Cryptography
Overview
Cryptography is the practice and study of techniques for secure communication in the presence of third parties (called adversaries
Adversary (cryptography)
In cryptography, an adversary is a malicious entity whose aim is to prevent the users of the cryptosystem from achieving their goal...

). More generally, it is about constructing and analyzing protocol
Communications protocol
A communications protocol is a system of digital message formats and rules for exchanging those messages in or between computing systems and in telecommunications...

s that overcome the influence of adversaries and which are related to various aspects in information security
Information security
Information security means protecting information and information systems from unauthorized access, use, disclosure, disruption, modification, perusal, inspection, recording or destruction....

 such as data confidentiality, data integrity
Data integrity
Data Integrity in its broadest meaning refers to the trustworthiness of system resources over their entire life cycle. In more analytic terms, it is "the representational faithfulness of information to the true state of the object that the information represents, where representational faithfulness...

, and authentication
Authentication
Authentication is the act of confirming the truth of an attribute of a datum or entity...

. Modern cryptography intersects the disciplines of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

, and electrical engineering
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

. Applications of cryptography include ATM cards
Automated teller machine
An automated teller machine or automatic teller machine, also known as a Cashpoint , cash machine or sometimes a hole in the wall in British English, is a computerised telecommunications device that provides the clients of a financial institution with access to financial transactions in a public...

, computer passwords
Password
A password is a secret word or string of characters that is used for authentication, to prove identity or gain access to a resource . The password should be kept secret from those not allowed access....

, and electronic commerce
Electronic commerce
Electronic commerce, commonly known as e-commerce, eCommerce or e-comm, refers to the buying and selling of products or services over electronic systems such as the Internet and other computer networks. However, the term may refer to more than just buying and selling products online...

.

Cryptology prior to the modern age was almost synonymous with encryption
Encryption
In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...

, the conversion of information from a readable state to apparent nonsense
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...

.
Encyclopedia
Cryptography is the practice and study of techniques for secure communication in the presence of third parties (called adversaries
Adversary (cryptography)
In cryptography, an adversary is a malicious entity whose aim is to prevent the users of the cryptosystem from achieving their goal...

). More generally, it is about constructing and analyzing protocol
Communications protocol
A communications protocol is a system of digital message formats and rules for exchanging those messages in or between computing systems and in telecommunications...

s that overcome the influence of adversaries and which are related to various aspects in information security
Information security
Information security means protecting information and information systems from unauthorized access, use, disclosure, disruption, modification, perusal, inspection, recording or destruction....

 such as data confidentiality, data integrity
Data integrity
Data Integrity in its broadest meaning refers to the trustworthiness of system resources over their entire life cycle. In more analytic terms, it is "the representational faithfulness of information to the true state of the object that the information represents, where representational faithfulness...

, and authentication
Authentication
Authentication is the act of confirming the truth of an attribute of a datum or entity...

. Modern cryptography intersects the disciplines of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...

, and electrical engineering
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

. Applications of cryptography include ATM cards
Automated teller machine
An automated teller machine or automatic teller machine, also known as a Cashpoint , cash machine or sometimes a hole in the wall in British English, is a computerised telecommunications device that provides the clients of a financial institution with access to financial transactions in a public...

, computer passwords
Password
A password is a secret word or string of characters that is used for authentication, to prove identity or gain access to a resource . The password should be kept secret from those not allowed access....

, and electronic commerce
Electronic commerce
Electronic commerce, commonly known as e-commerce, eCommerce or e-comm, refers to the buying and selling of products or services over electronic systems such as the Internet and other computer networks. However, the term may refer to more than just buying and selling products online...

.

Cryptology prior to the modern age was almost synonymous with encryption
Encryption
In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...

, the conversion of information from a readable state to apparent nonsense
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...

. The sender retained the ability to decrypt the information and therefore avoid unwanted persons being able to read it. Since World War I and the advent of the computer, the methods used to carry out cryptology have become increasingly complex and its application more widespread.

Modern cryptography follows a strongly scientific approach, and designs cryptographic algorithms around computational hardness assumptions, making such algorithms hard to break by an adversary. It is theoretically possible to break such a system but it is infeasible to do so by any practical means. These schemes are therefore computationally secure. There exist information-theoretically secure
Information theoretic security
A cryptosystem is information-theoretically secure if its security derives purely from information theory. That is, it is secure even when the adversary has unlimited computing power. The adversary simply does not have enough information to break the security...

 schemes that cannot be broken—an example is the one-time pad
One-time pad
In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...

—but these schemes are more difficult to implement than the theoretically breakable but computationally secure mechanisms.

