# Cryptography

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Cryptography (from Greek kryptós, "hidden", and gráphein, "to write") is the study of the principles and techniques by which information can be concealed in ciphers that are much more difficult to read for an unauthorized person than for a legitimate reader employing the decryption key.

Cryptography has four main goals:

1. message confidentiality: Only the authorised receiver should be able to extract the contents of the message from its encrypted form. In addition, it should not be possible to obtain information about the message contents (such as a statistical distribution of certain characters).
2. message integrity: The receiver should be able to determine if the message has been altered since transmission.
3. authentication: The receiver should be able to identify the sender. Furthermore, they should be able to verify that the sender did actually send the message.
4. non-repudiation: The sender should not be able to deny sending the message.

Not all cryptographic systems and algorithms achieve all of the above goals. Some are not practical (or necessary) in some contexts and require sophisticated algorithms needing many computations.

Although cryptography has a long and complex history, it wasn't until the 20th centry that it developed into a rigorous science supported by mathematics. Even then, it has taken the communication requirements of the internet to bring it into common usage in the public domain.

### Classic Cryptography

The earliest use of cryptography can be found with the use of non-standard hieroglyphics? by the Egyptians? around 1900 BCE. Hebrew scholars also made use of simple [substitution ciphers]? (such as the [Atbash cipher]?) around 500 to 600 BCE. Both cryptography and cryptanalysis featured in the [Babington plot]? during the reign of Queen Elizabeth I.

### World War II Cryptography

The Germans heavily used a system know as Enigma, which was cracked by Ultra.

### Modern Cryptography

The era of modern cryptography started with Claude Shannon, arguably the father of mathematical cryptography. In 1949 he published the paper [Communication Theory of Secrecy Systems]. This, in addition to his other works on information and communication theory established a strong mathematical basis for cryptography.

1976 saw two major advances. First was the DES (Data Encryption Standard) developed by IBM and the NSA in an effort to develop secure banking facilities (DES was later published as a FIPS (Federal Information Processing Standard) in 1977). DES, and more secure variants of it, are still used today. DES was effectively replaced by the AES (Advanced Encryption Standard) which became a FIPS on December 4 2001.

Secondly, and more importantly, was the publication of the paper [New Directions in Cryptography] by [Whitfield Diffie]? and [Martin Hellman]?. This paper introduced a radical new method of distrubting cryptographic keys, known as public key cryptography. This solved one of fundamental problems of cryptography, key distribution.

Prior to this, encryption keys were symmetric, and possession of the key would allow both encryption and decryption of the message. The key had to be exchanged between the communicating parties via a secure channel such as a trusted courier or face-to-face contact. This situation rapidly becomes unmanageable when the number of participants increases. In particular, a seperate key is required for each communicating pair if other parties are not to decrypt their messages. A system of this kind is also known as a "private key cryptosystem".

In public key cryptography, there are a pair of related keys, one of which is made public and used for encryption -- the public key. The private key is kept secret and used for decryption. A system of this kind is known as asymmetric. Only one key pair is now needed per receiver as possession of the public key does not compromise the security of the private key. In general the system is not reversable, i.e., a message encrypted with the private key can not be decrypted with the public key, although this is the case for RSA.

However, as is often the case with clandestine technologies such as cryptography, the development of public key cryptography was developed by a military agency before public research caught up. On December 17, 1997, GCHQ released documents claiming that they had developed public key cryptography before the publication of Diffie and Hellman's paper. Various classified papers were published during the 1960s and 1970s which eventually led to schemes similar to RSA and Diffie-Hellman in 1973 and 1974.

Public key cryptosystems (asymmetric algorithms):

Secret key cryptosystems (symmetric algorithms):

Terminology: