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 cryptanalysis, cracked, but requires the use of a single-use pre-shared key that is no smaller than the message being sent. In this technique, a plaintext is paired ...

. 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 Exclusive or, XOR operation to each bit of the plaintext with each bit of the keystream.
Message authentication codes (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 Md5, 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 function, 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 developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1 is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2 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 National Institute of Standards and Technology, NIST's overall hash algorithm toolkit."

Thus, a NIST hash function competition, hash function design competition was meant to select a new U.S. national standard, to be called SHA-3, 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.

Previously released as an MIT "Technical Memo" in April 1977, and published in Martin Gardner's ''Scientific American'' 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, asymmetric-key algorithms include the Cramer–Shoup cryptosystem, ElGamal encryption, and various Elliptic curve cryptography, elliptic curve techniques. A document published in 1997 by the Government Communications Headquarters (GCHQ), 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

Thus, a NIST hash function competition, hash function design competition was meant to select a new U.S. national standard, to be called SHA-3, 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.

one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cryptanalysis, cracked, but requires the use of a single-use pre-shared key that is no smaller than the message being sent. In this technique, a plaintext is paired ...

cipher is unbreakable, provided the key material is truly Statistical randomness, random, never reused, kept secret from all possible attackers, and of equal or greater length than the message. Most ciphers, 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 exponential time, 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, Eve may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example is gardening (cryptanalysis), gardening, 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, 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 cryptographic protocol, 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 2^{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 linear cryptanalysis attack against DES requires 2^{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
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 arithmetic function, integer-valued functions. German mathematician Carl Frie ...

of semiprimes and the difficulty of calculating discrete logarithms, both of which are not yet proven to be solvable in P (complexity), polynomial time using only a classical Turing completeness, Turing-complete computer. Much public-key cryptanalysis concerns designing algorithms in P that can solve these problems, or using other technologies, such as Quantum computing, quantum computers. For instance, the best-known algorithms for solving the elliptic curve cryptography, 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, other things being equal, to achieve an equivalent strength of attack resistance, factoring-based encryption techniques must use 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 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 (security), Social engineering and other attacks against humans (e.g., bribery, extortion, blackmail,

Until the development of the personal computer, 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.

''Foundations of Cryptography''

in two volumes, Cambridge University Press, 2001 and 2004. *

' by Jonathan Katz and Yehuda Lindell. * ''Alvin's Secret Code'' by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis). * Ibrahim A. Al-Kadi, "The Origins of Cryptology: the Arab Contributions," Cryptologia, vol. 16, no. 2 (April 1992), pp. 97–126.

Christof Paar

Jan Pelzl

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

Springer, 2009. (Slides, online cryptography lectures and other information are available on the companion web site.) Very accessible introduction to practical cryptography for non-mathematicians. * ''Introduction to Modern Cryptography'' by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs

PDF download

* Johann-Christoph Woltag, 'Coded Communications (Encryption)' in Rüdiger Wolfrum (ed) ''Max Planck Encyclopedia of Public International Law'' (Oxford University Press 2009). * , giving an overview of international law issues regarding cryptography. * Jonathan Arbib & John Dwyer, ''Discrete Mathematics for Cryptography'', 1st Edition . *

Crypto Glossary and Dictionary of Technical Cryptography

NSA's CryptoKids

Overview and Applications of Cryptology

by the CrypTool Team; PDF; 3.8 MB. July 2008

A Course in Cryptography

by Raphael Pass & Abhi Shelat – offered at Cornell in the form of lecture notes. * For more on the use of cryptographic elements in fiction, see:

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

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

'', "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 Signals intelligence, interception. ...

in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols
Protocol may refer to:
Sociology and politics
* Protocol (politics)Protocol originally (in Late Middle English, c. 15th century) meant the minute or logbook taken at a meeting, upon which an agreement was based. The term now commonly refers to an a ...

that prevent third parties or the public from reading private messages; various aspects in information security #REDIRECT Information security
Information security, sometimes shortened to infosec, is the practice of protecting information by mitigating information risks. It is part of Risk management information systems, information risk management. It typi ...

such as data confidentiality
Confidentiality involves a set of rules or a promise usually executed through confidentiality agreements that limits access or places restrictions on certain types of information
Information is processed, organised and structured data. I ...

