**Cryptography**, or **cryptology** is the practice and study of techniques for secure communication in the presence of adversarial behavior.^{[1]} More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages;^{[2]} various aspects in information security such as data confidentiality, data integrity, authentication, and non-repudiation^{[3]} 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.

Cryptography prior to the modern age was effectively synonymous with *encryption*, converting information from a readable state to unintelligible nonsense. The sender of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature often uses the names Alice ("A") for the sender, Bob ("B") for the intended recipient, and Eve ("eavesdropper") for the adversary.^{[4]} Since the development of rotor cipher machines in World War I and the advent of computers in World War II, cryptography methods have become increasingly complex and its applications more varied.

Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions, making such algorithms hard to break in actual practice by any adversary. While it is theoretically possible to break into a well-designed system, it is infeasible in actual practice to do so. Such schemes, if well designed, are therefore termed "computationally secure"; theoretical advances, e.g., improvements in integer factorization algorithms, and faster computing technology require these designs to be continually reevaluated, and if necessary, adapted. There exist information-theoretically secure schemes that provably cannot be broken even with unlimited computing power, such as the one-time pad, but these schemes are much more difficult to use in practice than the best theoretically breakable but computationally secure schemes.

The growth of cryptographic technology has raised a number of legal issues in the information age. Cryptography's potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or even prohibit its use and export.^{[5]} In some jurisdictions where the use of cryptography is legal, laws permit investigators to compel the disclosure of encryption keys for documents relevant to an investigation.^{[6]}^{[7]} Cryptography also plays a major role in digital rights management and copyright infringement disputes in regard to digital media.^{[8]}

## Terminology[]

The first use of the term *cryptograph* (as opposed to *cryptogram*) dates back to the 19th century—originating from *The Gold-Bug*, a story by Edgar Allan Poe.^{[9]}^{[10]}

Until modern times, cryptography referred almost exclusively to *encryption*, which is the process of converting ordinary information (called plaintext) into unintelligible form (called ciphertext).^{[11]} Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A *cipher* (or *cypher*) is a pair of algorithms that carry out the encryption and the reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and, in each instance, by a "key". The key is a secret (ideally known only to the communicants), usually a string of characters (ideally short so it can be remembered by the user), which is needed to decrypt the ciphertext. In formal mathematical terms, a "cryptosystem" is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, and the encryption and decryption algorithms which correspond to each key. Keys are important both formally and in actual practice, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless (or even counter-productive) for most purposes.

Historically, ciphers were often used directly for encryption or decryption without additional procedures such as authentication or integrity checks. There are, generally, two kinds of cryptosystems: symmetric and asymmetric. In symmetric systems, the only ones known until the 1970s, the same key (the secret key) is used to encrypt and decrypt a message. Data manipulation in symmetric systems is faster than asymmetric systems in part because they generally use shorter key lengths. Asymmetric systems use a "public key" to encrypt a message and a related "private key" to decrypt it. The use of asymmetric systems enhances the security of communication, largely because the relation between the two keys is very hard to discover.^{[12]} Examples of asymmetric systems include RSA (Rivest–Shamir–Adleman), and ECC (Elliptic Curve Cryptography). Quality symmetric algorithms include the commonly used AES (Advanced Encryption Standard) which replaced the older DES (Data Encryption Standard).^{[13]} Not very high quality symmetric algorithms include the assorted children's language tangling schemes such as Pig Latin or other cant, and indeed effectively all cryptographic schemes, however seriously intended, from any source prior to the invention of the one-time pad early in the 20th century.

In colloquial use, the term "code" is often used to mean any method of encryption or concealment of meaning. However, in cryptography, *code* has a more specific meaning: the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a code word (for example, "wallaby" replaces "attack at dawn"). A cypher, in contrast, is a scheme for changing or substituting an element below such a level (a letter, or a syllable or a pair of letters or ...) in order to produce a cyphertext.

Cryptanalysis is the term used for the study of methods for obtaining the meaning of encrypted information without access to the key normally required to do so; i.e., it is the study of how to "crack" encryption algorithms or their implementations.

Some use the terms *cryptography* and *cryptology* interchangeably in English, while others (including US military practice generally) use *cryptography* to refer specifically to the use and practice of cryptographic techniques and *cryptology* to refer to the combined study of cryptography and cryptanalysis.^{[14]}^{[15]}

The study of characteristics of languages that have some application in cryptography or cryptology (e.g. frequency data, letter combinations, universal patterns, etc.) is called *cryptolinguistics*.

## History of cryptography and cryptanalysis[]

Before the modern era, cryptography focused on 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 of that message). Encryption attempted to ensure secrecy in communications, such as those of spies, military leaders, and diplomats. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication, digital signatures, interactive proofs and secure computation, among others.

