Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''

one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...

. In a stream cipher, the output stream is created based on a hidden internal state that changes as the cipher operates. That internal state is initially set up using the secret key material. RC4 is a widely used stream cipher. Block ciphers can be used as stream ciphers by generating blocks of a keystream (in place of a Pseudorandom number generator) and applying an

Thus, a hash function design competition was meant to select a new U.S. national standard, to be called

Previously released as an MIT "Technical Memo" in April 1977, and published in

Thus, a hash function design competition was meant to select a new U.S. national standard, to be called

one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...

cipher is unbreakable, provided the key material is truly ^{55} decryptions, trying approximately half of the possible keys, to reach a point at which chances are better than even that the key sought will have been found. But this may not be enough assurance; a ^{43} known plaintexts (with their corresponding ciphertexts) and approximately 2^{43} DES operations. This is a considerable improvement over brute force attacks.
Public-key algorithms are based on the computational difficulty of various problems. The most famous of these are the difficulty of integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization.
When the numbers are su ...

of

Until the development of the

''Foundations of Cryptography''

in two volumes, Cambridge University Press, 2001 and 2004. * ''Alvin's Secret Code'' by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis). *

Introduction to Modern Cryptography

' by Jonathan Katz and Yehuda Lindell. * Ibrahim A. Al-Kadi, "The Origins of Cryptology: the Arab Contributions," Cryptologia, vol. 16, no. 2 (April 1992), pp. 97–126.

Jan Pelzl

''Understanding Cryptography, A Textbook for Students and Practitioners''.

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. * , giving an overview of international law issues regarding cryptography. * ''Introduction to Modern Cryptography'' by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs

PDF download

* * Tenzer, Theo (2021): ''SUPER SECRETO – The Third Epoch of Cryptography: Multiple, exponential, quantum-secure and above all, simple and practical Encryption for Everyone'', Norderstedt, . * Johann-Christoph Woltag, 'Coded Communications (Encryption)' in Rüdiger Wolfrum (ed) ''Max Planck Encyclopedia of Public International Law'' (Oxford University Press 2009).

Cryptography Works - web information portal

Crypto Glossary and Dictionary of Technical Cryptography

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:

at the Library of Congress has early editions of works of seventeenth-century English literature, publications relating to cryptography. {{Authority control, state=expanded Applied mathematics Banking technology Formal sciences

-logia
''-logy'' is a suffix in the English language, used with words originally adapted from Ancient Greek ending in ('). The earliest English examples were anglicizations of the French '' -logie'', which was in turn inherited from the Latin ''-logi ...

'', "study", respectively), is the practice and study of techniques for secure communication
Secure communication is when two entities are communicating and do not want a third party to listen in. For this to be the case, the entities need to communicate in a way that is unsusceptible to eavesdropping or interception. Secure communication ...

in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including ...

, information security
Information security, sometimes shortened to InfoSec, is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthoriz ...

, electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the ...

, digital signal processing, physics, and others. Core concepts related to information security
Information security, sometimes shortened to InfoSec, is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthoriz ...

( data confidentiality, data integrity
Data integrity is the maintenance of, and the assurance of, data accuracy and consistency over its entire life-cycle and is a critical aspect to the design, implementation, and usage of any system that stores, processes, or retrieves data. The ter ...

, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce
E-commerce (electronic commerce) is the activity of electronically buying or selling of products on online services or over the Internet. E-commerce draws on technologies such as mobile commerce, electronic funds transfer, supply chain manage ...

, chip-based payment cards, digital currencies, computer passwords, and military communications
Military communications or military signals involve all aspects of communications, or conveyance of information, by armed forces. Military communications span from pre-history to the present. The earliest military communications were delivered b ...

.
Cryptography prior to the modern age was effectively synonymous with encryption
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...

, converting readable information (plaintext
In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted.
Overview
With the advent of comp ...

) to unintelligible nonsense
Nonsense is a communication, via speech, writing, or any other symbolic system, that lacks any coherent meaning. Sometimes in ordinary usage, nonsense is synonymous with absurdity or the ridiculous. Many poets, novelists and songwriters have u ...

text ( ciphertext), which can only be read by reversing the process (decryption
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...

). The sender of an encrypted (coded) message shares the decryption (decoding) technique only with intended recipients to preclude access from adversaries. The cryptography literature often uses the names "Alice" (or "A") for the sender, "Bob" (or "B") for the intended recipient, and "Eve" (or "E") for the eavesdropping
Eavesdropping is the act of secretly or stealthily listening to the private conversation or communications of others without their consent in order to gather information.
Etymology
The verb ''eavesdrop'' is a back-formation from the noun ''eaves ...

adversary. Since the development of rotor cipher machines in World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, the United States, and the Ottoman Empire, with figh ...

and the advent of computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These pr ...

s in World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposi ...

, cryptography methods have become increasingly complex and their applications more varied.
Modern cryptography is heavily based on mathematical theory
A mathematical theory is a mathematical model of a branch of mathematics that is based on a set of axioms. It can also simultaneously be a body of knowledge (e.g., based on known axioms and definitions), and so in this sense can refer to an area ...

and computer science practice; cryptographic algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

s are designed around computational hardness assumption
In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where ''efficiently'' typically means "in polynomial time"). It is not known how to prove (uncondition ...

s, 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
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization.
When the numbers are su ...

algorithms) and faster computing technology require these designs to be continually reevaluated, and if necessary, adapted. Information-theoretically secure schemes that cannot be broken even with unlimited computing power, such as the one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...

, 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
The Information Age (also known as the Computer Age, Digital Age, Silicon Age, or New Media Age) is a historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during t ...

. 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. 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. Cryptography also plays a major role in digital rights management
Digital rights management (DRM) is the management of legal access to digital content. Various tools or technological protection measures (TPM) such as access control technologies can restrict the use of proprietary hardware and copyrighted works. ...

and copyright infringement
Copyright infringement (at times referred to as piracy) is the use of works protected by copyright without permission for a usage where such permission is required, thereby infringing certain exclusive rights granted to the copyright holder, ...

disputes in regard to digital media
Digital media is any communication media that operate in conjunction with various encoded machine-readable data formats. Digital media can be created, viewed, distributed, modified, listened to, and preserved on a digital electronics device. ' ...

.
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 byEdgar Allan Poe
Edgar Allan Poe (; Edgar Poe; January 19, 1809 – October 7, 1849) was an American writer, poet, editor, and literary critic. Poe is best known for his poetry and short stories, particularly his tales of mystery and the macabre. He is wide ...

.
Until modern times, cryptography referred almost exclusively to "encryption", which is the process of converting ordinary information (called plaintext
In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted.
Overview
With the advent of comp ...

) into an unintelligible form (called ciphertext). Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A cipher
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 i ...

(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
In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality ( encryption).
Typically, a cryptosystem consists of three algorithms: one for key generation, one f ...