, data integrityData 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 term ...

, authentication
Authentication (from ''authentikos'', "real, genuine", from αὐθέντης ''authentes'', "author") is the act of proving an assertion, such as the identity
Identity may refer to:
Social sciences
* Identity (social science), person ...

, and non-repudiationNon-repudiation refers to a situation where a statement's author cannot successfully dispute its authorship or the validity of an associated contract
A contract is a legally binding document between at least two parties that defines and governs th ...

are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no general consensus abo ...

, computer science
Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application.
Computer science is the study of , , and . Computer science ...

, 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 la ...

, communication science
Communication studies or communication science is an academic discipline
An academic discipline or academic field is a subdivision of knowledge
Knowledge is a familiarity, awareness, or understanding of someone or something, such as fac ...

, and physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of eve ...

. Applications of cryptography include electronic commerce
E-commerce (electronic commerce) is the activity of electronically buying or selling of Product (business), products on online services or over the Internet. E-commerce draws on technologies such as mobile commerce, electronic funds transfer, sup ...

, chip-based payment cards, digital currencies
Digital currency (digital money, electronic money or electronic currency) is any currency, money, or money-like asset that is primarily managed, stored or exchanged on digital computer systems, especially over the internet. Types of digital cur ...

, , and military communications
Military communications or military signals involve all aspects of communication
Communication (from Latin
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin wa ...

.
Cryptography prior to the modern age was effectively synonymous with , converting information from a readable state to unintelligible nonsense
Nonsense is a communication
Communication (from Latin ''communicare'', meaning "to share") is the act of developing Semantics, meaning among Subject (philosophy), entities or Organization, groups through the use of sufficiently mutually under ...

. The sender of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature often uses the names Alice ("A") for the sender, Bob ("B") for the intended recipient, and Eve ("eavesdropper
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 ...

") for the adversary. Since the development of rotor cipher machines in World War I
World War I or the First World War, often abbreviated as WWI or WW1, was a global war originating in Europe that lasted from 28 July 1914 to 11 November 1918. Contemporaneously known as the Great War, the World War, and "The war t ...

and the advent of computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern computers can perform generic sets of operations known as Computer program, programs. These programs enable compu ...

s in World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a World war, global war that lasted from 1939 to 1945. It involved World War II by country, the vast majority of the world's countries—including all of the gr ...

, cryptography methods have become increasingly complex and its applications more varied.
Modern cryptography is heavily based on mathematical theory
A mathematical theory is a mathematical model
A mathematical model is a description of a system
A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole.
A system ...

and computer science practice; cryptographic algorithms
of an algorithm ( Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers ''a'' and ''b'' in locations named A and B. The algorithm proceeds by successive subtractions in two loops: IF the test B ≥ A yields "yes" ...

are designed around computational hardness assumption
In computational complexity theory
Computational complexity theory focuses on classifying computational problems according to their resource usage, and relating these classes to each other. A computational problem is a task solved by a computer. A ...

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
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 arithmetic function, integer-valued functions. German mathematician Carl Frie ...

algorithms) and faster computing technology require these designs to be continually reevaluated, and if necessary, adapted. There exist information-theoretically secureInformation-theoretic security is security of a cryptosystem which derives purely from information theory; the system cannot be broken even if the adversary (cryptography), adversary has unlimited computing power. The cryptosystem is considered crypt ...

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 cryptanalysis, cracked, but requires the use of a single-use pre-shared key that is no smaller than the message being sent. In this technique, a plaintext is paired ...

, but these schemes are much more difficult to use in practice than the best theoretically breakable but computationally secure schemes.
The growth of cryptographic technology has raised a number of legal issues in the Information Age#REDIRECT Information Age
The Information Age (also known as the Computer Age, Digital Age, or New Media Age) is a historical periodHuman history is commonly divided into three main Era, eras — Ancient history, Ancient, Post-classical history, ...

