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In cryptography, a **cipher** (or **cypher**) is an algorithm for performing encryption or decryption —a series of well-defined steps that can be followed as a procedure. An alternative, less common term is *encipherment*. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography.

**Cryptography** or **cryptology** is the practice and study of techniques for secure communication in the presence of third parties called adversaries. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages; various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, electrical engineering, communication science, and physics. Applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.

In mathematics and computer science, an **algorithm** is a set of instructions, typically to solve a class of problems or perform a computation. Algorithms are unambiguous specifications for performing calculation, data processing, automated reasoning, and other tasks.

In cryptography, **encryption** is the process of encoding a message or information in such a way that only authorized parties can access it and those who are not authorized cannot. Encryption does not itself prevent interference, but denies the intelligible content to a would-be interceptor. In an encryption scheme, the intended information or message, referred to as plaintext, is encrypted using an encryption algorithm – a cipher – generating ciphertext that can be read only if decrypted. For technical reasons, an encryption scheme usually uses a pseudo-random encryption key generated by an algorithm. It is in principle possible to decrypt the message without possessing the key, but, for a well-designed encryption scheme, considerable computational resources and skills are required. An authorized recipient can easily decrypt the message with the key provided by the originator to recipients but not to unauthorized users.

- Etymology
- Versus codes
- Types
- Historical
- Modern
- Key size and vulnerability
- See also
- Notes
- References
- External links

Codes generally substitute different length strings of character in the output, while ciphers generally substitute the same number of characters as are input. There are exceptions and some cipher systems may use slightly more, or fewer, characters when output versus the number that were input.

Codes operated by substituting according to a large codebook which linked a random string of characters or numbers to a word or phrase. For example, "UQJHSE" could be the code for "Proceed to the following coordinates." When using a cipher the original information is known as plaintext, and the encrypted form as ciphertext. The ciphertext message contains all the information of the plaintext message, but is not in a format readable by a human or computer without the proper mechanism to decrypt it.

A **codebook** is a type of document used for gathering and storing codes. Originally codebooks were often literally books, but today codebook is a byword for the complete record of a series of codes, regardless of physical format.

In cryptography, **plaintext** usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. *Cleartext* usually refers to data that is transmitted or stored unencrypted.

In cryptography, **ciphertext** or **cyphertext** is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher to decrypt it. Decryption, the inverse of encryption, is the process of turning ciphertext into readable plaintext. Ciphertext is not to be confused with codetext because the latter is a result of a code, not a cipher.

The operation of a cipher usually depends on a piece of auxiliary information, called a key (or, in traditional NSA parlance, a *cryptovariable*). The encrypting procedure is varied depending on the key, which changes the detailed operation of the algorithm. A key must be selected before using a cipher to encrypt a message. Without knowledge of the key, it should be extremely difficult, if not impossible, to decrypt the resulting ciphertext into readable plaintext.

In cryptography, a **key** is a piece of information that determines the functional output of a cryptographic algorithm. For encryption algorithms, a key specifies the transformation of plaintext into ciphertext, and vice versa for decryption algorithms. Keys also specify transformations in other cryptographic algorithms, such as digital signature schemes and message authentication codes.

Most modern ciphers can be categorized in several ways

- By whether they work on blocks of symbols usually of a fixed size (block ciphers), or on a continuous stream of symbols (stream ciphers).
- By whether the same key is used for both encryption and decryption (symmetric key algorithms), or if a different key is used for each (asymmetric key algorithms). If the algorithm is symmetric, the key must be known to the recipient and sender and to no one else. If the algorithm is an asymmetric one, the enciphering key is different from, but closely related to, the deciphering key. If one key cannot be deduced from the other, the asymmetric key algorithm has the public/private key property and one of the keys may be made public without loss of confidentiality.

In cryptography, a **block cipher** is a deterministic algorithm operating on fixed-length groups of bits, called *blocks*, with an unvarying transformation that is specified by a symmetric key. Block ciphers operate as important elementary components in the design of many cryptographic protocols, and are widely used to implement encryption of bulk data.

A **stream cipher** is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream, to give a digit of the ciphertext stream. Since encryption of each digit is dependent on the current state of the cipher, it is also known as * state cipher*. In practice, a digit is typically a bit and the combining operation an exclusive-or (XOR).

