using cryptographic keys, which can provide a more secure and efficient method to authenticate users compared to traditional passwords. This key-based authentication reduces the risk of brute-force attacks and eliminates the need for transmitting passwords over the network, which can be intercepted by malicious actors.

Other methods mentioned, such as S/MIME, API, and ECDH, do not specifically focus on secure administrative access to devices. S/MIME is used primarily for securing email communication, API is a set of protocols for building and interacting with software applications, and ECDH is a key exchange algorithm that helps in securely exchanging cryptographic keys rather than providing the means to log in or configure devices. Thus, SSH is the appropriate choice for secure administrative logins.