Hi. As you may remember Yvonne talked about how the encryption works. If you see in this scheme, it is quite easy to understand that you get an encrypted message, you use a key, a password, a secret and you pass through an encryption process. So you create an encrypted message, if you can see here, the message through encryption becomes an encrypted message. Then what you get is in the other site. For example, in Bob's site, using the key, you can decrypt the message to recover the original message, remember? What is the main problem here, the main concern here? As you remember, Yvonne talked about how do you store the keys and how do you share the keys. So what happens when Alice and Bob want to share a secret and they need to share the initial password, or key, or encryption key, that should be very, very secret because this is the thing you will use to encrypt the other secrets. So this is the main problem here. So you have an option one that is to show the key physically when you live in the same city, for example, you can meet in a coffee shop, or wherever and meet the other person to put a paper with the password of the encryption and decryption key, and give to this person or agree the password and the secret key. So let's see that. The bird is in the gate. So let's go with the option two, that is very interesting and very powerful. With this option two, the ''Public Key Cryptography'', what we get is two different keys. It's the same process. You get a message that is going to be encrypted through an encryption process, you will get an encrypted message. Then you will decrypt this encrypted message with a different key. So there are two different keys in place. They are generated at the same time and they're linked, and they're different. Let's go for the details. In this model, Alice has a public key and a private key. This public key, here, is used to encrypt the message. So everyone who has this public key can encrypt a message for Alice because they are using Alice's public-key. Then, you encrypt the message and you pass to the process of decryption. If you see this private key is only in Alice's hands. So two questions. The very first one: Who can encrypt things for Alice? Everyone who knows the public key. Everyone, because it's public. You can publish this key everywhere in Internet, email, wherever. Everyone can get the key and encrypt for Alice. The second question: Who can decrypt the encrypted message? Only Alice, because Alice will keep the private key secret in custody, so she's the only person in the universe who knows or who has the secret to decrypt. Very important. In this different approach, if you see, we reversed the keys. We are using here the private key to encrypt. So Alice can encrypt using its private key, a message and send the encrypted message to a different person, for example, Bob. What will happen? Remember the two questions. Who can encrypt using the private key? Only Alice. Who can decrypt using the public key that everyone knows? Remember, because it's public, Bob, for example, using the public key, can't decrypt. Why he can't decrypt this message? Because was encrypted with a private key from Alice. Why this matters? Why is this very important? Because in this way you can verify that Alice, and only Alice, who is the person that has the secret key, the private key in custody, is the only person who can create an encrypted message with this private key. So Bob can verify that was Alice, and only Alice, the person who encrypted this message. But this is a public key? Yeah, it's public. This is not a secret key. No, not secret. So we cannot exchange the key by email, right? Yeah. Why are we here? So which are the benefits of the public key cryptography? If you see, the main one is that you have no need to share any key, because the private keys are in custody, the public keys, everyone can know that. So you can share the public key everywhere. So no need to share a secret in a difficult way, or using Spanish methods or whatever. The other one is that you should take your private key in custody. So be very careful where you store the key, and of course you have not shared the private key with anyone. So keep this secret in custody, very important. This is, remember when we use the private key to encrypt Alice encrypted a message using the private key, not the public key. This is because Alice want to be able to verify the identity of the encryptor, the people, or the person who is encrypting, you will be able to verify their identity. This is called a digital signature, very important. Alice encrypted with a private key, everyone who has the public key can verify that was Alice. Remember, very important. You sign using the private key digital signature. Okay, viral man. Had do you seen this approach? Public key approach, it's quite interesting. It's a different way to start with encryption, and the most important thing is that the public key cryptography allows safer communication because we don't need to serve the most sensitive part of the keys. We don't need to serve the private key. So it seems that we have everything solved. We don't need to serve the key so we start very safe communication, but do you really think it's the perfect solution? Yeah. It's a very good solution, but we have to solve a little thing, we will see in next units. See you then.