The word "cipher" (minority spelling "cypher") in former times meant "zero" and had the same origin: Middle French as * cifre* and Medieval Latin as

- Encoding often involved numbers.
- The Roman number system was very cumbersome because there was no concept of zero (or empty space). The concept of zero (which was also called "cipher"), which is now common knowledge, was alien to medieval Europe, so confusing and ambiguous to common Europeans that in arguments people would say "talk clearly and not so far fetched as a cipher". Cipher came to mean concealment of clear messages or encryption.
- The French formed the word "
*chiffre*" and adopted the Italian word "*zero*". - The English used "zero" for "0", and "cipher" from the word "ciphering" as a means of computing.
- The Germans used the words "Ziffer" (digit) and "Chiffre".
- The Dutch still use the word "cijfer" to refer to a numerical digit.
- The Slovaks, similarly, also use the word "cifra" to refer to a numerical digit.
- The Bosnians, Croats and Serbians use the word "cifra", which refers to a digit, or in some cases, any number. Besides "cifra", they use word "broj" for a number.
- The Italians and the Spanish also use the word "cifra" to refer to a digit.
- The Swedes use the word "siffra" which refers to a digit, and "chiffer".
- The Greeks use the word "τζίφρα" ("tzifra") to refer to a hard-to-read signature, especially one written with a single stroke of the pen.

- The French formed the word "

Ibrahim Al-Kadi concluded that the Arabic word *sifr*, for the digit zero, developed into the European technical term for encryption.^{ [1] }

As the decimal zero and its new mathematics spread from the Arabic world to Europe in the Middle Ages, words derived from *sifr* and *zephyrus* came to refer to calculation, as well as to privileged knowledge and secret codes. According to Ifrah, "in thirteenth-century Paris, a 'worthless fellow' was called a *'... cifre en algorisme'*, i.e., an 'arithmetical nothing'."^{ [2] } Cipher was the European pronunciation of sifr, and cipher came to mean a message or communication not easily understood.^{ [3] }

In non-technical usage, a "(secret) code" typically means a "cipher". Within technical discussions, however, the words "code" and "cipher" refer to two different concepts. Codes work at the level of meaning—that is, words or phrases are converted into something else and this chunking generally shortens the message.

An example of this is the Commercial Telegraph Code which was used to shorten long telegraph messages which resulted from entering into commercial contracts using exchanges of Telegrams.

Another example is given by whole word ciphers, which allow the user to replace an entire word with a symbol or character, much like the way Japanese utilize Kanji (Japanese) characters to supplement their language. ex "The quick brown fox jumps over the lazy dog" becomes "The quick brown 狐 jumps 过 the lazy 狗".

Ciphers, on the other hand, work at a lower level: the level of individual letters, small groups of letters, or, in modern schemes, individual bits and blocks of bits. Some systems used both codes and ciphers in one system, using superencipherment to increase the security. In some cases the terms codes and ciphers are also used synonymously to substitution and transposition.

Historically, cryptography was split into a dichotomy of codes and ciphers; and coding had its own terminology, analogous to that for ciphers: "*encoding*, *codetext*, *decoding*" and so on.

However, codes have a variety of drawbacks, including susceptibility to cryptanalysis and the difficulty of managing a cumbersome codebook. Because of this, codes have fallen into disuse in modern cryptography, and ciphers are the dominant technique.

There are a variety of different types of encryption. Algorithms used earlier in the history of cryptography are substantially different from modern methods, and modern ciphers can be classified according to how they operate and whether they use one or two keys.

Historical pen and paper ciphers used in the past are sometimes known as classical ciphers. They include simple substitution ciphers (such as Rot 13) and transposition ciphers (such as a Rail Fence Cipher). For example, "GOOD DOG" can be encrypted as "PLLX XLP" where "L" substitutes for "O", "P" for "G", and "X" for "D" in the message. Transposition of the letters "GOOD DOG" can result in "DGOGDOO". These simple ciphers and examples are easy to crack, even without plaintext-ciphertext pairs.^{ [4] }

Simple **ciphers** were replaced by polyalphabetic substitution ciphers (such as the Vigenère) which changed the substitution alphabet for every letter. For example, "GOOD DOG" can be encrypted as "PLSX TWF" where "L", "S", and "W" substitute for "O". With even a small amount of known or estimated plaintext, simple polyalphabetic substitution ciphers and letter transposition ciphers designed for pen and paper encryption are easy to crack.^{ [5] } It is possible to create a secure pen and paper cipher based on a one-time pad though, but the usual disadvantages of one-time pads apply.

During the early twentieth century, electro-mechanical machines were invented to do encryption and decryption using transposition, polyalphabetic substitution, and a kind of "additive" substitution. In rotor machines, several rotor disks provided polyalphabetic substitution, while plug boards provided another substitution. Keys were easily changed by changing the rotor disks and the plugboard wires. Although these encryption methods were more complex than previous schemes and required machines to encrypt and decrypt, other machines such as the British Bombe were invented to crack these encryption methods.

