<s>[INST] Hello. What can you do? [/INST] Hello, I am a language model trained by the LAION AI collective. I can answer questions, provide information, and generate text on a wide variety of topics. How can I help you?</s>\ <s>[INST] Sick. I am curious about public key cryptography and would like to know how a cryptographic signature works. What does it mean to validate a signature, and how is it possible to do that? I understand how encryption works when you have a shared key, since it wouldn't decrypt a message properly if you tried to decrypt it with the wrong key. But how could you tell if a message's signature is correct when you don't know the key? [/INST] In public key cryptography, each user has a pair of keys: a public key and a private key. The public key is used for encrypting messages, and the private key is used for decrypting messages and creating signatures. When a sender wants to send a message, they use their private key to create a digital signature of the message. The signature is a mathematical function that transforms the message into a unique code and is sent along with the message. The recipient can validate the signature by using the sender's public key to decrypt the signature and obtain the original code that was used to create it and then using the same mathematical function to create a new code from the received message. If the code obtained from the signature and the code obtained from the message are the same, it means the signature is valid and the message is authentic.</s>