Sending Messages Across the Battlefield
For thousands of years people have been trying to hiding information. The Nazis had the Enigma, Julius Caesar used a Caesar Cipher, the Freemasons had the Pigpen Cipher, and Mary Queen of Scots used a substitution cipher alphabet while imprisioned by her cousin.
The Caesar Cipher was particularly weak, as letters were just shifted three places to obscure the message. While initially useful, once discovered the messages could be easily intersepted.
The Freemasons used the Pigpen Cipher. This substituted letters for symbols, which allowed easy hiding of messages. Though once the codebook was discovered, the messages transmitted could again be easily intersepted.
Mary Queen of Scots was imprisioned by her cousin (Queen Elisabeth I) for plotting to take the throne. She, and her Catholic supporters were in communication where she consented to the assasination of the Protestant Queen. Little did she know, she responded directly to Elisabeth's spymaster, who had already broken the code.
While these examples use substituions or codebooks, symmetric ciphers use keys which are traded, which allow the sender and recipient to communicate.
There does however seem to be a very glaring issue here. How do you share a key with a person you've never met? If you send the key, how could you trust that intermediate party isn't trying to steal your secrets?
Exchanging a Key
Up until the 1970's, the only way to share a key was to physically share the key. But in 1976 the a paper which discussed generating a mutually agreed key from public and private keys was published. This is known as the Diffie Hellman Key Exchange after its creators Whitfield Diffie and Martin Hellman.
Diffie Hellman Key Exchange
In this example, we're using a simplified explanation of the key exchange using colours. This works as an example, as it allows us to show how you could create a secret colour between two parties who have never met, while not providing enough information for a third party to calculate the secret.
In reality, large primes are used as keys as they're more difficult to calculate (as we want to make it as difficult as possible to break), and the numbers are multiplied instead of added.