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What difference we can observe when connecting using the certificate generated using the RADIUS and the credentials that we define in RADIUS like username & password.

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Certificates are more secure.

With password submission, an opponent who succeed to impersonate the Radius identity will receive the challenge-response from the clients. He can bruteforce them to retrieve the original password which as possible as the password is strong.

With certificates, the private key can be bruteforced in a similar way. But bruteforcing an asymmetric key is not achievable as it is composed of many many more bits than a regular password.

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Sibwara has a good response, but I want to add a little more nuance to it.

First, your EAP connection should always be encrypted with TLS. So you should use a form of EAP authentication which does that, such as EAP-TLS or EAP-TTLS. Ideally, you will also restrict the cipher suites to secure ones which provide perfect forward secrecy.

In general, certificates are stronger than passwords because passwords as a rule lack as much entropy as the typical certificate. However, if you assign credentials to users or they pick strong, pseudorandom passwords (both of which essentially require password managers), then the password can be just as secure or more. I generally pick pseudorandom passwords with 200 or more bits of entropy, whereas a typical 3072-bit RSA provides 128 bits of security. However, I am not your typical user, and if users provide their own passwords, they will often pick poorly.

Certificates are generally not memorable and therefore must be stored independently. If generated securely, they are not subject to brute-forcing. They also have the benefit that an attacker who can intercept the connection (because of a misconfigured TLS root certificate store, broken security software, or other misconfiguration) cannot learn anything about the connection, since the signature operation from the private key won't leak anything about private key itself. Passwords are often sent in plaintext in some inner EAP protocols, and other protocols use weak hashing, so in this case, the password could be exposed.

In a typical scenario, attackers cannot intercept the connection if the configuration is correct. TLS is presently considered secure.

If you're unsure, you should use certificates: either RSA with 3072 bits or more, or ECDSA with 256 bits or more. If your organization requires a 192-bit security level, use ECDSA with a 384-bit curve.

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