Cryptography (or cryptology; derived from Greek κρυπτός kryptós "hidden," and the verb γράφω gráfo "write"). In modern times, it has become a branch of information theory, as the mathematical study of information and especially its transmission from place to place. The noted cryptographer Ron Rivest has observed that "cryptography is about communication in the presence of adversaries." It is a central contributor to several fields: information security and related issues, particularly, authentication, and access control. One of cryptography's primary purposes is hiding the meaning of messages, not usually the existence of such messages. In modern times, cryptography also contributes to computer science. Cryptography is central to the techniques used in computer and network security for such things as access control and information confidentiality. Cryptography is also used in many applications encountered in everyday life; the security of ATM cards, computer passwords, and electronic commerce all depend on cryptography.

Before the modern era, cryptography was concerned solely with message confidentiality (i.e., encryption) — conversion of messages from a comprehensible form into an incomprehensible one, and back again at the other end, rendering it unreadable by interceptors or eavesdroppers without secret knowledge (namely, the key needed for decryption). In recent decades, the field has expanded beyond confidentiality concerns to include techniques for authentication of message integrity or sender/receiver identity, digital signatures, interactive proofs, and secure computation.

The earliest forms of secret writing required little more than pen and paper. The main classical cipher types are transposition ciphers, which rearrange the order of letters in a message (e.g. 'help me' becomes 'ehpl em' in a trivially simple rearrangement scheme); and substitution ciphers, which systematically replace letters or groups of letters with other letters or groups of letters (e.g., 'fly at once' becomes 'gmz bu podf' by replacing each letter with the one following it in the alphabet). Simple versions of either offered little confidentiality, and still don't. An early substitution cipher was the Caesar cipher, in which each letter in the plaintext was replaced by a letter some fixed number of positions further down the alphabet. It was named after Julius Caesar who is reported to have used it, with a shift of 3, to communicate with his generals during his military campaigns.

Encryption attempts to ensure secrecy in communications, such as those of spies, military leaders, and diplomats, but it has also had religious applications. For instance, early Christians used cryptography to obfuscate some aspects of their religious writings to avoid the near certain persecution they would have faced had they been less obscured; famously, 666, the Number of the Beast from the Christian New Testament Book of Revelation, is sometimes thought to be a ciphertext referring to the Roman Emperor Nero, one of whose policies was persecution of Christians.Eerdmans Commentary on the Bible, James D G Dunn, John W Rogerson, eds., Wm. B. Eerdmans Publishing, 2003, ISBN 0-8028-3711-5 There is record of several, even earlier, Hebrew ciphers as well. Cryptography is recommended in the Kama Sutra as a way for lovers to communicate without inconvenient discovery.Kama Sutra, Sir Richard F. Burton, translator, Part I, Chapter III, 44th and 45th arts. Steganography (i.e., hiding even the existence of a message so as to keep it confidential) was also first developed in ancient times. An early example, from Herodotus, concealed a message - a tattoo on a slave's shaved head - by regrown hair.David Kahn, The Codebreakers, 1967, ISBN 0-684-83130-9. More modern examples of steganography include the use of invisible ink, microdots, and digital watermarks to conceal information .

Ciphertexts produced by classical ciphers always reveal statistical information about the plaintext, which can often be used to break them. After the Arab discovery of frequency analysis (around the year 1000), nearly all such ciphers became more or less readily breakable by an informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzles (see cryptogram). Essentially all ciphers remained vulnerable to cryptanalysis using this technique until the invention of the polyalphabetic cipher by Leon Battista Alberti around the year 1467. Alberti's innovation was to use different ciphers (ie, substitution alphabets) for various parts of a message (often each successive plaintext letter). He also invented what was probably the first automatic cipher device, a wheel which implemented a partial realization of his invention. In the polyalphabetic Vigenère cipher encryption uses a key word, which controls letter substitution depending on which letter of the key word is used. Despite this improvement, polyalphabetic ciphers of this type remained partially vulnerable to frequency analysis techniques, though this was undiscovered until the mid 1800s by Babbage.


