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Public key explained

What is meant by "public key cryptography"? Here we give a brief introduction to the concept and the history of its discovery.
An open padlock

In all the previous examples of ciphers that we have seen, the key used for encryption and decryption must be kept secret. In the 1970s, however, it was realised that one could create a cipher whose encryption key is publicly available to anyone (with only the decryption key secret) and this still be used to securely communicate.

Ralph Merkle, in his abstract from his 1975 paper Secure Communications over Insecure Channels (which was published in Communications of the ACM in 1978) wrote:

When two people wish to communicate over some distance, they will send some form of message. To prevent some enemy from understanding the message, they can encrypt it. If the enemy were to learn the encryption method, he could read the message. It would seem obvious that the method of encryption cannot be transmitted, in the clear, over the communications channel, and still be useful. This, however, is not so. If the two communicants transmit the encryption method in the proper fashion, then they will be able to understand what is going on, but any enemy will become hopelessly confused. This can be done with a modest, and virtually fixed amount of memory.
This paper didn’t suggest any practical methods to implement this idea, but it was the first time such an idea had been postulated publicly. However, in files declassified in 1997, the British spy agency GCHQ revealed one of their employees, James Ellis, first had the idea in January 1970. In the abstract to The Possibility of Secure Non-Secret Digital Encryption he wrote:
This report considers the problem of achieving secure transmission of digital information in the circumstances where there is no information initially possessed in common by the two legitimate communicators which is not also known to the interceptor.

These are frequently known as public key cryptosystems since the key used for encryption is public knowledge. Another term for this is asymmetric encryption since the key for encryption is different from the key needed for decryption (as opposed to symmetric key cryptosystems where the two keys are identical, which is the case for all the other systems we’ve looked at previously). Although it has not gained traction, the original term used by James Ellis was non-secret encryption.

In the next few articles we will look at two of the most common public key encryption systems. The Diffie-Hellman key exchange is a method for creating a shared secret key, and the RSA system is a way to send messages securely between two parties.

Both these systems are in use today, but in reality they are both used to create and share a secret key, which is then used in a symmetric key system. This is because traditional ciphers are much faster when it comes to encrypting and decrypting messages.

© University of York
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The Mathematics of Cryptography: From Ancient Rome to a Quantum Future

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