. Cryptography's potential for use as a tool for espionage
Espionage or spying is the act of obtaining secret
Secrecy is the practice of hiding information
Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both it ...

and sedition
Sedition is overt conduct, such as speech
Speech is human vocal communication using language. Each language uses Phonetics, phonetic combinations of vowel and consonant sounds that form the sound of its words (that is, all English words sound ...

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) tools or technological protection measures (TPM) are a set of access control
In the fields of physical security and information security, access control (AC) is the selective restriction of access to a place o ...

and copyright infringement
Copyright infringement (at times referred to as piracy) is the use of works
Works may refer to:
People
* Caddy Works
Pierce "Caddy" Works (January 2, 1896 – July 19, 1982) was an American basketball and baseball coach. He was the head ba ...

disputes in regard to digital media
Digital media means any that operate with the use of any of various encoded formats. Digital media can be created, viewed, distributed, modified, listened to, and preserved on a s device. ''Digital'' can be defined as any data represented by a ...

.
Terminology

The first use of the term " cryptograph" (as opposed to "") dates back to the 19th century—originating from "The Gold-Bug
"The Gold-Bug" is a short story by Edgar Allan Poe published in 1843. The plot follows William Legrand, who was bitten by a gold-colored bug. His servant Jupiter fears that Legrand is going insane and goes to Legrand's friend, an unnamed narrator, ...

," a story by Edgar Allan Poe
Edgar Allan Poe (; born Edgar Poe; January 19, 1809 – October 7, 1849) was an American writer, poet, editor, and literary criticism, literary critic. Poe is best known for his poetry and short stories, particularly his tales of mystery and ...

.
Until modern times, cryptography referred almost exclusively to "encryption", which is the process of converting ordinary information (called plaintext) into unintelligible form (called ciphertext). Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A (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
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in t ...

" is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, and the encryption and decryption algorithms which correspond to each key. Keys are important both formally and in actual practice, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless (or even counter-productive) for most purposes.
Historically, ciphers were often used directly for encryption or decryption without additional procedures such as authentication
Authentication (from ''authentikos'', "real, genuine", from αὐθέντης ''authentes'', "author") is the act of proving an assertion, such as the identity
Identity may refer to:
Social sciences
* Identity (social science), person ...

or integrity checks. There are, generally, two kinds of cryptosystems: symmetric and asymmetric. In symmetric systems, the only ones known until the 1970s, the same key (the secret key) is used to encrypt and decrypt a message. Data manipulation in symmetric systems is faster than asymmetric systems, in part because they generally use shorter key lengths. Asymmetric systems use a " public key" to encrypt a message and a related "private key" to decrypt it. The use of asymmetric systems enhances the security of communication, largely because the relation between the two keys is very hard to discover. Examples of asymmetric systems include RSA (Rivest–Shamir–Adleman
RSA (Rivest–Shamir–Adleman) is a public-key cryptography, public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonar ...

), and 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 Finite field, Galois fields) ...

). Quality 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
In cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', ...

) 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 applications, it has been highly influential in the advancement of cryptograph ...

). Not very high quality symmetric algorithms include the assorted children's language tangling schemes such as Pig Latin
Pig Latin (or, in Pig Latin, "Igpay Atinlay") is a language game or argot in which English language, English words are altered, usually by adding a fabricated suffix or by moving the Syllable#Onset, onset or initial consonant or consonant cluste ...

or other cantCANT may refer to:
*CANT, a solo project from Grizzly Bear bass guitarist and producer, Chris Taylor (Grizzly Bear musician), Chris Taylor.
*Cantieri Aeronautici e Navali Triestini, an aviation company
See also
* Cant (disambiguation)
{{dab ...

, and indeed effectively all cryptographic schemes, however seriously intended, from any source prior to the invention of the one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cryptanalysis, cracked, but requires the use of a single-use pre-shared key that is no smaller than the message being sent. In this technique, a plaintext is paired ...

early in the 20th century.
In colloquial
Colloquialism or colloquial language is the style (sociolinguistics), linguistic style used for casual (informal) communication. It is the most common functional style of speech, the idiom normally employed in conversation and other informal conte ...

use, the term " code" is often used to mean any method of encryption or concealment of meaning. However, in cryptography, code has a more specific meaning: the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a code word (for example, "wallaby" replaces "attack at dawn"). A cypher, in contrast, is a scheme for changing or substituting an element below such a level (a letter, or a syllable or a pair of letters, etc.) in order to produce a cyphertext.
Cryptanalysis
cipher machine
Cryptanalysis (from the Greek language, Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information system
An information system (IS) is a formal, sociotechnical
Sociotechnical ...