### Early history[]

The main classical cipher types are transposition ciphers, which rearrange the order of letters in a message (e.g., 'hello world' becomes 'ehlol owrdl' 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 Latin alphabet). Simple versions of either have never offered much confidentiality from enterprising opponents. 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. Suetonius reports that Julius Caesar used it with a shift of three to communicate with his generals. Atbash is an example of an early Hebrew cipher. The earliest known use of cryptography is some carved ciphertext on stone in Egypt (ca 1900 BCE), but this may have been done for the amusement of literate observers rather than as a way of concealing information.

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, was a message tattooed on a slave's shaved head and concealed under the regrown hair.^{[11]} More modern examples of steganography include the use of invisible ink, microdots, and digital watermarks to conceal information.

In India, the 2000-year-old Kamasutra of Vātsyāyana speaks of two different kinds of ciphers called Kautiliyam and Mulavediya. In the Kautiliyam, the cipher letter substitutions are based on phonetic relations, such as vowels becoming consonants. In the Mulavediya, the cipher alphabet consists of pairing letters and using the reciprocal ones.^{[11]}

In Sassanid Persia, there were two secret scripts, according to the Muslim author Ibn al-Nadim: the *šāh-dabīrīya* (literally "King's script") which was used for official correspondence, and the *rāz-saharīya* which was used to communicate secret messages with other countries.^{[16]}

### Cryptanalysis[]

David Kahn notes in *The Codebreakers* that modern cryptology originated among the Arabs, the first people to systematically document cryptanalytic methods.^{[17]} Al-Khalil (717–786) wrote the *Book of Cryptographic Messages*, which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels.^{[18]}

Ciphertexts produced by a classical cipher (and some modern ciphers) will reveal statistical information about the plaintext, and that information can often be used to break the cipher. After the discovery of frequency analysis, by the Arab mathematician and polymath Al-Kindi (also known as *Alkindus*) in the 9th century,^{[19]}^{[20]}^{[21]} nearly all such ciphers could be broken by an informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzles. Al-Kindi wrote a book on cryptography entitled *Risalah fi Istikhraj al-Mu'amma* (*Manuscript for the Deciphering Cryptographic Messages*), which described the first known use of frequency analysis and cryptanalysis techniques.^{[19]}^{[22]} An important contribution of Ibn Adlan (1187–1268) was on sample size for use of frequency analysis.^{[18]}

Language letter frequencies may offer little help for some extended historical encryption techniques such as homophonic cipher that tend to flatten the frequency distribution. For those ciphers, language letter group (or n-gram) frequencies may provide an attack.

Essentially all ciphers remained vulnerable to cryptanalysis using the frequency analysis technique until the development of the polyalphabetic cipher. While it was known to Al-Kindi to some extent,^{[22]}^{[23]} it was first clearly described in the work of Al-Qalqashandi (1355–1418), based on the earlier work of Ibn al-Durayhim (1312–1359), describing a polyalphabetic cipher in which each plaintext letter is assigned more than one substitute.^{[24]} It was later also described by Leon Battista Alberti around the year 1467, though there is some indication that Alberti's method was to use different ciphers (i.e., substitution alphabets) for various parts of a message (perhaps for each successive plaintext letter at the limit). He also invented what was probably the first automatic cipher device, a wheel that implemented a partial realization of his invention. In the Vigenère cipher, a polyalphabetic cipher, encryption uses a *key word*, which controls letter substitution depending on which letter of the key word is used. In the mid-19th century Charles Babbage showed that the Vigenère cipher was vulnerable to Kasiski examination, but this was first published about ten years later by Friedrich Kasiski.^{[25]}

Although frequency analysis can be a powerful and general technique against many ciphers, encryption has still often been effective in practice, as many a would-be cryptanalyst was unaware of the technique. Breaking a message without using frequency analysis essentially required knowledge of the cipher used and perhaps of the key involved, thus making espionage, bribery, burglary, defection, etc., more attractive approaches to the cryptanalytically uninformed. It was finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible nor practical safeguard of message security; in fact, it was further realized that any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary fully understands the cipher algorithm itself. Security of the key used should alone be sufficient for a good cipher to maintain confidentiality under an attack. This fundamental principle was first explicitly stated in 1883 by Auguste Kerckhoffs and is generally called Kerckhoffs's Principle; alternatively and more bluntly, it was restated by Claude Shannon, the inventor of information theory and the fundamentals of theoretical cryptography, as *Shannon's Maxim*—'the enemy knows the system'.