" is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, and the encryption and decryption algorithms that 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 two main types of cryptosystems: symmetric and asymmetric. In symmetric systems, the only ones known until the 1970s, the same secret key encrypts and decrypts a message. Data manipulation in symmetric systems is significantly faster than in asymmetric systems. Asymmetric systems use a "public key" to encrypt a message and a related "private key" to decrypt it. The advantage of asymmetric systems is that the public key can be freely published, allowing parties to establish secure communication without having a shared secret key. In practice, asymmetric systems are used to first exchange a secret key, and then secure communication proceeds via a more efficient symmetric system using that key. Examples of asymmetric systems include Diffie–Hellman key exchange
Diffie–Hellman key exchangeSynonyms of Diffie–Hellman key exchange include:
* Diffie–Hellman–Merkle key exchange
* Diffie–Hellman key agreement
* Diffie–Hellman key establishment
* Diffie–Hellman key negotiation
* Exponential key exc ...

, RSA ( Rivest–Shamir–Adleman), ECC (Elliptic Curve Cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide ...

), and Post-quantum cryptography. Secure symmetric algorithms include the commonly used AES (Advanced Encryption Standard
The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.
AES is a variant ...

) which replaced the older DES (Data Encryption Standard
The Data Encryption Standard (DES ) is a symmetric-key algorithm for the encryption of digital data. Although its short key length of 56 bits makes it too insecure for modern applications, it has been highly influential in the advancement of cry ...

). Insecure symmetric algorithms include children's language tangling schemes such as Pig Latin or other cant, and all historical cryptographic schemes, however seriously intended, prior to the invention of the one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...

early in the 20th century.
In colloquial
Colloquialism (), also called colloquial language, everyday language or general parlance, is the linguistic style used for casual (informal) communication. It is the most common functional style of speech, the idiom normally employed in conversa ...

use, the term "code
In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication c ...

" 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
In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, ...

(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, a syllable, or a pair of letters, etc.) in order to produce a cyphertext.
Cryptanalysis
Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic s ...

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. Oded Goldreich, ''Foundations of Cryptography, Volume 1: Basic Tools'', Cambridge University Press, 2001, English is more flexible than several other languages in which "cryptology" (done by cryptologists) is always used in the second sense above. advises that steganography is sometimes included in cryptology.
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

Before the modern era, cryptography focused on message confidentiality (i.e., encryption)—conversion ofmessages
A message is a discrete unit of communication intended by the source for consumption by some recipient or group of recipients. A message may be delivered by various means, including courier, telegraphy, carrier pigeon and electronic bus.
...

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
Secrecy is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals. That which is kept hidden is known as the secret.
Secrecy is often controvers ...

in communications, such as those of spies, military leaders, and diplomat
A diplomat (from grc, δίπλωμα; romanized ''diploma'') is a person appointed by a state or an intergovernmental institution such as the United Nations or the European Union to conduct diplomacy with one or more other states or internati ...

s. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication, digital signature
A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient very high confidence that the message was created b ...

s, interactive proofs and secure computation, among others.
Classic cryptography

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), andsubstitution cipher
In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, tri ...

s, 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
Gaius Julius Caesar (; ; 12 July 100 BC – 15 March 44 BC), was a Roman general and statesman. A member of the First Triumvirate, Caesar led the Roman armies in the Gallic Wars before defeating his political rival Pompey in a civil war, an ...

used it with a shift of three to communicate with his generals. Atbash
Atbash ( he, אתבש; also transliterated Atbaš) is a monoalphabetic substitution cipher originally used to encrypt the Hebrew alphabet. It can be modified for use with any known writing system with a standard collating order.
Encryption
...

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.
The Greeks of Classical times are said to have known of ciphers (e.g., the scytale transposition cipher claimed to have been used by the Sparta
Sparta (Doric Greek: Σπάρτα, ''Spártā''; Attic Greek: Σπάρτη, ''Spártē'') was a prominent city-state in Laconia, in ancient Greece. In antiquity, the city-state was known as Lacedaemon (, ), while the name Sparta referred ...

n military). 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
Herodotus ( ; grc, , }; BC) was an ancient Greek historian and geographer from the Greek city of Halicarnassus, part of the Persian Empire (now Bodrum, Turkey) and a later citizen of Thurii in modern Calabria (Italy). He is known for havin ...

, was a message tattooed on a slave's shaved head and concealed under the regrown hair. More modern examples of steganography include the use of invisible ink
Invisible ink, also known as security ink or sympathetic ink, is a substance used for writing, which is invisible either on application or soon thereafter, and can later be made visible by some means, such as heat or ultraviolet light. Invisibl ...

, microdots, and digital watermark
A digital watermark is a kind of marker covertly embedded in a noise-tolerant signal such as audio, video or image data. It is typically used to identify ownership of the copyright of such signal. "Watermarking" is the process of hiding digital inf ...

s 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.
In Sassanid Persia
The Sasanian () or Sassanid Empire, officially known as the Empire of Iranians (, ) and also referred to by historians as the Neo-Persian Empire, was the last Iranian empire before the early Muslim conquests of the 7th-8th centuries AD. Named ...

, there were two secret scripts, according to the Muslim author Ibn al-Nadim
Abū al-Faraj Muḥammad ibn Isḥāq al-Nadīm ( ar, ابو الفرج محمد بن إسحاق النديم), also ibn Abī Ya'qūb Isḥāq ibn Muḥammad ibn Isḥāq al-Warrāq, and commonly known by the ''nasab'' (patronymic) Ibn al-Nadīm ...

: 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.
David Kahn notes in '' The Codebreakers'' that modern cryptology originated among the Arabs
The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, ...

, the first people to systematically document cryptanalytic methods. Al-Khalil
Hebron ( ar, الخليل or ; he, חֶבְרוֹן ) is a State of Palestine, Palestinian. city in the southern West Bank, south of Jerusalem. Nestled in the Judaean Mountains, it lies Above mean sea level, above sea level. The second-lar ...

(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.
Ciphertexts produced by a classical cipher
In cryptography, a classical cipher is a type of cipher that was used historically but for the most part, has fallen into disuse. In contrast to modern cryptographic algorithms, most classical ciphers can be practically computed and solved by hand ...

(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
In cryptanalysis, frequency analysis (also known as counting letters) is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers.
Frequency analysis is based on th ...

, perhaps by the Arab mathematician and polymath
A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...

Al-Kindi
Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ar, أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; la, Alkindus; c. 801–873 AD) was an Arab Muslim philosopher, polymath, mathematician, physician ...

(also known as ''Alkindus'') in the 9th century, nearly all such ciphers could be broken by an informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzle
A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together ( or take them apart) in a logical way, in order to arrive at the correct or fun solution of the puzzle ...

s (see cryptogram). 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 cryptanalysis techniques.
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, most clearly by Leon Battista Alberti
Leon Battista Alberti (; 14 February 1404 – 25 April 1472) was an Italian Renaissance humanist author, artist, architect, poet, priest, linguist, philosopher, and cryptographer; he epitomised the nature of those identified now as polymaths. H ...

around the year 1467, though there is some indication that it was already known to Al-Kindi. Alberti's innovation 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
A polyalphabetic cipher substitution, using multiple substitution alphabets. The Vigenère cipher is probably the best-known example of a polyalphabetic cipher, though it is a simplified special case. The Enigma machine is more complex but is sti ...

, 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
Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer.
Babbage is considered ...

showed that the Vigenère cipher was vulnerable to Kasiski examination, but this was first published about ten years later by Friedrich Kasiski.
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
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory".
As a 21-year-old master's degree student at the Massachusetts Inst ...

, the inventor of information theory
Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...