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
Oded Goldreich ( he, עודד גולדרייך; b. 1957) is a professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most c ...

, ''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 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 of cryptography and cryptanalysis

Before the modern era, cryptography focused on message confidentiality (i.e., encryption)—conversion ofmessages
A message is a discrete unit of communication
Communication (from Latin ''communicare'', meaning "to share") is the act of developing Semantics, meaning among Subject (philosophy), entities or Organization, groups through the use of suffi ...

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 controve ...

in communications
Communication (from Latin ''communicare'', meaning "to share" or "to be in relation with") is "an apparent answer to the painful divisions between self and other, private and public, and inner thought and outer world." As this definition indica ...

, such as those of , military leaders, and diplomat
A diplomat (from grc, δίπλωμα; romanized
Romanization or romanisation, in linguistics
Linguistics is the scientific study of language
A language is a structured system of communication used by humans, including speech ( ...

s. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication
Authentication (from ''authentikos'', "real, genuine", from αὐθέντης ''authentes'', "author") is the act of proving an assertion, such as the identity
Identity may refer to:
Social sciences
* Identity (social science), person ...

, 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 strong reason to believe that the message was ...

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

The main classical cipher types aretransposition cipher
In cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia
''-logy'' is a suffix
In linguistics
Linguistics is the science, scientific study of lan ...

s, which rearrange the order of letters in a message (e.g., 'hello world' becomes 'ehlol owrdl' in a trivially simple rearrangement scheme), and substitution cipher
In cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in ...

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
The Latin alphabet or Roman alphabet is the collection of letters originally used by the ancient Romans
In historiography
Historiography is the study of the methods of historian
( 484– 425 BC) was a Greek historian who lived ...

). Simple versions of either have never offered much confidentiality from enterprising opponents. An early substitution cipher was the Caesar cipher
In cryptography, a Caesar cipher, also known as Caesar's cipher, the shift cipher, Caesar's code or Caesar shift, is one of the simplest and most widely known encryption techniques. It is a type of substitution cipher in which each letter in the ...

, in which each letter in the plaintext was replaced by a letter some fixed number of positions further down the alphabet. Suetonius
Gaius Suetonius Tranquillus (), commonly known as Suetonius ( ; c. AD 69 – after AD 122), was a Roman historianRoman historiography stretches back to at least the 3rd century BC and was indebted to earlier Greek historiography. The Romans ...

reports that Julius Caesar
Gaius Julius Caesar (; 12 July 100 BC – 15 March 44 BC) was a Roman
Roman or Romans most often refers to:
*, the capital city of Italy
*, Roman civilization from 8th century BC to 5th century AD
*, the people of ancient Rome
*', shortened ...

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
The Hebrew alphabet ( he, wikt:אלפבית, אָלֶף־בֵּית עִבְרִי, ), known variously ...

is an example of an early Hebrew cipher. The earliest known use of cryptography is some carved ciphertext on stone in Egypt
Egypt ( ar, مِصر, Miṣr), officially the Arab Republic of Egypt, is a spanning the and the of . It is bordered by the to , the () and to , the to the east, to , and to . In the northeast, the , which is the northern arm of the R ...

(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
Doric or Dorian ( grc, Δωρισμός, Dōrismós) was an . Its variants were spoken in the southern and eastern as well as in , , , , , some islands in the southern and some cities on the south east coast of ...

n military). Steganography
Steganography ( ) is the practice of concealing a message within another message or a physical object. In computing/electronic contexts, a computer file, message, image, or video is concealed within another file, message, image, or video. The wor ...

(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, Ἡρόδοτος, Hēródotos, ; BC) was an ancient Greek
Ancient Greek includes the forms of the Greek language
Greek ( el, label=Modern Greek
Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), ge ...