Although frequency analysis is a powerful and general technique, encryption was still often effective in practice: many a would-be cryptanalyst was unaware of the technique. Breaking a message without frequency analysis essentially required knowledge of the cipher used, thus encouraging espionage, bribery, burglary, defection, etc. to discover it. It was finally recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible, nor practical, safeguard: in fact, any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary knows the cipher algorithm itself. Secrecy of the key should alone be sufficient for confidentiality when under attack -- for good ciphers This fundamental principle was first explicitly stated in 1883 by Auguste Kerckhoffs and is called Kerckhoffs' principle; alternatively and more bluntly, it was restated by Claude Shannon as Shannon's Maxim -- 'the enemy knows the system'.

Various physical devices and aids have been used to assist with ciphers. One of the earliest may have been the scytale of ancient Greece, a rod supposedly used by the Spartans as an aid for a transposition cipher. In medieval times, other aids were invented such as the cipher grille, also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's own cipher disk, Johannes Trithemius' tabula recta scheme, and Thomas Jefferson's multi-cylinder (invented independently by Bazeries around 1900). Early in the 20th century, several mechanical encryption/decryption devices were invented, and many patented, including rotor machines — most famously the Enigma machine used by Germany in World War II. The ciphers implemented by the better of these designs brought about a substantial increase in cryptanalytic difficulty.James Gannon, Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century, Washington, D.C., Brassey's, 2001, ISBN 1-57488-367-4.

The development of digital computers and electronics after WWII made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data that is represented by computers in binary unlike classical ciphers which only encrypted written text, dissolving the need for a linguistic approach to cryptanalysis. Many computer ciphers can be characterised by their operation on binary bits (sometimes in groups or blocks), unlike classical and mechanical schemes, which generally manipulate traditional characters (i.e., letters and digits). However, computers have also assisted cryptanalysis, which has compensated to some extent for increased cipher complexity. Nonetheless, good modern ciphers have stayed ahead of cryptanalysis: it is usually the case that use of a quality cipher is very efficient, while breaking it requires an effort many orders of magnitude larger, making cryptanalysis so inefficient and impractical as to be effectively impossible.



Extensive open academic research into cryptography is relatively recent — it began only in the mid-1970s with the public specification of DES (the Data Encryption Standard) by the NBS, the Diffie-Hellman paper,Whitfield Diffie and Martin Hellman, "New Directions in Cryptography", IEEE Transactions on Information Theory, vol. IT-22, Nov. 1976, pp: 644-654. (pdf), and the public release of the RSA algorithm. Since then, cryptography has become a widely used tool in communications, computer networks, and computer security generally. The security of many modern cryptographic techniques is based on the difficulty of certain computational problems, such as the integer factorisation problem or the discrete logarithm problem. In many cases, there are proofs that cryptographic techniques are secure if a certain computational problem cannot be solved efficiently.Oded Goldreich, Foundations of Cryptography, Volume 1: Basic Tools", Cambridge University Press, 2001, ISBN 0-521-79172-3 With one notable exception - the one-time pad - these contingent, and thus not definitive, proofs are the best available for cryptographic algorithms and protocols.

As well as being aware of cryptographic history, cryptographic algorithm and system designers must also sensibly consider probable future developments in their designs. For instance, the continued improvements in computer processing power has increased the scope of brute-force attacks when specifying key lengths. The potential effects of quantum computing are already being considered by some cryptographic system designers.AJ Menezes, PC van Oorschot, and SA Vanstone, Handbook of Applied Cryptography ISBN 0-8493-8523-7.

Essentially, prior to the early 20th century, cryptography was chiefly concerned with linguistic patterns. Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory, computational complexity, statistics, combinatorics, abstract algebra, and number theory. Cryptography is also a branch of engineering, but an unusual one as it deals with active, intelligent, and malevolent opposition (see cryptographic engineering and security engineering); all other kinds of engineering need deal only with neutral natural forces. There is also active research examining the relationship between cryptographic problems and quantum physics (see quantum cryptography and quantum computing).