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
Thomas Jefferson (April 13, 1743 – July 4, 1826) was an American statesman, diplomat, lawyer, architect, philosopher, and Founding Fathers of the United States, Founding Father who served as the third president of the United States from 18 ...

'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
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

. The ciphers implemented by better quality examples of these machine designs brought about a substantial increase in cryptanalytic difficulty after WWI.Early computer-era cryptography

Cryptanalysis of the new mechanical ciphering devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts atBletchley Park
Bletchley Park is an English country house and estate in Bletchley, Milton Keynes (Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following 1 ...

during WWII spurred the development of more efficient means for carrying out repetitious tasks, such as military code breaking (decryption). 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, beginning in the mid-1970s. In the early 1970s IBM personnel designed the Data Encryption Standard (DES) algorithm that became the first federal government cryptography standard in the United States. In 1976 Whitfield Diffie and Martin Hellman
Martin Edward Hellman (born October 2, 1945) is an American cryptologist and mathematician, best known for his involvement with public key cryptography in cooperation with Whitfield Diffie and Ralph Merkle. Hellman is a longtime contributor to t ...

published the Diffie–Hellman key exchange algorithm. In 1977 the RSA algorithm was published in Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lew ...

's ''Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

'' column. Since then, cryptography has become a widely used tool in communications, computer networks, and computer security
Computer security, cybersecurity (cyber security), or information technology security (IT security) is the protection of computer systems and computer network, networks from attack by malicious actors that may result in unauthorized informati ...

generally.
Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable, such as the integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization.
When the numbers are su ...

or the discrete logarithm
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b ...

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
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...

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.''Cryptography: Theory and Practice'', Third Edition (Discrete Mathematics and Its Applications), 2005, by Douglas R. Stinson, Chapman and Hall/CRC
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 attack
In cryptography, a brute-force attack consists of an attacker submitting many passwords or passphrases with the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct ...

s, so when specifying key length
In cryptography, key size, key length, or key space refer to the number of bits in a key used by a cryptographic algorithm (such as a cipher).
Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fast ...

s, the required key lengths are similarly advancing. The potential impact of quantum computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...

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.
Modern cryptography

Prior to the early 20th century, cryptography was mainly concerned with linguistic and lexicographic patterns. Since then cryptography has broadened in scope, and now makes extensive use of mathematical subdisciplines, includinginformation theory
Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...

, computational complexity
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) ...

, statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industr ...

, combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ap ...

, abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The ter ...

, number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

, and finite mathematics. Cryptography is also a branch of engineering
Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

, 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
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...

.
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

Symmetric-key cryptography

Symmetric-key cryptography refers to encryption methods in which both the sender and receiver share the same key (or, less commonly, in which their keys are different, but related in an easily computable way). This was the only kind of encryption publicly known until June 1976. Symmetric key ciphers are implemented as either block ciphers or stream ciphers. A block cipher enciphers input in blocks of plaintext as opposed to individual characters, the input form used by a stream cipher. TheData Encryption Standard
The Data Encryption Standard (DES ) is a symmetric-key algorithm for the encryption of digital data. Although its short key length of 56 bits makes it too insecure for modern applications, it has been highly influential in the advancement of cry ...

(DES) and the Advanced Encryption Standard
The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.
AES is a variant ...

(AES) are block cipher designs that have been designated cryptography standards by the US government (though DES's designation was finally withdrawn after the AES was adopted). Despite its deprecation as an official standard, DES (especially its still-approved and much more secure triple-DES variant) remains quite popular; it is used across a wide range of applications, from ATM encryption to e-mail privacy and secure remote access. Many other block ciphers have been designed and released, with considerable variation in quality. Many, even some designed by capable practitioners, have been thoroughly broken, such as FEAL
In cryptography, FEAL (the Fast data Encipherment ALgorithm) is a block cipher proposed as an alternative to the Data Encryption Standard (DES), and designed to be much faster in software. The Feistel based algorithm was first published in 198 ...

.
Stream ciphers, in contrast to the 'block' type, create an arbitrarily long stream of key material, which is combined with the plaintext bit-by-bit or character-by-character, somewhat like the XOR
Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false).
It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...

operation to each bit of the plaintext with each bit of the keystream.
Message authentication code
In cryptography, a message authentication code (MAC), sometimes known as a ''tag'', is a short piece of information used for authenticating a message. In other words, to confirm that the message came from the stated sender (its authenticity) and ...

s (MACs) are much like cryptographic hash functions, except that a secret key can be used to authenticate the hash value upon receipt; this additional complication blocks an attack scheme against bare digest algorithms, and so has been thought worth the effort. Cryptographic hash functions are a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed-length hash, which can be used in (for example) a digital signature. For good hash functions, an attacker cannot find two messages that produce the same hash. MD4 is a long-used hash function that is now broken; MD5, a strengthened variant of MD4, is also widely used but broken in practice. The US National Security Agency
The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collectio ...

developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1
In cryptography, SHA-1 (Secure Hash Algorithm 1) is a cryptographically broken but still widely used hash function which takes an input and produces a 160-bit (20-byte) hash value known as a message digest – typically rendered as 40 hexadecim ...

is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. They are built using the Merkle–Damgård construction, from a one-way compressi ...

family improves on SHA-1, but is vulnerable to clashes as of 2011; and the US standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness of NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

's overall hash algorithm toolkit."Thus, a hash function design competition was meant to select a new U.S. national standard, to be called

SHA-3
SHA-3 (Secure Hash Algorithm 3) is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August 5, 2015. Although part of the same series of standards, SHA-3 is internally different from the MD5-like struct ...

, by 2012. The competition ended on October 2, 2012, when the NIST announced that Keccak would be the new SHA-3 hash algorithm. Unlike block and stream ciphers that are invertible, cryptographic hash functions produce a hashed output that cannot be used to retrieve the original input data. Cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security.
Public-key cryptography

Symmetric-key cryptosystems use the same key for encryption and decryption of a message, although a message or group of messages can have a different key than others. A significant disadvantage of symmetric ciphers is thekey management
Key management refers to management of cryptographic keys in a cryptosystem. This includes dealing with the generation, exchange, storage, use, crypto-shredding (destruction) and replacement of keys. It includes cryptographic protocol design, k ...

necessary to use them securely. Each distinct pair of communicating parties must, ideally, share a different key, and perhaps for each ciphertext exchanged as well. The number of keys required increases as the square of the number of network members, which very quickly requires complex key management schemes to keep them all consistent and secret.
In a groundbreaking 1976 paper, Whitfield Diffie and Martin Hellman proposed the notion of ''public-key'' (also, more generally, called ''asymmetric key'') cryptography in which two different but mathematically related keys are used—a ''public'' key and a ''private'' key. A public key system is so constructed that calculation of one key (the 'private key') is computationally infeasible from the other (the 'public key'), even though they are necessarily related. Instead, both keys are generated secretly, as an interrelated pair. Ralph Merkle was working on similar ideas at the time and encountered publication delays, and Hellman has suggested that the term used should be Diffie–Hellman–Merkle aysmmetric key cryptography. The historian David Kahn described public-key cryptography as "the most revolutionary new concept in the field since polyalphabetic substitution emerged in the Renaissance".
In public-key cryptosystems, the public key may be freely distributed, while its paired private key must remain secret. In a public-key encryption system, the ''public key'' is used for encryption, while the ''private'' or ''secret key'' is used for decryption. While Diffie and Hellman could not find such a system, they showed that public-key cryptography was indeed possible by presenting the Diffie–Hellman key exchange
Diffie–Hellman key exchangeSynonyms of Diffie–Hellman key exchange include:
* Diffie–Hellman–Merkle key exchange
* Diffie–Hellman key agreement
* Diffie–Hellman key establishment
* Diffie–Hellman key negotiation
* Exponential key exc ...

protocol, a solution that is now widely used in secure communications to allow two parties to secretly agree on a shared encryption key.
The X.509 standard defines the most commonly used format for public key certificates
In cryptography, a public key certificate, also known as a digital certificate or identity certificate, is an electronic document used to prove the validity of a public key. The certificate includes information about the key, information about th ...