Cryptology-related technology has raised a number of legal issues. In the United Kingdom, additions to the Regulation of Investigatory Powers Act 2000
Regulation of Investigatory Powers Act 2000
The Regulation of Investigatory Powers Act 2000 is an Act of the Parliament of the United Kingdom, regulating the powers of public bodies to carry out surveillance and investigation, and covering the interception of communications...

 requires a suspected criminal to hand over their encryption key if asked by law enforcement. Otherwise the user will face a criminal charge. The Electronic Frontier Foundation
Electronic Frontier Foundation
The Electronic Frontier Foundation is an international non-profit digital rights advocacy and legal organization based in the United States...

 is involved in a case in the Supreme Court of the United States
Supreme Court of the United States
The Supreme Court of the United States is the highest court in the United States. It has ultimate appellate jurisdiction over all state and federal courts, and original jurisdiction over a small range of cases...

, which will ascertain if requiring suspected criminals to provide their encryption keys to law enforcement is unconstitutional. The EFF
Electronic Frontier Foundation
The Electronic Frontier Foundation is an international non-profit digital rights advocacy and legal organization based in the United States...

 is arguing that this is a violation of the right of not being forced to incriminate oneself, as given in the fifth amendment
Fifth Amendment to the United States Constitution
The Fifth Amendment to the United States Constitution, which is part of the Bill of Rights, protects against abuse of government authority in a legal procedure. Its guarantees stem from English common law which traces back to the Magna Carta in 1215...

.

Terminology

Until modern times cryptography referred almost exclusively to encryption, which is the process of converting ordinary information (called plaintext
Plaintext
In cryptography, plaintext is information a sender wishes to transmit to a receiver. Cleartext is often used as a synonym. Before the computer era, plaintext most commonly meant message text in the language of the communicating parties....

) into unintelligible gibberish (called ciphertext
Ciphertext
In cryptography, ciphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher...

). Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A cipher
Cipher
In cryptography, a cipher 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. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...

(or cypher) is a pair of algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

s that create 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
Key (cryptography)
In cryptography, a key is a piece of information that determines the functional output of a cryptographic algorithm or cipher. Without a key, the algorithm would produce no useful result. In encryption, a key specifies the particular transformation of plaintext into ciphertext, or vice versa...

. This is a secret parameter (ideally known only to the communicants) for a specific message exchange context. A "cryptosystem
Cryptosystem
There are two different meanings of the word cryptosystem. One is used by the cryptographic community, while the other is the meaning understood by the public.- General meaning :...

" 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, 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.

In colloquial use, the term "code
Code (cryptography)
In cryptography, a code is a method used to transform a message into an obscured form, preventing those who do not possess special information, or key, required to apply the transform from understanding what is actually transmitted. The usual method is to use a codebook with a list of common...

" is often used to mean any method of encryption or concealment of meaning. However, in cryptography, code has a more specific meaning. It means the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a code word
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...

 (for example, wallaby replaces attack at dawn). Codes are no longer used in serious cryptography—except incidentally for such things as unit designations (e.g., Bronco Flight or Operation Overlord)—since properly chosen ciphers are both more practical and more secure than even the best codes and also are better adapted to computer
Computer
A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...

s.

Cryptanalysis
Cryptanalysis
Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...

 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. English is more flexible than several other languages in which cryptology (done by cryptologists) is always used in the second sense above. In the English Wikipedia the general term used for the entire field is cryptography (done by cryptographers).

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

History of cryptography and cryptanalysis

Before the modern era, cryptography was concerned solely with message confidentiality (i.e., encryption)—conversion of messages
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...

 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 was used to (attempt to) ensure secrecy
Secrecy
Secrecy is the practice of hiding information from certain individuals or groups, perhaps while sharing it with other individuals...

 in communications, such as those of spies
SPY
SPY is a three-letter acronym that may refer to:* SPY , ticker symbol for Standard & Poor's Depositary Receipts* SPY , a satirical monthly, trademarked all-caps* SPY , airport code for San Pédro, Côte d'Ivoire...

, military leaders, and diplomat
Diplomat
A diplomat is a person appointed by a state to conduct diplomacy with another state or international organization. The main functions of diplomats revolve around the representation and protection of the interests and nationals of the sending state, as well as the promotion of information and...

s. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication
Authentication
Authentication is the act of confirming the truth of an attribute of a datum or entity...

, digital signature
Digital signature
A digital signature or digital signature scheme is a mathematical scheme for demonstrating the authenticity of a digital message or document. A valid digital signature gives a recipient reason to believe that the message was created by a known sender, and that it was not altered in transit...

s, interactive proof
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. The parties, the verifier and the prover, interact by exchanging messages in order to ascertain whether a given string belongs to a...

s and secure computation
Secure multiparty computation
Secure multi-party computation is a sub field of cryptography. The goal of methods for secure multi-party computation is to enable parties to jointly compute a function over their inputs, while at the same time keeping these inputs private...

