What is the best method to implement secure authentication to third-party websites without using users' passwords?

The most effective method for implementing secure authentication to third-party websites without utilizing users' passwords is OAuth. This protocol allows users to grant third-party access to their resources without sharing their password directly. Instead, users authenticate with the service they are using, and then OAuth provides a token that can be used by the third-party application to access user data securely.

This method enhances security because it minimizes the risk of exposing user credentials. OAuth allows users to manage permissions and revoke access without changing their password, adding another layer of security. Conversely, while SSO is about enabling users to log in once and gain access to multiple applications, it still generally involves password-based mechanisms for the initial authentication and does not eliminate the need for passwords. SAML is primarily used for exchanging authentication and authorization data between parties, but it also typically relies on users entering their credentials initially. PAP (Password Authentication Protocol), on the other hand, directly involves passwords, which is contrary to the goal of avoiding password use.

Thus, OAuth is specifically designed to provide secure delegated access without handling user passwords directly, making it the optimal choice for this scenario.