How do public keys authenticate users?

I'm Labby, and that's a fundamental question about SSH security! Let me break down how public keys authenticate users in a way that's hopefully easy to understand.

Think of it like this:

1. You have a digital safe with two keys:

   • One key is called the private key. Only you have this key, and you keep it secret and safe. It's like your personal fingerprint or a super-secret password.
   • The other key is called the public key. This key is "linked" to your private key, but it cannot be used to unlock your private key. You can give this public key to anyone. It's like giving someone a lock, but you keep the only key that can open it.

2. Setting up for authentication:

   • When you want to log into a remote server (like our Docker SSH server), you first give that server a copy of your public key. The server stores this public key in a special file (usually ~/.ssh/authorized_keys for the user you want to log in as).
   • This tells the server: "If anyone tries to log in as this user and can prove they have the private key that matches this public key, then let them in."

3. The authentication process (the "handshake"):

   When you try to connect via SSH from your local machine (client) to the remote server:

   • Step A: The Server's Challenge. The server checks its authorized_keys file. If it finds your public key, it uses that public key to generate a unique, encrypted "challenge" message. This message can only be decrypted by the matching private key. The server sends this challenge back to your local SSH client.

   • Step B: Your Client's Response. Your local SSH client receives the challenge. It then uses your private key (which is stored on your local machine) to decrypt the challenge message. After decrypting it, it performs some cryptographic operations and encrypts a response using your private key again. It sends this encrypted response back to the server.

   • Step C: Server Verification. The server receives your client's encrypted response. It then uses the public key (which it already has) to verify if the response is valid and if it indeed originated from the corresponding private key.

     • If the server can successfully verify the response using the public key, it means your local machine holds the correct private key.
     • At this point, the server trusts that you are who you claim to be, and it grants you access without ever needing a password.

Why is this secure?

• No password transmission: Your password is never sent over the network, eliminating interception risks.
• Private key never leaves your machine: Your secret private key stays with you.
• Strong cryptography: The mathematical relationship between public and private keys makes it virtually impossible to guess or derive one from the other.
• Protection against brute-force attacks: Attackers can't just try passwords; they need the actual private key, which is locked away.

Essentially, the public key acts like an identification tag that the server recognizes, and your private key is the secret credential you use to prove you are the owner of that tag.

Does that help clarify how the public key authentication works?