, among others.

Classic cryptography

The earliest forms of secret writing required little more than local pen and paper analogs, as most people could not read. More literacy, or literate opponents, required actual cryptography. The main classical cipher types are transposition cipher
Transposition cipher
In cryptography, a transposition cipher is a method of encryption by which the positions held by units of plaintext are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext. That is, the order of the units is changed...

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
Substitution cipher
In cryptography, a substitution cipher is a method of encryption by which units of plaintext are replaced with ciphertext according to a regular system; the "units" may be single letters , pairs of letters, triplets of letters, mixtures of the above, and so forth...

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
Latin alphabet
The Latin alphabet, also called the Roman alphabet, is the most recognized alphabet used in the world today. It evolved from a western variety of the Greek alphabet called the Cumaean alphabet, which was adopted and modified by the Etruscans who ruled early Rome...

). Simple versions of either have never offered much confidentiality from enterprising opponents. An early substitution cipher was the Caesar cipher
Caesar cipher
In cryptography, a Caesar cipher, also known as a 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 plaintext is replaced by a letter some fixed number...

, in which each letter in the plaintext was replaced by a letter some fixed number of positions further down the alphabet. Suetonius
Suetonius
Gaius Suetonius Tranquillus, commonly known as Suetonius , was a Roman historian belonging to the equestrian order in the early Imperial era....

 reports that Julius Caesar
Julius Caesar
Gaius Julius Caesar was a Roman general and statesman and a distinguished writer of Latin prose. He played a critical role in the gradual transformation of the Roman Republic into the Roman Empire....

 used it with a shift of three to communicate with his generals. Atbash
Atbash
Atbash is a simple substitution cipher for the Hebrew alphabet. It consists in substituting aleph for tav , beth for shin , and so on, reversing the alphabet. In the Book of Jeremiah, Lev Kamai is Atbash for Kasdim , and Sheshakh is Atbash for Bavel...

 is an example of an early Hebrew cipher. The earliest known use of cryptography is some carved ciphertext on stone in Egypt (ca 1900 BC), but this may have been done for the amusement of literate observers rather than as a way of concealing information. Cryptography is recommended in the Kama Sutra
Kama Sutra
The Kama Sutra is an ancient Indian Hindu text widely considered to be the standard work on human sexual behavior in Sanskrit literature written by Vātsyāyana. A portion of the work consists of practical advice on sexual intercourse. It is largely in prose, with many inserted anustubh poetry verses...

 as a way for lovers to communicate without inconvenient discovery.

The Greeks of Classical times
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...

 are said to have known of ciphers (e.g., the scytale transposition cipher claimed to have been used by the Sparta
Sparta
Sparta or Lacedaemon, was a prominent city-state in ancient Greece, situated on the banks of the River Eurotas in Laconia, in south-eastern Peloponnese. It emerged as a political entity around the 10th century BC, when the invading Dorians subjugated the local, non-Dorian population. From c...

n military). Steganography
Steganography
Steganography is the art and science of writing hidden messages in such a way that no one, apart from the sender and intended recipient, suspects the existence of the message, a form of security through obscurity...

 (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
Herodotus was an ancient Greek historian who was born in Halicarnassus, Caria and lived in the 5th century BC . He has been called the "Father of History", and was the first historian known to collect his materials systematically, test their accuracy to a certain extent and arrange them in a...

, concealed a message—a tattoo on a slave's shaved head—under the regrown hair. Another Greek method was developed by Polybius
Polybius
Polybius , Greek ) was a Greek historian of the Hellenistic Period noted for his work, The Histories, which covered the period of 220–146 BC in detail. The work describes in part the rise of the Roman Republic and its gradual domination over Greece...

 (now called the "Polybius Square"). More modern examples of steganography include the use of invisible ink
Invisible ink
Invisible ink, also known as security ink, is a substance used for writing, which is invisible either on application or soon thereafter, and which later on can be made visible by some means. Invisible ink is one form of steganography, and it has been used in espionage...

, microdot
Microdot
A microdot is text or an image substantially reduced in size onto a 1mm disc to prevent detection by unintended recipients. Microdots are normally circular around one millimetre in diameter but can be made into different shapes and sizes and made from various materials such as polyester...

s, and digital watermarks to conceal information.

Ciphertexts produced by a classical cipher
Classical cipher
A cipher is a means of concealing a message, where letters of the message are substituted or transposed for other letters, letter pairs, and sometimes for many letters. In cryptography, a classical cipher is a type of cipher that was used historically but now has fallen, for the most part, into...