, 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
300px, A coded letter from Peggy Shippen Arnold is interspersed with coded communication in Arnold's hand.
Invisible ink, also known as security ink or sympathetic ink, is a substance used for writing, which is invisible either on application or ...

, microdot
A microdot is text or an image substantially reduced in size to prevent detection by unintended recipients. Microdots are normally circular and around one millimetre in diameter but can be made into different shapes and sizes and made from various ...

s, and digital watermarkA digital watermark is a kind of marker covertly embedded in a noise-tolerant signal
In signal processing
Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio ...

s to conceal information.
In India, the 2000-year-old Kamasutra
The ''Kama Sutra'' (; sa, कामसूत्र, , ; ) is an ancient Indian Sanskrit
Sanskrit (, attributively , ''saṃskṛta-'', nominalization, nominally , ''saṃskṛtam'') is a classical language of South Asia belonging to th ...

of Vātsyāyana
Vātsyāyana is an ancient Indian philosopher, known for authoring the '' Kama Sutra''. He lived in India during the second or third century CE, probably in Pataliputra (modern day Patna).
He is not to be confused with Pakṣilasvāmin Vātsyā ...

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 (Middle Persian: 𐭠𐭩𐭥𐭠𐭭𐭱𐭲𐭥𐭩 ''Iran (word), Ērānshahr''), and called the Neo-Persian Empire by historians, was the last Persian Empire, Pe ...

, 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, ISO 233
The international standard
An international standard is a technical standard
A technical standard is an established norm (social), norm or requirement for a repeatable technica ...

, the first people to systematically document cryptanalytic methods. Al-Khalil
Hebron ( ar, الخليل أو الخليل الرحمن ; he, חֶבְרוֹן ) is a State of Palestine, Palestinian. city in the southern West Bank, south of Jerusalem. Nestled in the Judaean Mountains, it lies 930 meters (3,050 ft) Abo ...

(717–786) wrote the ''Book of Cryptographic Messages'', which contains the first use of permutations and combinations
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting
Counting is the process of determining the number of Element (math ...

to list all possible Arabic
Arabic (, ' or , ' or ) is a Semitic language
The Semitic languages are a branch of the Afroasiatic language family originating in the Middle East
The Middle East is a list of transcontinental countries, transcontinental region ...

words with and without vowels.
Ciphertexts produced by a classical cipher
In cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia
''-logy'' is a suffix in the English language, used with words originally adapted from Ancient Gree ...

(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 letter frequencies, frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers.
Frequency analy ...

, 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 prob ...

Al-Kindi
Abu 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
The Arabs (singular Arab ; singular ar, عَرَب ...

(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 solving, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together in a logical way, in order to arrive at the correct or fun solution of the puzzle. There ...

s (see cryptogram
A cryptogram is a type of puzzle that consists of a short piece of encrypted
In cryptography, encryption is the process of Code, encoding information. This process converts the original representation of the information, known as plaintext, i ...

). 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
cipher machine
Cryptanalysis (from the Greek language, Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information system
An information system (IS) is a formal, sociotechnical
Sociotechnical ...

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
Renaissance humanism was a revival in the study of classical antiquity, at first Italian Renaissance, in Italy and then spreading across Western Eu ...