Different 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, which was 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 wheel cypher (not publicly known, and reinvented independently by Bazeries around 1900). Many mechanical encryption/decryption devices were invented early in the 20th century, and several patented, among them rotor machines—famously including the Enigma machine used by the German government and military from the late 1920s and during World War II.^{[26]} The ciphers implemented by better quality examples of these machine designs brought about a substantial increase in cryptanalytic difficulty after WWI.^{[27]}

### Computer era[]

Prior to the early 20th century, cryptography was mainly concerned with linguistic and lexicographic 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, number theory, and finite mathematics generally. Cryptography is also a branch of engineering, but an unusual one since it deals with active, intelligent, and malevolent opposition; other kinds of engineering (e.g., civil or chemical engineering) need deal only with neutral natural forces. There is also active research examining the relationship between cryptographic problems and quantum physics.

Just as the development of digital computers and electronics helped in cryptanalysis, it made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this was new and significant. Computer use has thus supplanted linguistic cryptography, both for cipher design and cryptanalysis. Many computer ciphers can be characterized by their operation on binary bit sequences (sometimes in groups or blocks), unlike classical and mechanical schemes, which generally manipulate traditional characters (i.e., letters and digits) directly. 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 typically the case that use of a quality cipher is very efficient (i.e., fast and requiring few resources, such as memory or CPU capability), while breaking it requires an effort many orders of magnitude larger, and vastly larger than that required for any classical cipher, making cryptanalysis so inefficient and impractical as to be effectively impossible.

### Modern cryptography[]

Cryptanalysis of the new mechanical devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts at Bletchley Park during WWII spurred the development of more efficient means for carrying out repetitious tasks. This culminated in the development of the Colossus, the world's first fully electronic, digital, programmable computer, which assisted in the decryption of ciphers generated by the German Army's Lorenz SZ40/42 machine.

Extensive open academic research into cryptography is relatively recent; it began only in the mid-1970s. In recent times, IBM personnel designed the algorithm that became the Federal (i.e., US) Data Encryption Standard; Whitfield Diffie and Martin Hellman published their key agreement algorithm;^{[28]} and the RSA algorithm was published in Martin Gardner's *Scientific American* column. Since then, cryptography has become a widely used tool in communications, computer networks, and computer security generally.

Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable, such as the integer factorization or the discrete logarithm problems, so there are deep connections with abstract mathematics. There are very few cryptosystems that are proven to be unconditionally secure. The one-time pad is one, and was proven to be so by Claude Shannon. There are a few important algorithms that have been proven secure under certain assumptions. For example, the infeasibility of factoring extremely large integers is the basis for believing that RSA is secure, and some other systems, but even so, proof of unbreakability is unavailable since the underlying mathematical problem remains open. In practice, these are widely used, and are believed unbreakable in practice by most competent observers. There are systems similar to RSA, such as one by Michael O. Rabin that are provably secure provided factoring *n = pq* is impossible; it is quite unusable in practice. The discrete logarithm problem is the basis for believing some other cryptosystems are secure, and again, there are related, less practical systems that are provably secure relative to the solvability or insolvability discrete log problem.^{[29]}

As well as being aware of cryptographic history, cryptographic algorithm and system designers must also sensibly consider probable future developments while working on their designs. For instance, continuous improvements in computer processing power have increased the scope of brute-force attacks, so when specifying key lengths, the required key lengths are similarly advancing.^{[30]} The potential effects of quantum computing are already being considered by some cryptographic system designers developing post-quantum cryptography; the announced imminence of small implementations of these machines may be making the need for preemptive caution rather more than merely speculative.^{[3]}

### Data security[]

In the 1970s, Egyptian cryptographer Mohamed M. Atalla was a pioneer in data security^{[31]} and modern cryptography.^{[32]} In 1972,^{[32]} he founded Atalla Technovation,^{[33]} later called Atalla Corporation, which dealt with safety problems of banking and financial institutions.^{[34]} He invented the first hardware security module (HSM),^{[35]} the so-called "Atalla Box", a security system that secures a majority of transactions from ATMs today. At the same time, Atalla contributed to the development of the personal identification number (PIN) system, which has developed among others in the banking industry as the standard for identification.