.
Diffie and Hellman's publication sparked widespread academic efforts in finding a practical public-key encryption system. This race was finally won in 1978 by Ronald Rivest, Adi Shamir, and Len Adleman
Leonard Adleman (born December 31, 1945) is an American computer scientist. He is one of the creators of the RSA encryption algorithm, for which he received the 2002 Turing Award, often called the Nobel prize of Computer science. He is also k ...

, whose solution has since become known as the RSA algorithm.Previously released as an MIT "Technical Memo" in April 1977, and published in

Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lew ...

's ''Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...

'' Mathematical recreations column
The Diffie–Hellman and RSA algorithms, in addition to being the first publicly known examples of high-quality public-key algorithms, have been among the most widely used. Other asymmetric-key algorithms include the Cramer–Shoup cryptosystem The Cramer–Shoup system is an asymmetric key encryption algorithm, and was the first efficient scheme proven to be secure against adaptive chosen ciphertext attack using standard cryptographic assumptions. Its security is based on the computationa ...

, ElGamal encryption, and various elliptic curve techniques.
A document published in 1997 by the Government Communications Headquarters (GCHQ
Government Communications Headquarters, commonly known as GCHQ, is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance (IA) to the government and armed forces of the Un ...

), a British intelligence organization, revealed that cryptographers at GCHQ had anticipated several academic developments. Reportedly, around 1970, James H. Ellis had conceived the principles of asymmetric key cryptography. In 1973, Clifford Cocks invented a solution that was very similar in design rationale to RSA. In 1974, Malcolm J. Williamson is claimed to have developed the Diffie–Hellman key exchange.
Public-key cryptography is also used for implementing digital signature
A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient very high confidence that the message was created b ...

schemes. A digital signature is reminiscent of an ordinary signature
A signature (; from la, signare, "to sign") is a handwritten (and often stylized) depiction of someone's name, nickname, or even a simple "X" or other mark that a person writes on documents as a proof of identity and intent. The writer of a ...

; they both have the characteristic of being easy for a user to produce, but difficult for anyone else to forge
A forge is a type of hearth used for heating metals, or the workplace (smithy) where such a hearth is located. The forge is used by the smith to heat a piece of metal to a temperature at which it becomes easier to shape by forging, or to th ...

. Digital signatures can also be permanently tied to the content of the message being signed; they cannot then be 'moved' from one document to another, for any attempt will be detectable. In digital signature schemes, there are two algorithms: one for ''signing'', in which a secret key is used to process the message (or a hash of the message, or both), and one for ''verification'', in which the matching public key is used with the message to check the validity of the signature. RSA and DSA are two of the most popular digital signature schemes. Digital signatures are central to the operation of public key infrastructure
A public key infrastructure (PKI) is a set of roles, policies, hardware, software and procedures needed to create, manage, distribute, use, store and revoke digital certificates and manage public-key encryption. The purpose of a PKI is to facilit ...

s and many network security schemes (e.g., SSL/TLS, many VPNs, etc.).
Public-key algorithms are most often based on the computational complexity
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) ...

of "hard" problems, often from number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

. For example, the hardness of RSA is related to the integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization.
When the numbers are su ...

problem, while Diffie–Hellman and DSA are related to the discrete logarithm
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b ...

problem. The security of elliptic curve cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide ...

is based on number theoretic problems involving elliptic curve
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

s. Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular
Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a s ...

multiplication and exponentiation, which are much more computationally expensive than the techniques used in most block ciphers, especially with typical key sizes. As a result, public-key cryptosystems are commonly hybrid cryptosystems, in which a fast high-quality symmetric-key encryption algorithm is used for the message itself, while the relevant symmetric key is sent with the message, but encrypted using a public-key algorithm. Similarly, hybrid signature schemes are often used, in which a cryptographic hash function is computed, and only the resulting hash is digitally signed.
Cryptographic hash functions

Cryptographic hash functions are cryptographic algorithms that generate and use keys to encrypt data, and such functions may be viewed as keys themselves. They take a message of any length as input, and output a short, fixed-length hash, which can be used in (for example) a digital signature. For good hash functions, an attacker cannot find two messages that produce the same hash. MD4 is a long-used hash function that is now broken; MD5, a strengthened variant of MD4, is also widely used but broken in practice. The USNational Security Agency
The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collectio ...

developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1
In cryptography, SHA-1 (Secure Hash Algorithm 1) is a cryptographically broken but still widely used hash function which takes an input and produces a 160-bit (20-byte) hash value known as a message digest – typically rendered as 40 hexadecim ...

is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. They are built using the Merkle–Damgård construction, from a one-way compressi ...

family improves on SHA-1, but is vulnerable to clashes as of 2011; and the US standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness of NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...

's overall hash algorithm toolkit."Thus, a hash function design competition was meant to select a new U.S. national standard, to be called

SHA-3
SHA-3 (Secure Hash Algorithm 3) is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August 5, 2015. Although part of the same series of standards, SHA-3 is internally different from the MD5-like struct ...

, by 2012. The competition ended on October 2, 2012, when the NIST announced that Keccak would be the new SHA-3 hash algorithm. Unlike block and stream ciphers that are invertible, cryptographic hash functions produce a hashed output that cannot be used to retrieve the original input data. Cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security.
Cryptanalysis

The goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion. It is a common misconception that every encryption method can be broken. In connection with his WWII work atBell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984),
then AT&T Bell Laboratories (1984–1996)
and Bell Labs Innovations (1996–2007),
is an American industrial research and scientific development company owned by mul ...

, Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory".
As a 21-year-old master's degree student at the Massachusetts Inst ...

proved that the random
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual rando ...

, never reused, kept secret from all possible attackers, and of equal or greater length than the message. Most cipher
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 i ...

s, apart from the one-time pad, can be broken with enough computational effort by brute force attack, but the amount of effort needed may be exponentially dependent on the key size, as compared to the effort needed to make use of the cipher. In such cases, effective security could be achieved if it is proven that the effort required (i.e., "work factor", in Shannon's terms) is beyond the ability of any adversary. This means it must be shown that no efficient method (as opposed to the time-consuming brute force method) can be found to break the cipher. Since no such proof has been found to date, the one-time-pad remains the only theoretically unbreakable cipher. Although well-implemented one-time-pad encryption cannot be broken, traffic analysis is still possible.
There are a wide variety of cryptanalytic attacks, and they can be classified in any of several ways. A common distinction turns on what Eve (an attacker) knows and what capabilities are available. In a ciphertext-only attack, Eve has access only to the ciphertext (good modern cryptosystems are usually effectively immune to ciphertext-only attacks). In a known-plaintext attack, Eve has access to a ciphertext and its corresponding plaintext (or to many such pairs). In a chosen-plaintext attack
A chosen-plaintext attack (CPA) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts.Ross Anderson, ''Security Engineering: A Guide to Building Dependable Distributed Systems''. ...