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 , a wheel which implemented a partial realization of his invention. In the Vigenère cipher, a polyalphabetic cipher, encryption uses a ''key word'', which controls letter substitution depending on which letter of the key word is used. In the mid-19th century Charles Babbage showed that the Vigenère cipher was vulnerable to Kasiski examination, but this was first published about ten years later by Friedrich Kasiski.
Although frequency analysis can be a powerful and general technique against many ciphers, encryption has still often been effective in practice, as many a would-be cryptanalyst was unaware of the technique. Breaking a message without using frequency analysis essentially required knowledge of the cipher used and perhaps of the key involved, thus making espionage, bribery, burglary, defection, etc., more attractive approaches to the cryptanalytically uninformed. It was finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible nor practical safeguard of message security; in fact, it was further realized that any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary fully understands the cipher algorithm itself. Security of the key used should alone be sufficient for a good cipher to maintain confidentiality under an attack. This fundamental principle was first explicitly stated in 1883 by Auguste Kerckhoffs and is generally called Kerckhoffs's Principle; alternatively and more bluntly, it was restated by Claude Shannon, the inventor of information theory and the fundamentals of theoretical cryptography, as ''Shannon's Maxim''—'the enemy knows the system'.
Different physical devices and aids have been used to assist with ciphers. One of the earliest may have been the scytale of ancient Greece, a rod supposedly used by the Spartans as an aid for a transposition cipher. In medieval times, other aids were invented such as the grille (cryptography), cipher grille, which was also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's own cipher disk, Johannes Trithemius' tabula recta scheme, and Thomas Jefferson's Jefferson disk, 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. The ciphers implemented by better quality examples of these machine designs brought about a substantial increase in cryptanalytic difficulty after WWI.
Computer era

Prior to the early 20th century, cryptography was mainly concerned with language, linguistic and lexicographic code, lexicographic patterns. Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory, computational complexity theory, computational complexity, statistics, combinatorics, abstract algebra, number theory, and finite mathematics generally. Cryptography is also a branch of engineering, but an unusual one since it deals with active, intelligent, and malevolent opposition; other kinds of engineering (e.g., civil or chemical engineering) need deal only with neutral natural forces. There is also active research examining the relationship between cryptographic problems and quantum physics. Just as the development of digital computers and electronics helped in cryptanalysis, it made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this was new and significant. Computer use has thus supplanted linguistic cryptography, both for cipher design and cryptanalysis. Many computer ciphers can be characterized by their operation on binary numeral system, 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.Advent of modern cryptography

Cryptanalysis
cipher machine
Cryptanalysis (from the Greek language, Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information system
An information system (IS) is a formal, sociotechnical
Sociotechnical ...

of the new mechanical devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts at Bletchley Park during WWII spurred the development of more efficient means for carrying out repetitious tasks. This culminated in the development of the Colossus computer, Colossus, the world's first fully electronic, digital, computer programming, programmable computer, which assisted in the decryption of ciphers generated by the German Army's Lorenz SZ40/42 machine.
Extensive open academic research into cryptography is relatively recent; it began only in the mid-1970s. In recent times, IBM personnel designed the algorithm that became the Federal (i.e., US) Data Encryption Standard
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 applications, it has been highly influential in the advancement of cryptograph ...

; Whitfield Diffie and Martin Hellman published Diffie–Hellman key exchange, their key agreement algorithm; and the RSA (algorithm), RSA algorithm was published in Martin Gardner's ''Scientific American'' column. Since then, cryptography has become a widely used tool in communications, computer networks, and computer security generally.
Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are Computational complexity theory#Intractability, intractable, such as the integer factorization
In 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 arithmetic function, integer-valued functions. German mathematician Carl Frie ...

or the discrete logarithm problems, so there are deep connections with abstract mathematics. There are very few cryptosystems that are proven to be unconditionally secure. The one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cryptanalysis, cracked, but requires the use of a single-use pre-shared key that is no smaller than the message being sent. In this technique, a plaintext is paired ...

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 (cryptosystem), 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 attacks, so when specifying key lengths, the required key lengths are similarly advancing. The potential effects of quantum computing are already being considered by some cryptographic system designers developing post-quantum cryptography; the announced imminence of small implementations of these machines may be making the need for preemptive caution rather more than merely speculative.
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 applications, it has been highly influential in the advancement of cryptograph ...

(DES) and the Advanced Encryption Standard
The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption
In cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', ...

