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We present new insights on public key and symmetric encryption.
3.1 The Basic Idea of Cryptography
Cryptography is an old subject dating back at least as far as 1500 BCE. A technique developed by Porta associated also with Vigenère in the Middle Ages is close to the cutting edge of part of modern cryptography. Additionally, cryptography is closely connected to information theory and error‐correction, with many fundamental ideas going back to Claude Shannon. Further details about Shannon and the history of cryptography are provided in Chapter 1.
Cryptography is the art of keeping messages secret. Imagine that A, B are two entities who wish to communicate in secret. Assume A wants to send a secret message to B.
The procedure is as follows (Figure 3.1). First, A scrambles the message using a cryptographic key. The process of scrambling the message is called encryption: alternatively, A enciphers the message.
Figure 3.1 General encryption.
The encryption or enciphering scrambles the message
In summary, the sender A encrypts or enciphers the message
Using the decryption or deciphering key, and using the deciphering algorithm (decryption algorithm), the receiver B then decrypts or deciphers
Evidently, everything depends on B being the sole possessor of the decryption key, apart possibly from A. (If the decryption and encryption keys are the same – as they are in symmetric encryption, then A also has the decryption key).
Generally speaking, a key is a mathematical object such as a number (or several numbers) or a string of zeros and ones, i.e. a binary string such as the binary string (1 1 0 1) of length 4.
The enciphering and deciphering operations are usually mathematical procedures. For example, let us suppose that the enciphering key is the number 7 and that the enciphering operation is “add 7.” Suppose the secret message that A wants to transmit to B is the number 6. (For example A might be directing her stockbroker B to buy six thousand shares of a given security on the stock market).
Then, A calculates the cipher text 13 ( = 6 plus 7) and transmits this to B. Now, B knows that the enciphering transformation is “add 7.” To undo, or invert this, B subtracts 7 from 13 (as this is the deciphering operation) and ends up recovering the original message transmitted by A, namely 6.
It should be mentioned that the cryptographic keys above need not be mathematical objects: in fact, historically, they often were not. A famous example, mentioned in Chapter 1, occurred in World War II when, in effect, the key was an entire language! This was the Navajo language used by the Navajo tribe in Arizona and adapted for encryption purposes by the US armed forces around 1942. Enciphering consisted of translating messages from English into the Navajo language, while deciphering simply meant translating Navajo back to English at the other end. At that time, this symmetric encryption was extremely effective.
Using encryption for storing messages and files is another important function of encryption in today's society. As an example, we mention