, Eve may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example is gardening
Gardening is the practice of growing and cultivating plants as part of horticulture. In gardens, ornamental plants are often grown for their flowers, foliage, or overall appearance; useful plants, such as root vegetables, leaf vegetables, f ...

, used by the British during WWII. In a chosen-ciphertext attack, Eve may be able to ''choose'' ciphertexts and learn their corresponding plaintexts. Finally in a man-in-the-middle attack Eve gets in between Alice (the sender) and Bob (the recipient), accesses and modifies the traffic and then forwards it to the recipient. Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of the protocols involved).
Cryptanalysis of symmetric-key ciphers typically involves looking for attacks against the block ciphers or stream ciphers that are more efficient than any attack that could be against a perfect cipher. For example, a simple brute force attack against DES requires one known plaintext and 2linear cryptanalysis
In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two m ...

attack against DES requires 2semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many pri ...

s and the difficulty of calculating discrete logarithm
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b ...

s, both of which are not yet proven to be solvable in polynomial time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...

(P) using only a classical Turing-complete computer. Much public-key cryptanalysis concerns designing algorithms in P that can solve these problems, or using other technologies, such as quantum computers. For instance, the best-known algorithms for solving the elliptic curve-based version of discrete logarithm are much more time-consuming than the best-known algorithms for factoring, at least for problems of more or less equivalent size. Thus, to achieve an equivalent strength of encryption, techniques that depend upon the difficulty of factoring large composite numbers, such as the RSA cryptosystem, require larger keys than elliptic curve techniques. For this reason, public-key cryptosystems based on elliptic curves have become popular since their invention in the mid-1990s.
While pure cryptanalysis uses weaknesses in the algorithms themselves, other attacks on cryptosystems are based on actual use of the algorithms in real devices, and are called '' side-channel attacks''. If a cryptanalyst has access to, for example, the amount of time the device took to encrypt a number of plaintexts or report an error in a password or PIN character, he may be able to use a timing attack
In cryptography, a timing attack is a side-channel attack in which the attacker attempts to compromise a cryptosystem by analyzing the time taken to execute cryptographic algorithms. Every logical operation in a computer takes time to execute, and ...

to break a cipher that is otherwise resistant to analysis. An attacker might also study the pattern and length of messages to derive valuable information; this is known as traffic analysis and can be quite useful to an alert adversary. Poor administration of a cryptosystem, such as permitting too short keys, will make any system vulnerable, regardless of other virtues. Social engineering and other attacks against humans (e.g., bribery
Bribery is the offering, giving, receiving, or soliciting of any item of value to influence the actions of an official, or other person, in charge of a public or legal duty. With regard to governmental operations, essentially, bribery is "Corru ...

, extortion
Extortion is the practice of obtaining benefit through coercion. In most jurisdictions it is likely to constitute a criminal offence; the bulk of this article deals with such cases. Robbery is the simplest and most common form of extortion, ...

, blackmail
Blackmail is an act of coercion using the threat of revealing or publicizing either substantially true or false information about a person or people unless certain demands are met. It is often damaging information, and it may be revealed to fa ...

, espionage, torture
Torture is the deliberate infliction of severe pain or suffering on a person for reasons such as punishment, extracting a confession, interrogation for information, or intimidating third parties. Some definitions are restricted to acts c ...

, ...) are usually employed due to being more cost-effective and feasible to perform in a reasonable amount of time compared to pure cryptanalysis by a high margin.
Cryptographic primitives

Much of the theoretical work in cryptography concerns cryptographic ''primitives''—algorithms with basic cryptographic properties—and their relationship to other cryptographic problems. More complicated cryptographic tools are then built from these basic primitives. These primitives provide fundamental properties, which are used to develop more complex tools called ''cryptosystems'' or ''cryptographic protocols'', which guarantee one or more high-level security properties. Note, however, that the distinction between cryptographic ''primitives'' and cryptosystems, is quite arbitrary; for example, the RSA algorithm is sometimes considered a cryptosystem, and sometimes a primitive. Typical examples of cryptographic primitives include pseudorandom functions, one-way functions, etc.Cryptosystems

One or more cryptographic primitives are often used to develop a more complex algorithm, called a cryptographic system, or ''cryptosystem''. Cryptosystems (e.g., El-Gamal encryption) are designed to provide particular functionality (e.g., public key encryption) while guaranteeing certain security properties (e.g., chosen-plaintext attack (CPA) security in the random oracle model). Cryptosystems use the properties of the underlying cryptographic primitives to support the system's security properties. As the distinction between primitives and cryptosystems is somewhat arbitrary, a sophisticated cryptosystem can be derived from a combination of several more primitive cryptosystems. In many cases, the cryptosystem's structure involves back and forth communication among two or more parties in space (e.g., between the sender of a secure message and its receiver) or across time (e.g., cryptographically protectedbackup
In information technology, a backup, or data backup is a copy of computer data taken and stored elsewhere so that it may be used to restore the original after a data loss event. The verb form, referring to the process of doing so, is "back up", ...

data). Such cryptosystems are sometimes called ''cryptographic protocol
A security protocol (cryptographic protocol or encryption protocol) is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods, often as sequences of cryptographic primitives. A protocol describ ...

s''.
Some widely known cryptosystems include RSA, Schnorr signature, ElGamal encryption, and Pretty Good Privacy (PGP). More complex cryptosystems include electronic cash systems, signcryption In cryptography, signcryption is a public-key primitive that simultaneously performs the functions of both digital signature and encryption.
Encryption and digital signature are two fundamental cryptographic tools that can guarantee the confident ...

systems, etc. Some more 'theoretical' cryptosystems include interactive proof system
In computational complexity theory, an interactive proof system is an abstract machine that models computation as the exchange of messages between two parties: a ''prover'' and a ''verifier''. The parties interact by exchanging messages in order t ...

s, (like zero-knowledge proof
In cryptography, a zero-knowledge proof or zero-knowledge protocol is a method by which one party (the prover) can prove to another party (the verifier) that a given statement is true while the prover avoids conveying any additional information ...

s), systems for secret sharing, etc.
Lightweight cryptography

Lightweight cryptography (LWC) concerns cryptographic algorithms developed for a strictly constrained environment. The growth of Internet of Things (IoT) has spiked research into the development of lightweight algorithms that are better suited for the environment. An IoT environment requires strict constraints on power consumption, processing power, and security. Algorithms such asPRESENT
The present (or here'' and ''now) is the time that is associated with the events perceived directly and in the first time, not as a recollection (perceived more than once) or a speculation (predicted, hypothesis, uncertain). It is a period of ...

, AES, and SPECK are examples of the many LWC algorithms that have been developed to achieve the standard set by the National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...