(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 Shell, 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.
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 Thus, a NIST hash function competition, hash function design competition was meant to select a new U.S. national standard, to be called SHA-3, 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 the key management 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 (algebra), 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 protocol, a solution that is now widely used in secure communications to allow two parties to secretly agree on a symmetric-key algorithm, shared encryption key. The X.509 standard defines the most commonly used format for public key certificates. 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, whose solution has since become known as the RSA (algorithm), RSA algorithm.Previously released as an MIT "Technical Memo" in April 1977, and published in Martin Gardner's ''Scientific American'' 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, asymmetric-key algorithms include the Cramer–Shoup cryptosystem, ElGamal encryption, and various Elliptic curve cryptography, elliptic curve techniques. A document published in 1997 by the Government Communications Headquarters (GCHQ), 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 strong reason to believe that the message was ...

schemes. A digital signature is reminiscent of an ordinary signature; they both have the characteristic of being easy for a user to produce, but difficult for anyone else to forgery, forge. 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 Digital Signature Algorithm, DSA are two of the most popular digital signature schemes. Digital signatures are central to the operation of public key infrastructures and many network security schemes (e.g., Transport Layer Security, SSL/TLS, many VPNs, etc.).
Public-key algorithms are most often based on the computational complexity theory, computational complexity of "hard" problems, often from number theory. For example, the hardness of RSA is related to the integer factorization
In 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 arithmetic function, integer-valued functions. German mathematician Carl Frie ...

problem, while Diffie–Hellman and DSA are related to the discrete logarithm problem. The security of elliptic curve cryptography is based on number theoretic problems involving elliptic curves. Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular arithmetic, modular 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 are ways to generate and utilize specific keys to encrypt data for either symmetric or asymmetric encryption, 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 function, 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 developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1 is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2 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 National Institute of Standards and Technology, NIST's overall hash algorithm toolkit."Thus, a NIST hash function competition, hash function design competition was meant to select a new U.S. national standard, to be called SHA-3, 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 at Bell Labs, Claude Shannon proved that theespionage
Espionage or spying is the act of obtaining secret
Secrecy is the practice of hiding information
Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both it ...

, torture, ...) 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 primitive, 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), 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., ElGamal encryption, El-Gamal encryption) are designed to provide particular functionality (e.g., public key encryption) while guaranteeing certain security properties (e.g., Chosen-plaintext attack, 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 protected backup data). Such cryptosystems are sometimes called ''cryptographic protocols''. Some widely known cryptosystems include RSA (algorithm), RSA encryption, Schnorr signature, ElGamal encryption, El-Gamal encryption, Pretty Good Privacy, PGP, etc. More complex cryptosystems include electronic cash systems, signcryption systems, etc. Some more 'theoretical' cryptosystems include interactive proof systems, (like zero-knowledge proofs), 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, 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 as PRESENT, Advanced Encryption Standard, AES, and Speck (cipher), 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.Applications

In general

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.In cybersecurity

Cryptography can be used to secure communications by encrypting them. Websites use encryption via HTTPS. "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 Signal (software), Signal and WhatsApp. 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 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. More radically, encryption is sometimes used to encrypt one's entire drive. For example, University College London has implemented BitLocker (a program by Microsoft) to render drive data opaque without users logging in.In electronic money, blockchain, and cryptocurrency

Social issues

Legal issues

Prohibitions

Cryptography has long been of interest to intelligence gathering and law enforcement agency, law enforcement agencies. Secret communications may be criminal or even treasonous . Because of its facilitation of privacy, 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 significantly restricted the use of cryptography domestically, though it has since relaxed many of these rules. In People's Republic of China, China and Islamic Republic of Iran, Iran, 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, Kazakhstan, Mongolia, Pakistan, Singapore, Tunisia, and Vietnam. In the United States, 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 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, 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 the source code for Philip Zimmermann's Pretty Good Privacy (PGP) encryption program found its way onto the Internet in June 1991, a complaint by RSA Security (then called RSA Data Security, Inc.) resulted in a lengthy criminal investigation of Zimmermann by the US Customs Service and the Federal Bureau of Investigation, FBI, though no charges were ever filed. Daniel J. Bernstein, then a graduate student at UC Berkeley, brought a lawsuit against the US government challenging some aspects of the restrictions based on 1st Amendment, free speech 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 freedom of speech, free speech by the United States Constitution. In 1996, thirty-nine countries signed the Wassenaar Arrangement, 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-Export of cryptography, exported mass-market software. Since this relaxation in US export restrictions, and because most personal computers connected to the Internet include US-sourced web browsers such as Firefox or Internet Explorer, almost every Internet user worldwide has potential access to quality cryptography via their browsers (e.g., via Transport Layer Security). The Mozilla Thunderbird and Microsoft Outlook E-mail client programs similarly can transmit and receive emails via TLS, and can send and receive email encrypted with S/MIME. Many Internet users don't realize that their basic application software contains such extensivecryptosystem
In cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in t ...

