serious cryptography a practical introduction to modern encryption

PKI certificates are documents that act as digital passports, assigned to any entity that wants to participate in a PKI-secured conversation. But remember, PKI is widely used because, in addition to encrypting messages, it also lets you know that the person with whom you're exchanging encrypted messages is who they say they are. So that covers how data is encrypted within a public key infrastructure. If you want to get into the weeds on this form of encryption, known as asymmetrical cryptography, HowStuffWorks has a good deep dive. The two keys are related by a complex mathematical formula that would be difficult to derive from brute force.

There's a public key, which you can tell to anyone who asks and is used to encode a message sent to you, and a private key, which you keep secret and use to decrypt the message when you receive it. PKI gets its name because each participant in a secured communications channel has two keys. One of the ways it's different gets around a somewhat obvious problem with the Caesar cipher: you have to somehow let your recipient know the key used to encode the encrypted message. Obviously the mathematics behind modern encryption is much more complicated than this. To decode its message, your recipient would need know not only that you were using the Caesar cipher but that your key was 3. For instance, if you used the ancient and simple Caesar cipher with a cryptographic key of 3, that would mean that every letter in your message is replaced by one three letters later in the alphabet - A becomes D, B becomes E, and so forth. A key, as already noted, is a long string of bits - a number, in other words - that's used to encrypt data. The most important concepts to understand to grasp how PKI works are keys and certificates.

Serious cryptography a practical introduction to modern encryption