.
Applications

General

Cryptography is widely used on the internet to help protect user-data and prevent eavesdropping. To ensure secrecy during transmission, many systems use private key cryptography to protect transmitted information. With public-key systems, one can maintain secrecy without a master key or a large number of keys. But, some algorithms likeBitlocker
BitLocker is a full volume encryption feature included with Microsoft Windows versions starting with Windows Vista. It is designed to protect data by providing encryption for entire volumes. By default, it uses the AES encryption algorithm in ...

and Veracrypt are generally not private-public key cryptography. Such as Veracrypt, it uses a password hash to generate the single private key. However, it can be configured to run in public-private key systems. The C++ opensource encryption library OpenSSL provides free and opensource encryption software and tools. The most commonly used encryption cipher suit is AES, as it has hardware acceleration for all x86
x86 (also known as 80x86 or the 8086 family) is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel based on the Intel 8086 microprocessor and its 8088 variant. The 8086 was introd ...

based processors that has AES-NI
An Advanced Encryption Standard instruction set is now integrated into many processors. The purpose of the instruction set is to improve the speed and security of applications performing encryption and decryption using Advanced Encryption Standard ...

. A close contender is ChaCha20-Poly1305
ChaCha20-Poly1305 is an authenticated encryption with additional data (AEAD) algorithm, that combines the ChaCha20 stream cipher with the Poly1305 message authentication code. Its usage in IETF protocols is standardized in RFC 8439. It has fast s ...

, which is a stream cipher
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 ...

, however it is commonly used for mobile devices as they are ARM based which does not feature AES-NI instruction set extension.
Cybersecurity

Cryptography can be used to secure communications by encrypting them. Websites use encryption viaHTTPS
Hypertext Transfer Protocol Secure (HTTPS) is an extension of the Hypertext Transfer Protocol (HTTP). It is used for secure communication over a computer network, and is widely used on the Internet. In HTTPS, the communication protocol is enc ...

. "End-to-end" encryption, where only sender and receiver can read messages, is implemented for email in Pretty Good Privacy and for secure messaging in general in WhatsApp
WhatsApp (also called WhatsApp Messenger) is an internationally available freeware, cross-platform, centralized instant messaging (IM) and voice-over-IP (VoIP) service owned by American company Meta Platforms (formerly Facebook). It allows use ...

, Signal
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing' ...

and Telegram.
Operating systems use encryption to keep passwords secret, conceal parts of the system, and ensure that software updates are truly from the system maker. Instead of storing plaintext passwords, computer systems store hashes thereof; then, when a user logs in, the system passes the given password through a cryptographic hash function
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography:
* the probability of a particular n-bit output re ...

and compares it to the hashed value on file. In this manner, neither the system nor an attacker has at any point access to the password in plaintext.
Encryption is sometimes used to encrypt one's entire drive. For example, University College London has implemented BitLocker
BitLocker is a full volume encryption feature included with Microsoft Windows versions starting with Windows Vista. It is designed to protect data by providing encryption for entire volumes. By default, it uses the AES encryption algorithm in ...

(a program by Microsoft) to render drive data opaque without users logging in.
Cryptocurrencies and cryptoeconomics

Cryptographic techniques enablecryptocurrency
A cryptocurrency, crypto-currency, or crypto is a digital currency designed to work as a medium of exchange through a computer network that is not reliant on any central authority, such as a government or bank, to uphold or maintain it. It ...

technologies, such as distributed ledger technologies (e.g., blockchains), which finance cryptoeconomics applications such as decentralized finance (DeFi). Key cryptographic techniques that enable cryptocurrencies and cryptoeconomics include, but are not limited to: cryptographic keys, cryptographic hash functions, asymmetric (public key) encryption, Multi-Factor Authentication (MFA), End-to-End Encryption (E2EE), and Zero Knowledge Proofs (ZKP).
Legal issues

Prohibitions

Cryptography has long been of interest to intelligence gathering andlaw enforcement agencies
A law enforcement agency (LEA) is any government agency responsible for the law enforcement, enforcement of the laws.
Jurisdiction
LEAs which have their ability to apply their powers restricted in some way are said to operate within a juris ...

. Secret communications may be criminal or even treason
Treason is the crime of attacking a state authority to which one owes allegiance. This typically includes acts such as participating in a war against one's native country, attempting to overthrow its government, spying on its military, its diplo ...

ous . Because of its facilitation of privacy
Privacy (, ) is the ability of an individual or group to seclude themselves or information about themselves, and thereby express themselves selectively.
The domain of privacy partially overlaps with security, which can include the concepts of ...

, and the diminution of privacy attendant on its prohibition, cryptography is also of considerable interest to civil rights supporters. Accordingly, there has been a history of controversial legal issues surrounding cryptography, especially since the advent of inexpensive computers has made widespread access to high-quality cryptography possible.
In some countries, even the domestic use of cryptography is, or has been, restricted. Until 1999, France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan area e ...

significantly restricted the use of cryptography domestically, though it has since relaxed many of these rules. In China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and ...

and Iran
Iran, officially the Islamic Republic of Iran, and also called Persia, is a country located in Western Asia. It is bordered by Iraq and Turkey to the west, by Azerbaijan and Armenia to the northwest, by the Caspian Sea and Tur ...

, a license is still required to use cryptography. Many countries have tight restrictions on the use of cryptography. Among the more restrictive are laws in Belarus
Belarus,, , ; alternatively and formerly known as Byelorussia (from Russian ). officially the Republic of Belarus,; rus, Республика Беларусь, Respublika Belarus. is a landlocked country in Eastern Europe. It is bordered by ...

, Kazakhstan, Mongolia
Mongolia; Mongolian script: , , ; lit. "Mongol Nation" or "State of Mongolia" () is a landlocked country in East Asia, bordered by Russia to the north and China to the south. It covers an area of , with a population of just 3.3 million, m ...

, Pakistan, Singapore, Tunisia, and Vietnam
Vietnam or Viet Nam ( vi, Việt Nam, ), officially the Socialist Republic of Vietnam,., group="n" is a country in Southeast Asia, at the eastern edge of mainland Southeast Asia, with an area of and population of 96 million, making it ...

.
In the United States
The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 states, a federal district, five major unincorporated territorie ...

, cryptography is legal for domestic use, but there has been much conflict over legal issues related to cryptography. One particularly important issue has been the export of cryptography and cryptographic software and hardware. Probably because of the importance of cryptanalysis in World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

and an expectation that cryptography would continue to be important for national security, many Western governments have, at some point, strictly regulated export of cryptography. After World War II, it was illegal in the US to sell or distribute encryption technology overseas; in fact, encryption was designated as auxiliary military equipment and put on the United States Munitions List.Until the development of the

personal computer
A personal computer (PC) is a multi-purpose microcomputer whose size, capabilities, and price make it feasible for individual use. Personal computers are intended to be operated directly by an end user, rather than by a computer expert or te ...

, asymmetric key algorithms (i.e., public key techniques), and the Internet, this was not especially problematic. However, as the Internet grew and computers became more widely available, high-quality encryption techniques became well known around the globe.
Export controls

In the 1990s, there were several challenges to US export regulation of cryptography. After thesource code
In computing, source code, or simply code, is any collection of code, with or without comments, written using a human-readable programming language, usually as plain text. The source code of a program is specially designed to facilitate the ...

for Philip Zimmermann's Pretty Good Privacy (PGP) encryption program found its way onto the Internet in June 1991, a complaint by RSA Security
RSA Security LLC, formerly RSA Security, Inc. and doing business as RSA, is an American computer and network security company with a focus on encryption and encryption standards. RSA was named after the initials of its co-founders, Ron Rivest ...