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 the National Security Agency on cipher development and policy. The NSA was involved with the design of Data Encryption Standard, DES during its development at IBM and its consideration by the National Bureau of Standards as a possible Federal Standard for cryptography. DES was designed to be resistant to differential cryptanalysis, 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, 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 affair, an encryption microchip intended to be part of the Capstone (cryptography), Capstone cryptography-control initiative. Clipper was widely criticized by cryptographers for two reasons. The cipher algorithm (called Skipjack (cipher), 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 key escrow, escrow key held by the government for use by law enforcement (i.e. Telephone tapping, wiretapping).Digital rights management

Cryptography is central to digital rights management (DRM), a group of techniques for technologically controlling use of copyrighted material, being widely implemented and deployed at the behest of some copyright holders. In 1998, U.S. President Bill Clinton signed the Digital Millennium Copyright Act (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 Directive on the harmonisation of certain aspects of copyright and related rights in the information society, EU Copyright Directive. Similar restrictions are called for by treaties signed by World Intellectual Property Organization member-states. The United States Department of Justice and Federal Bureau of Investigation, FBI 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 Corporation, Intel security design for fear of prosecution under the DMCA. Cryptologist Bruce Schneier has argued that the DMCA encourages vendor lock-in, while inhibiting actual measures toward cyber-security. Both Alan Cox (longtime Linux kernel developer) and Edward Felten (and some of his students at Princeton) have encountered problems related to the Act. Dmitry Sklyarov 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 and HD DVD content scrambling were AACS encryption key controversy, discovered and released onto the Internet. In both cases, the MPAA, Motion Picture Association of America sent out numerous DMCA takedown notices, and there was a massive Internet backlash triggered by the perceived impact of such notices on fair use and free speech.Forced disclosure of encryption keys

In the United Kingdom, the Regulation of Investigatory Powers Act 2000, 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 an encryption passphrase or password. The Electronic Frontier Foundation (EFF) argued that this is a violation of the protection from self-incrimination given by the Fifth Amendment to the United States Constitution, 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 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 Data remanence, drive which has been securely wiped).See also

* ** ** ** ** * – first cryptography chart * * * * * * * * World Wide Web Consortium's * Collision attackReferences

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 (author), James Gannon, ''Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century'', Washington, D.C., Brassey's, 2001, . *Oded Goldreich
Oded Goldreich ( he, עודד גולדרייך; b. 1957) is a professor
Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other post-secondary education and research institutions in most c ...

''Foundations of Cryptography''

in two volumes, Cambridge University Press, 2001 and 2004. *

' by Jonathan Katz and Yehuda Lindell. * ''Alvin's Secret Code'' by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis). * Ibrahim A. Al-Kadi, "The Origins of Cryptology: the Arab Contributions," Cryptologia, vol. 16, no. 2 (April 1992), pp. 97–126.

Christof Paar

Jan Pelzl

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

Springer, 2009. (Slides, online cryptography lectures and other information are available on the companion web site.) Very accessible introduction to practical cryptography for non-mathematicians. * ''Introduction to Modern Cryptography'' by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs

PDF download

* Johann-Christoph Woltag, 'Coded Communications (Encryption)' in Rüdiger Wolfrum (ed) ''Max Planck Encyclopedia of Public International Law'' (Oxford University Press 2009). * , giving an overview of international law issues regarding cryptography. * Jonathan Arbib & John Dwyer, ''Discrete Mathematics for Cryptography'', 1st Edition . *

External links

* * *Crypto Glossary and Dictionary of Technical Cryptography

NSA's CryptoKids

Overview and Applications of Cryptology

by the CrypTool Team; PDF; 3.8 MB. July 2008

A Course in Cryptography

by Raphael Pass & Abhi Shelat – offered at Cornell in the form of lecture notes. * For more on the use of cryptographic elements in fiction, see:

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