The unbreakable cipher is called a one-time-pad cipher, and it was discovered in 1918, near the end of World War 1. It came from the Vigenère cipher, which used a poly-alphabetical substitution method. The Vigenère cipher could be broken because it only was encrypted by a more complex form of Caesar substitution with more than just 1 key.
The one-time-pad cipher uses a random key which is hundreds of letters long so as to be able to encrypt messages of all lengths. However, it can only be used once and a new key must be used for each message.
Because of this, the one-time-pad cipher was never used widely. Keys needed to be distributed to everyone. And you have to make sure that both persons are using the same key at a time. If not, the decrypted plaintext may be gibberish or if someone is very unlucky, it will decrypt into a totally different message. This is the most secure part of the one-time-pad cipher. Any group of words of the same length as the plaintext can be obtained if the key used is wrong.
If a wrong key is used on the same ciphertext, it might generate a different plaintext:
Even though this cipher has been mathematically proven to be unbreakable, it is not widely used because it is very difficult to keep track of which keys are being used and which keys have been used. Millions of keys per minute would be needed if everyone uses this system to protect their messages. Also, distributing the keys would be even more difficult as everyone needed to know when to use them.
So, this one-time-pad cipher is used only when someone really needs ultra-high security. For example, the hotline between America 's president and Russia 's president is protected by a one-time-pad cipher.
In the future, quantum theory may be used to send the keys to other people without fear of the keys being intercepted. Then, the one-time-pad cipher is used to encrypt the messages, making it a truly unbreakable code.