(then called RSA Data Security, Inc.) resulted in a lengthy criminal investigation of Zimmermann by the US Customs Service and the FBI
The Federal Bureau of Investigation (FBI) is the domestic intelligence and security service of the United States and its principal federal law enforcement agency. Operating under the jurisdiction of the United States Department of Justice, ...

, though no charges were ever filed. Daniel J. Bernstein, then a graduate student at UC Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant uni ...

, brought a lawsuit against the US government challenging some aspects of the restrictions based on free speech
Freedom of speech is a principle that supports the freedom of an individual or a community to articulate their opinions and ideas without fear of retaliation, censorship, or legal sanction. The right to freedom of expression has been recogni ...

grounds. The 1995 case '' Bernstein v. United States'' ultimately resulted in a 1999 decision that printed source code for cryptographic algorithms and systems was protected as free speech
Freedom of speech is a principle that supports the freedom of an individual or a community to articulate their opinions and ideas without fear of retaliation, censorship, or legal sanction. The right to freedom of expression has been recogni ...

by the United States Constitution.
In 1996, thirty-nine countries signed the Wassenaar Arrangement
The Wassenaar Arrangement on Export Controls for Conventional Arms and Dual-Use Goods and Technologies is a multilateral export control regime (MECR) with 42 participating states including many former Comecon (Warsaw Pact) countries established ...

, an arms control treaty that deals with the export of arms and "dual-use" technologies such as cryptography. The treaty stipulated that the use of cryptography with short key-lengths (56-bit for symmetric encryption, 512-bit for RSA) would no longer be export-controlled. Cryptography exports from the US became less strictly regulated as a consequence of a major relaxation in 2000; there are no longer very many restrictions on key sizes in US- exported mass-market software. Since this relaxation in US export restrictions, and because most personal computers connected to the Internet include US-sourced web browser
A web browser is application software for accessing websites. When a user requests a web page from a particular website, the browser retrieves its files from a web server and then displays the page on the user's screen. Browsers are used on ...

s such as Firefox
Mozilla Firefox, or simply Firefox, is a free and open-source web browser developed by the Mozilla Foundation and its subsidiary, the Mozilla Corporation. It uses the Gecko rendering engine to display web pages, which implements current and ...

or Internet Explorer
Internet Explorer (formerly Microsoft Internet Explorer and Windows Internet Explorer, commonly abbreviated IE or MSIE) is a series of graphical web browsers developed by Microsoft which was used in the Windows line of operating systems (in W ...

, almost every Internet user worldwide has potential access to quality cryptography via their browsers (e.g., via Transport Layer Security
Transport Layer Security (TLS) is a cryptographic protocol designed to provide communications security over a computer network. The protocol is widely used in applications such as email, instant messaging, and voice over IP, but its use in securi ...

). The Mozilla Thunderbird
Mozilla Thunderbird is a free and open-source cross-platform email client, personal information manager, news client, RSS and chat client developed by the Mozilla Foundation and operated by subsidiary MZLA Technologies Corporation. The proje ...

and Microsoft Outlook
Microsoft Outlook is a personal information manager software system from Microsoft, available as a part of the Microsoft Office and Microsoft 365 software suites. Though primarily an email client, Outlook also includes such functions as ca ...

E-mail client
An email client, email reader or, more formally, message user agent (MUA) or mail user agent is a computer program used to access and manage a user's email.
A web application which provides message management, composition, and reception funct ...

programs similarly can transmit and receive emails via TLS, and can send and receive email encrypted with S/MIME S/MIME (Secure/Multipurpose Internet Mail Extensions) is a standard for public key encryption and signing of MIME data. S/MIME is on an IETF standards track and defined in a number of documents, most importantly . It was originally developed by ...

. Many Internet users don't realize that their basic application software contains such extensive cryptosystem
In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality ( encryption).
Typically, a cryptosystem consists of three algorithms: one for key generation, one f ...

s. These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally don't find it practical to do much to control distribution or use of cryptography of this quality, so even when such laws are in force, actual enforcement is often effectively impossible.
NSA involvement

Another contentious issue connected to cryptography in the United States is the influence of theNational Security Agency
The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collectio ...

on cipher development and policy. The NSA was involved with the design of DES during its development at IBM and its consideration by the National Bureau of Standards
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sc ...

as a possible Federal Standard for cryptography. DES was designed to be resistant to differential cryptanalysis
Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in information input can aff ...

, a powerful and general cryptanalytic technique known to the NSA and IBM, that became publicly known only when it was rediscovered in the late 1980s. According to Steven Levy
Steven Levy (born 1951) is an American journalist and Editor at Large for ''Wired'' who has written extensively for publications on computers, technology, cryptography, the internet, cybersecurity, and privacy. He is the author of the 1984 book ...

, IBM discovered differential cryptanalysis, but kept the technique secret at the NSA's request. The technique became publicly known only when Biham and Shamir re-discovered and announced it some years later. The entire affair illustrates the difficulty of determining what resources and knowledge an attacker might actually have.
Another instance of the NSA's involvement was the 1993 Clipper chip
The Clipper chip was a chipset that was developed and promoted by the United States National Security Agency (NSA) as an encryption device that secured "voice and data messages" with a built-in backdoor that was intended to "allow Federal, State, ...

affair, an encryption microchip intended to be part of the Capstone cryptography-control initiative. Clipper was widely criticized by cryptographers for two reasons. The cipher algorithm (called Skipjack) was then classified (declassified in 1998, long after the Clipper initiative lapsed). The classified cipher caused concerns that the NSA had deliberately made the cipher weak in order to assist its intelligence efforts. The whole initiative was also criticized based on its violation of Kerckhoffs's Principle, as the scheme included a special escrow key held by the government for use by law enforcement (i.e. wiretapping
Telephone tapping (also wire tapping or wiretapping in American English) is the monitoring of telephone and Internet-based conversations by a third party, often by covert means. The wire tap received its name because, historically, the monitori ...

).
Digital rights management

Cryptography is central to digital rights management (DRM), a group of techniques for technologically controlling use ofcopyright
A copyright is a type of intellectual property that gives its owner the exclusive right to copy, distribute, adapt, display, and perform a creative work, usually for a limited time. The creative work may be in a literary, artistic, education ...

ed material, being widely implemented and deployed at the behest of some copyright holders. In 1998, U.S. President Bill Clinton
William Jefferson Clinton (né Blythe III; born August 19, 1946) is an American politician who served as the 42nd president of the United States from 1993 to 2001. He previously served as governor of Arkansas from 1979 to 1981 and again ...

signed the Digital Millennium Copyright Act
The Digital Millennium Copyright Act (DMCA) is a 1998 United States copyright law that implements two 1996 treaties of the World Intellectual Property Organization (WIPO). It criminalizes production and dissemination of technology, devices, or ...