Modern encryption methods can be divided by two criteria: by type of key used, and by type of input data.

By type of key used ciphers are divided into:

- symmetric key algorithms (Private-key cryptography), where one same key is used for encryption and decryption, and
- asymmetric key algorithms (Public-key cryptography), where two different keys are used for encryption and decryption.

In a symmetric key algorithm (e.g., DES and AES), the sender and receiver must have a shared key set up in advance and kept secret from all other parties; the sender uses this key for encryption, and the receiver uses the same key for decryption. The Feistel cipher uses a combination of substitution and transposition techniques. Most block cipher algorithms are based on this structure. In an asymmetric key algorithm (e.g., RSA), there are two separate keys: a *public key* is published and enables any sender to perform encryption, while a *private key* is kept secret by the receiver and enables only him to perform correct decryption.

Ciphers can be distinguished into two types by the type of input data:

- block ciphers, which encrypt block of data of fixed size, and
- stream ciphers, which encrypt continuous streams of data.

In a pure mathematical attack, (i.e., lacking any other information to help break a cipher) two factors above all count:

- Computational power available, i.e., the computing power which can be brought to bear on the problem. It is important to note that average performance/capacity of a single computer is not the only factor to consider. An adversary can use multiple computers at once, for instance, to increase the speed of exhaustive search for a key (i.e., "brute force" attack) substantially.
- Key size, i.e., the size of key used to encrypt a message. As the key size increases, so does the complexity of exhaustive search to the point where it becomes impractical to crack encryption directly.

Since the desired effect is computational difficulty, in theory one would choose an algorithm and desired difficulty level, thus decide the key length accordingly.

An example of this process can be found at Key Length which uses multiple reports to suggest that a symmetric cipher with 128 bits, an asymmetric cipher with 3072 bit keys, and an elliptic curve cipher with 512 bits, all have similar difficulty at present.

Claude Shannon proved, using information theory considerations, that any theoretically unbreakable cipher must have keys which are at least as long as the plaintext, and used only once: one-time pad.

- ↑ Ibrahim A. Al-Kadi, "Cryptography and Data Security: Cryptographic Properties of Arabic", proceedings of the Third Saudi Engineering Conference. Riyadh, Saudi Arabia: Nov 24-27, Vol 2:910-921., 1991.
- ↑ Ifrah, Georges (2000).
*The Universal History of Numbers: From Prehistory to the Invention of the Computer*. Wiley. ISBN 0-471-39340-1. - ↑ The Muslim next door : the Qur'an, the media, and that veil thing, Sumbul Ali-Karamali, 2008, pp. 240-241
- ↑ Saltzman, Benjamin A. "Ut hkskdkxt: Early Medieval Cryptography, Textual Errors, and Scribal Agency (Speculum, forthcoming)".
*Speculum*. - ↑ Stinson , p. 45

**Cryptanalysis** is the study of analyzing information systems in order to study the hidden aspects of the systems. Cryptanalysis is used to breach cryptographic security systems and gain access to the contents of encrypted messages, even if the cryptographic key is unknown.

In cryptography, a **substitution cipher** is a method of encrypting by which units of plaintext are replaced with ciphertext, according to a fixed system; the "units" may be single letters, pairs of letters, triplets of letters, mixtures of the above, and so forth. The receiver deciphers the text by performing the inverse substitution.

**Symmetric-key algorithms** are algorithms for cryptography that use the same cryptographic keys for both encryption of plaintext and decryption of ciphertext. The keys may be identical or there may be a simple transformation to go between the two keys. The keys, in practice, represent a shared secret between two or more parties that can be used to maintain a private information link. This requirement that both parties have access to the secret key is one of the main drawbacks of symmetric key encryption, in comparison to public-key encryption.

A **chosen-plaintext attack** (**CPA**) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts. The goal of the attack is to gain information that reduces the security of the encryption scheme.

The **Vigenère cipher** is a method of encrypting alphabetic text by using a series of interwoven Caesar ciphers, based on the letters of a keyword. It employs a form of polyalphabetic substitution.

In cryptography, an **initialization vector** (**IV**) or **starting variable** (**SV**) is a fixed-size input to a cryptographic primitive that is typically required to be random or pseudorandom. Randomization is crucial for encryption schemes to achieve semantic security, a property whereby repeated usage of the scheme under the same key does not allow an attacker to infer relationships between segments of the encrypted message. For block ciphers, the use of an IV is described by the modes of operation. Randomization is also required for other primitives, such as universal hash functions and message authentication codes based thereon.

