Cryptography is the study of information hiding and verification. It includes the protocols, algorithms and strategies to securely and consistently prevent or delay unauthorized access to sensitive information and enable verifiability of every component in a communication.
Cryptography is derived from the Greek words: kryptós, "hidden", and gráphein, "to write" - or "hidden writing". People who study and develop cryptography are called cryptographers. The study of how to circumvent the use of cryptography for unintended recipients is called cryptanalysis, or codebreaking. Cryptography and cryptanalysis are sometimes grouped together under the umbrella term cryptology, encompassing the entire subject. In practice, "cryptography" is also often used to refer to the field as a whole, especially as an applied science.
Cryptography is an interdisciplinary subject, drawing from several fields. Before the time of computers, it was closely related to linguistics. Nowadays the emphasis has shifted, and cryptography makes extensive use of technical areas of mathematics, especially those areas collectively known as discrete mathematics. This includes topics from number theory, information theory, computational complexity, statistics and combinatorics. It is also a branch of engineering, but an unusual one as it must deal with active, intelligent and malevolent opposition.
An example of the sub-fields of cryptography is steganography — the study of hiding the very existence of a message, and not necessarily the contents of the message itself (for example, microdots, or invisible ink) — and traffic analysis, which is the analysis of patterns of communication in order to learn secret information.
When information is transformed from a useful form of understanding to an opaque form of understanding, this is called encryption. When the information is reverted back into a useful form, it is called decryption. Intended recipients or authorized use of the information is determined by whether the user has a certain piece of secret knowledge. Only users with the secret knowledge can transform the opaque information back into its useful form. The secret knowledge is commonly called the key, though the secret knowledge may include the entire process or algorithm that is used in the encryption/decryption. The information in its useful form is called plaintext (or cleartext); in its encrypted form it is called ciphertext. The algorithm used for encryption and decryption is called a cipher (or cypher).
Common goals in cryptography 
In essence, cryptography concerns four main goals. They are:
- message confidentiality (or privacy): Only an authorized recipient should be able to extract the contents of the message from its encrypted form. Resulting from steps to hide, stop or delay free access to the encrypted information.
- message integrity: The recipient should be able to determine if the message has been altered.
- sender authentication: The recipient should be able to verify from the message, the identity of the sender, the origin or the path it traveled (or combinations) so to validate claims from emitter or to validated the recipient expectations.
- sender non-repudiation: The emitter should not be able to deny sending the message.
Not all cryptographic systems achieve all of the above goals. Some applications of cryptography have different goals; for example some situations require repudiation where a participant can plausibly deny that they are a sender or receiver of a message, or extend this goals to include variations like:
- message access control: Who are the valid recipients of the message.
- message availability: By providing means to limit the validity of the message, channel, emitter or recipient in time or space.
Common forms of cryptography 
Cryptography involves all legitimate users of information having the keys required to access that information.
- If the sender and recipient must have the same key in order to encode or decode the protected information, then the cipher is a symmetric key cipher since everyone uses the same key for the same message. The main problem is that the secret key must somehow be given to both the sender and recipient privately. For this reason, symmetric key ciphers are also called private key (or secret key) ciphers.
- If the sender and recipient have different keys respective to the communication roles they play, then the cipher is an asymmetric key cipher as different keys exist for encoding and decoding the same message. It is also called public key encryption as the user publicly distributes one of the keys without a care for secrecy. In the case of confidential messages to the user, they distribute the encryption key. Asymmetric encryption relies on the fact that possession of the encryption key will not reveal the decryption key.
- Digital Signatures are a form of authentication with some parallels to public-key encryption. The two keys are the public verification key and the secret signature key. As in public-key encryption, the verification key can be distributed to other people, with the same caveat that the distribution process should in some way authenticate the owner of the secret key. Security relies on the fact that possession of the verification key will not reveal the signature key.
- Hash Functions are unkeyed message digests with special properties.
Poorly designed, or poorly implemented, crypto systems achieve them only by accident or bluff or lack of interest on the part of the opposition. Users can, and regularly do, find weaknesses in even well-designed cryptographic schemes from those of high reputation.
Even with well designed, well implemented, and properly used crypto systems, some goals aren't practical (or desirable) in some contexts. For example, the sender of the message may wish to be anonymous, and would therefore deliberately choose not to bother with non-repudiation. Alternatively, the system may be intended for an environment with limited computing resources, or message confidentiality might not be an issue.
In classical cryptography, messages are typically enciphered and transmitted from one person or group to some other person or group. In modern cryptography, there are many possible options for "sender" or "recipient". Some examples, for real crypto systems in the modern world, include:
- a computer program running on a local computer,
- a computer program running on a 'nearby' computer which 'provides security services' for users on other nearby systems,
- a human being (usually understood as 'at the keyboard'). However, even in this example, the presumed human is not generally taken to actually encrypt or sign or decrypt or authenticate anything. Rather, he or she instructs a computer program to perform these actions. This 'blurred separation' of human action from actions which are presumed (without much consideration) to have 'been done by a human' is a source of problems in crypto system design, implementation, and use. Such problems are often quite subtle and correspondingly obscure; indeed, generally so, even to practicing cryptographers with knowledge, skill, and good engineering sense.
When confusion on these points is present (e.g., at the design stage, during implementation, by a user after installation, or ...), failures in reaching each of the stated goals can occur quite easily -- often without notice to any human involved, and even given a perfect cryptosystem. Such failures are most often due to extra-cryptographic issues; each such failure demonstrates that good algorithms, good protocols, good system design, and good implementation do not alone, nor even in combination, provide 'security'. Instead, careful thought is required regarding the entire crypto system design and its use in actual production by real people on actual equipment running 'production' system software (e.g., operating systems) -- too often, this is absent or insufficient in practice with real-world crypto systems.
Although cryptography has a long and complex history, it wasn't until the 19th century that it developed anything more than ad hoc approaches to either encryption or cryptanalysis (the science of finding weaknesses in crypto systems). Examples of the latter include Charles Babbage's Crimean War era work on mathematical cryptanalysis of polyalphabetic ciphers, repeated publicly rather later by the Prussian Kasiski. During this time, there was little theoretical foundation for cryptography; rather, understanding of cryptography generally consisted of hard-won fragments of knowledge and rules of thumb; see, for example, Auguste Kerckhoffs' crypto writings in the latter 19th century. An increasingly mathematical trend accelerated up to World War II (notably in William F. Friedman's application of statistical techniques to cryptography and in Marian Rejewski's initial break into the German Army's version of the Enigma system). Both cryptography and cryptanalysis have become far more mathematical since WWII. Even then, it has taken the wide availability of computers, and the Internet as a communications medium, to bring effective cryptography into common use by anyone other than national governments or similarly large enterprise.