(DMCA), which criminalized all production, dissemination, and use of certain cryptanalytic techniques and technology (now known or later discovered); specifically, those that could be used to circumvent DRM technological schemes. This had a noticeable impact on the cryptography research community since an argument can be made that any cryptanalytic research violated the DMCA. Similar statutes have since been enacted in several countries and regions, including the implementation in the EU Copyright Directive. Similar restrictions are called for by treaties signed by World Intellectual Property Organization
The World Intellectual Property Organization (WIPO; french: link=no, Organisation mondiale de la propriété intellectuelle (OMPI)) is one of the 15 specialized agencies of the United Nations (UN). Pursuant to the 1967 Convention Establishin ...

member-states.
The United States Department of Justice and FBI
The Federal Bureau of Investigation (FBI) is the domestic intelligence and security service of the United States and its principal federal law enforcement agency. Operating under the jurisdiction of the United States Department of Justice, ...

have not enforced the DMCA as rigorously as had been feared by some, but the law, nonetheless, remains a controversial one. Niels Ferguson, a well-respected cryptography researcher, has publicly stated that he will not release some of his research into an Intel security design for fear of prosecution under the DMCA. Cryptologist Bruce Schneier
Bruce Schneier (; born January 15, 1963) is an American cryptographer, computer security professional, privacy specialist, and writer. Schneier is a Lecturer in Public Policy at the Harvard Kennedy School and a Fellow at the Berkman Klein Center ...

has argued that the DMCA encourages vendor lock-in
In economics, vendor lock-in, also known as proprietary lock-in or customer lock-in, makes a customer dependent on a vendor for products, unable to use another vendor without substantial switching costs.
The use of open standards and alternative ...

, while inhibiting actual measures toward cyber-security. Both Alan Cox (longtime Linux kernel
The Linux kernel is a free and open-source, monolithic, modular, multitasking, Unix-like operating system kernel. It was originally authored in 1991 by Linus Torvalds for his i386-based PC, and it was soon adopted as the kernel for the GNU op ...

developer) and Edward Felten (and some of his students at Princeton) have encountered problems related to the Act. Dmitry Sklyarov
''United States v. ElcomSoft and Dmitry Sklyarov'' was a 2001–2002 criminal case in which Dmitry Sklyarov and his employer ElcomSoft were charged with alleged violation of the DMCA. The case raised some concerns of civil rights and legal proces ...

was arrested during a visit to the US from Russia, and jailed for five months pending trial for alleged violations of the DMCA arising from work he had done in Russia, where the work was legal. In 2007, the cryptographic keys responsible for Blu-ray
The Blu-ray Disc (BD), often known simply as Blu-ray, is a digital optical disc data storage format. It was invented and developed in 2005 and released on June 20, 2006 worldwide. It is designed to supersede the DVD format, and capable of sto ...

and HD DVD
HD DVD (short for High Definition Digital Versatile Disc) is an obsolete high-density optical disc format for storing data and playback of high-definition video. Supported principally by Toshiba, HD DVD was envisioned to be the successor to the ...

content scrambling were discovered and released onto the Internet. In both cases, the Motion Picture Association of America
The Motion Picture Association (MPA) is an American trade association representing the five major film studios of the United States, as well as the video streaming service Netflix. Founded in 1922 as the Motion Picture Producers and Distribu ...

sent out numerous DMCA takedown notices, and there was a massive Internet backlash triggered by the perceived impact of such notices on fair use
Fair use is a doctrine in United States law that permits limited use of copyrighted material without having to first acquire permission from the copyright holder. Fair use is one of the limitations to copyright intended to balance the interests ...

and free speech
Freedom of speech is a principle that supports the freedom of an individual or a community to articulate their opinions and ideas without fear of retaliation, censorship, or legal sanction. The right to freedom of expression has been recogni ...

.
Forced disclosure of encryption keys

In the United Kingdom, the Regulation of Investigatory Powers Act gives UK police the powers to force suspects to decrypt files or hand over passwords that protect encryption keys. Failure to comply is an offense in its own right, punishable on conviction by a two-year jail sentence or up to five years in cases involving national security. Successful prosecutions have occurred under the Act; the first, in 2009, resulted in a term of 13 months' imprisonment. Similar forced disclosure laws in Australia, Finland, France, and India compel individual suspects under investigation to hand over encryption keys or passwords during a criminal investigation. In the United States, the federal criminal case of '' United States v. Fricosu'' addressed whether a search warrant can compel a person to reveal anencryption
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...

passphrase
A passphrase is a sequence of words or other text used to control access to a computer system, program or data. It is similar to a password in usage, but a passphrase is generally longer for added security. Passphrases are often used to control ...

or password. The Electronic Frontier Foundation
The Electronic Frontier Foundation (EFF) is an international non-profit digital rights group based in San Francisco, California. The foundation was formed on 10 July 1990 by John Gilmore, John Perry Barlow and Mitch Kapor to promote Internet ...

(EFF) argued that this is a violation of the protection from self-incrimination given by the Fifth Amendment. In 2012, the court ruled that under the All Writs Act, the defendant was required to produce an unencrypted hard drive for the court.
In many jurisdictions, the legal status of forced disclosure remains unclear.
The 2016 FBI–Apple encryption dispute
The FBI–Apple encryption dispute concerns whether and to what extent courts in the United States can compel manufacturers to assist in unlocking cell phones whose data are cryptographically protected. There is much debate over public acces ...

concerns the ability of courts in the United States to compel manufacturers' assistance in unlocking cell phones whose contents are cryptographically protected.
As a potential counter-measure to forced disclosure some cryptographic software supports plausible deniability, where the encrypted data is indistinguishable from unused random data (for example such as that of a drive which has been securely wiped).
See also

*Collision attack
In cryptography, a collision attack on a cryptographic hash tries to find two inputs producing the same hash value, i.e. a hash collision. This is in contrast to a preimage attack where a specific target hash value is specified.
There are rough ...

*
*
*
*
*
*
*
**
**
**
**
* Secure cryptoprocessor
*
* – first cryptography chart
* World Wide Web Consortium
The World Wide Web Consortium (W3C) is the main international standards organization for the World Wide Web. Founded in 1994 and led by Tim Berners-Lee, the consortium is made up of member organizations that maintain full-time staff working ...

's
References

Further reading

* * 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, . 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, . * Oded Goldreich''Foundations of Cryptography''

in two volumes, Cambridge University Press, 2001 and 2004. * ''Alvin's Secret Code'' by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis). *

Introduction to Modern Cryptography

' by Jonathan Katz and Yehuda Lindell. * Ibrahim A. Al-Kadi, "The Origins of Cryptology: the Arab Contributions," Cryptologia, vol. 16, no. 2 (April 1992), pp. 97–126.

Jan Pelzl

''Understanding Cryptography, A Textbook for Students and Practitioners''.

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. * , giving an overview of international law issues regarding cryptography. * ''Introduction to Modern Cryptography'' by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs

PDF download

* * Tenzer, Theo (2021): ''SUPER SECRETO – The Third Epoch of Cryptography: Multiple, exponential, quantum-secure and above all, simple and practical Encryption for Everyone'', Norderstedt, . * Johann-Christoph Woltag, 'Coded Communications (Encryption)' in Rüdiger Wolfrum (ed) ''Max Planck Encyclopedia of Public International Law'' (Oxford University Press 2009).

External links

* * *Cryptography Works - web information portal

Crypto Glossary and Dictionary of Technical Cryptography

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:

at the Library of Congress has early editions of works of seventeenth-century English literature, publications relating to cryptography. {{Authority control, state=expanded Applied mathematics Banking technology Formal sciences