The work of Atalla in the early 1970s led to the use of high security modules. His "Atalla Box", a security system which encrypts PIN and ATM messages, and protected offline devices with an un-guessable PIN-generating key.^{[36]} He commercially released the "Atalla Box" in 1973.^{[36]} A key innovation of the Atalla Box was the key block, which is required to securely interchange symmetric keys or PINs with other actors of the banking industry. This secure interchange is performed using the Atalla Key Block (AKB) format, which lies at the root of all cryptographic block formats used within the Payment Card Industry Data Security Standard (PCI DSS) and American National Standards Institute (ANSI) standards.^{[37]}

Fearful that Atalla would dominate the market, banks and credit card companies began working on an international standard.^{[38]} Its PIN verification process was similar to the later IBM 3624.^{[39]} Atalla was an early competitor to IBM in the banking market, and was cited as an influence by IBM employees who worked on the Data Encryption Standard (DES).^{[40]} In recognition of his work on the PIN system of information security management, Atalla has been referred to as the "Father of the PIN"^{[41]}^{[42]}^{[43]} and as a father of information security technology.^{[44]}

At the National Association of Mutual Savings Banks (NAMSB) conference in January 1976, Atalla announced an upgrade to its Identikey system, called the Interchange Identikey. It added the capabilities of processing online transactions and dealing with network security. Designed with the focus of taking bank transactions online, the Identikey system was extended to shared-facility operations. It was consistent and compatible with various switching networks, and was capable of resetting itself electronically to any one of 64,000 irreversible nonlinear algorithms as directed by card data information. The Interchange Identikey device was released in March 1976. It was the first product designed to deal with online transactions^{[45]} In 1979, Atalla introduced the first network security processor (NSP).^{[46]}

The Atalla Box protected over 90% of all ATM networks in operation as of 1998,^{[47]} and secured 85% of all ATM transactions worldwide as of 2006.^{[48]} Atalla products still secure the majority of the world's ATM transactions, as of 2014.^{[49]}

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## Further reading[]

- Becket, B (1988).
*Introduction to Cryptology*. Blackwell Scientific Publications. ISBN 978-0-632-01836-9. OCLC 16832704. Excellent coverage of many classical ciphers and cryptography concepts and of the "modern" DES and RSA systems. *Cryptography and Mathematics*by Bernhard Esslinger, 200 pages, part of the free open-source package CrypTool, "PDF download" (PDF). Archived from the original on 22 July 2011. Retrieved 23 December 2013.`{{cite web}}`

: CS1 maint: bot: original URL status unknown (link). CrypTool is the most widespread e-learning program about cryptography and cryptanalysis, open source.*In Code: A Mathematical Journey*by Sarah Flannery (with David Flannery). Popular account of Sarah's award-winning project on public-key cryptography, co-written with her father.- 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. - Oded Goldreich,
*Foundations of Cryptography*, in two volumes, Cambridge University Press, 2001 and 2004. *Introduction to Modern Cryptography*by Jonathan Katz and Yehuda Lindell.*Alvin's Secret Code*by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis).- Ibrahim A. Al-Kadi, "The Origins of Cryptology: the Arab Contributions," Cryptologia, vol. 16, no. 2 (April 1992), pp. 97–126.
- Christof Paar, Jan Pelzl,
*Understanding Cryptography, A Textbook for Students and Practitioners*. Archived 31 October 2020 at the Wayback Machine Springer, 2009. (Slides, online cryptography lectures and other information are available on the companion web site.) Very accessible introduction to practical cryptography for non-mathematicians. *Introduction to Modern Cryptography*by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs. PDF download.- Johann-Christoph Woltag, 'Coded Communications (Encryption)' in Rüdiger Wolfrum (ed)
*Max Planck Encyclopedia of Public International Law*(Oxford University Press 2009). - "Max Planck Encyclopedia of Public International Law"., giving an overview of international law issues regarding cryptography.
- Jonathan Arbib & John Dwyer,
*Discrete Mathematics for Cryptography*, 1st Edition ISBN 978-1-907934-01-8. - Stallings, William (March 2013).
*Cryptography and Network Security: Principles and Practice*(6th ed.). Prentice Hall. ISBN 978-0-13-335469-0.

## External links[]

Wikiquote has a collection of quotations related to: Cryptography |

Wikibooks has more on the topic of: Cryptography |

Library resources about Cryptography |

- Crypto Glossary and Dictionary of Technical Cryptography
- NSA's CryptoKids.
- Overview and Applications of Cryptology by the CrypTool Team; PDF; 3.8 MB. July 2008
- A Course in Cryptography by Raphael Pass & Abhi Shelat – offered at Cornell in the form of lecture notes.
- For more on the use of cryptographic elements in fiction, see: Dooley, John F., William and Marilyn Ingersoll Professor of Computer Science, Knox College (23 August 2012). "Cryptology in Fiction". Archived from the original on 29 July 2020. Retrieved 20 February 2015.
`{{cite web}}`

: CS1 maint: multiple names: authors list (link) - The George Fabyan Collection at the Library of Congress has early editions of works of seventeenth-century English literature, publications relating to cryptography.