In cryptography, a **block cipher mode of operation** is an algorithm that uses a block cipher to provide information security such as confidentiality or authenticity. A block cipher by itself is only suitable for the secure cryptographic transformation of one fixed-length group of bits called a block. A mode of operation describes how to repeatedly apply a cipher's single-block operation to securely transform amounts of data larger than a block.

In cryptography, a **rotor machine** is an electro-mechanical stream cipher device used for encrypting and decrypting secret messages. Rotor machines were the cryptographic state-of-the-art for a prominent period of history; they were in widespread use in the 1920s–1970s. The most famous example is the German Enigma machine, whose messages were deciphered by the Allies during World War II, producing intelligence code-named *Ultra*.

The **affine cipher** is a type of monoalphabetic substitution cipher, wherein each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and converted back to a letter. The formula used means that each letter encrypts to one other letter, and back again, meaning the cipher is essentially a standard substitution cipher with a rule governing which letter goes to which. As such, it has the weaknesses of all substitution ciphers. Each letter is enciphered with the function (*ax* + *b*) mod 26, where b is the magnitude of the shift.

Cryptography, the use of codes and ciphers to protect secrets, began thousands of years ago. Until recent decades, it has been the story of what might be called classic cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids. In the early 20th century, the invention of complex mechanical and electromechanical machines, such as the Enigma rotor machine, provided more sophisticated and efficient means of encryption; and the subsequent introduction of electronics and computing has allowed elaborate schemes of still greater complexity, most of which are entirely unsuited to pen and paper.

In cryptography, a **classical cipher** is a type of cipher that was used historically but now has fallen, for the most part, into disuse. In contrast to modern cryptographic algorithms, most classical ciphers can be practically computed and solved by hand. However, they are also usually very simple to break with modern technology. The term includes the simple systems used since Greek and Roman times, the elaborate Renaissance ciphers, World War II cryptography such as the Enigma machine and beyond.

**Probabilistic encryption** is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield different ciphertexts. The term "probabilistic encryption" is typically used in reference to public key encryption algorithms, however various symmetric key encryption algorithms achieve a similar property. To be semantically secure, that is, to hide even partial information about the plaintext, an encryption algorithm must be probabilistic.

**Multiple encryption** is the process of encrypting an already encrypted message one or more times, either using the same or a different algorithm. It is also known as **cascade encryption**, **cascade ciphering**, **multiple encryption**, and **superencipherment**. **Superencryption** refers to the outer-level encryption of a multiple encryption.

**Encryption software** is software that uses cryptography to prevent unauthorized access to digital information. Cryptography is used to protect digital information on computers as well as the digital information that is sent to other computers over the Internet.

In cryptanalysis, **attack models** or **attack types** are a classification of cryptographic attacks specifying the kind of access a cryptanalyst has to a system under attack when attempting to "break" an encrypted message generated by the system. The greater the access the cryptanalyst has to the system, the more useful information he can get to utilize for breaking the cypher.

The **Beaufort cipher,** created by Sir Francis Beaufort, is a substitution cipher similar to the Vigenère cipher, with a slightly modified enciphering mechanism and tableau. Its most famous application was in a rotor-based cipher machine, the Hagelin M-209. The Beaufort cipher is based on the Beaufort square which is essentially the same as a Vigenère square but in reverse order starting with the letter "Z" in the first row, where the first row and the last column serve the same purpose.

- Richard J. Aldrich,
*GCHQ: The Uncensored Story of Britain's Most Secret Intelligence Agency*, HarperCollins July 2010. - Helen Fouché Gaines, "Cryptanalysis", 1939, Dover. ISBN 0-486-20097-3
- Ibrahim A. Al-Kadi, "The origins of cryptology: The Arab contributions", Cryptologia, 16(2) (April 1992) pp. 97–126.
- David Kahn,
*The Codebreakers - The Story of Secret Writing*( ISBN 0-684-83130-9) (1967) - David A. King, The ciphers of the monks - A forgotten number notation of the Middle Ages, Stuttgart: Franz Steiner, 2001 ( ISBN 3-515-07640-9)
- Abraham Sinkov,
*Elementary Cryptanalysis: A Mathematical Approach*, Mathematical Association of America, 1966. ISBN 0-88385-622-0 - William Stallings,
*Cryptography and Network Security, principles and practices, 4th Edition* - Stinson, Douglas R. (1995),
*Cryptogtaphy / Theory and Practice*, CRC Press, ISBN 0-8493-8521-0

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