 (and some modern ciphers) always reveal statistical information about the plaintext, which can often be used to break them. After the discovery of frequency analysis
Frequency analysis
In cryptanalysis, frequency analysis 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....

 perhaps by the Arab mathematician and polymath
Polymath
A polymath is a person whose expertise spans a significant number of different subject areas. In less formal terms, a polymath may simply be someone who is very knowledgeable...

, Al-Kindi
Al-Kindi
' , known as "the Philosopher of the Arabs", was a Muslim Arab philosopher, mathematician, physician, and musician. Al-Kindi was the first of the Muslim peripatetic philosophers, and is unanimously hailed as the "father of Islamic or Arabic philosophy" for his synthesis, adaptation and promotion...

 (also known as Alkindus), in the 9th century, nearly all such ciphers became more or less readily breakable by any informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzle
Puzzle
A puzzle is a problem or enigma that tests the ingenuity of the solver. In a basic puzzle, one is intended to put together pieces in a logical way in order to come up with the desired solution...

s (see cryptogram
Cryptogram
A cryptogram is a type of puzzle which consists of a short piece of encrypted text. Generally the cipher used to encrypt the text is simple enough that cryptogram can be solved by hand. Frequently used are substitution ciphers where each letter is replaced by a different letter or number. To solve...

). Al-Kindi wrote a book on cryptography entitled Risalah fi Istikhraj al-Mu'amma (Manuscript for the Deciphering Cryptographic Messages), in which described the first cryptanalysis
Cryptanalysis
Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...

 techniques.
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 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
Alberti cipher disk
thumb|right|250px|A Treatise on Ciphers. The Alberti Cipher Disk.The Alberti cipher disk, also called formula, is a cipher disc which was described by Leon Battista Alberti in his treatise De Cifris of 1467...

, a wheel which implemented a partial realization of his invention. In the polyalphabetic Vigenère cipher
Vigenère cipher
The Vigenère cipher is a method of encrypting alphabetic text by using a series of different Caesar ciphers based on the letters of a keyword. It is a simple form of polyalphabetic substitution....

, 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
Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer...

 showed that the Vigenère cipher was vulnerable to Kasiski examination
Kasiski examination
In cryptanalysis, Kasiski examination is a method of attacking polyalphabetic substitution ciphers, such as the Vigenère cipher...

, but this was first published about ten years later by Friedrich Kasiski
Friedrich Kasiski
Major Friedrich Wilhelm Kasiski was a Prussian infantry officer, cryptographer and archeologist. Kasiski was born in Schlochau, West Prussia .-Military service:...

.

Although frequency analysis is a powerful and general technique against many ciphers, encryption has still been often effective in practice; 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
Auguste Kerckhoffs
Auguste Kerckhoffs was a Dutch linguist and cryptographer who was professor of languages at the École des Hautes Études Commerciales in Paris in the late 19th century....

 and is generally called Kerckhoffs's Principle; alternatively and more bluntly, it was restated by Claude Shannon, the inventor of information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

 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
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...

, a rod supposedly used by the Spartans as an aid for a transposition cipher (see image above). In medieval times, other aids were invented such as the cipher grille
Grille (cryptography)
In the history of cryptography, a grille cipher was a technique for encrypting a plaintext by writing it onto a sheet of paper through a pierced sheet . The earliest known description is due to the polymath Girolamo Cardano in 1550...

, 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
Cipher disk
A cipher disk is an enciphering and deciphering tool developed in 1470 by the Italian architect and author Leon Battista Alberti. He constructed a device, consisting of two concentric circular plates mounted one on top of the other...

, Johannes Trithemius
Johannes Trithemius
Johannes Trithemius , born Johann Heidenberg, was a German abbot, lexicographer, historian, cryptographer, polymath and occultist who had an influence on later occultism. The name by which he is more commonly known is derived from his native town of Trittenheim on the Mosel in Germany.-Life:He...

' tabula recta
Tabula recta
In cryptography, the tabula recta is a square table of alphabets, each row of which is made by shifting the previous one to the left...

 scheme, and Thomas Jefferson
Thomas Jefferson
Thomas Jefferson was the principal author of the United States Declaration of Independence and the Statute of Virginia for Religious Freedom , the third President of the United States and founder of the University of Virginia...

's multi-cylinder
Jefferson disk
The Jefferson disk, or wheel cypher as Jefferson named it, also known as the Bazeries Cylinder, is a cipher system using a set of wheels or disks, each with the 26 letters of the alphabet arranged around their edge. The order of the letters is different for each disk and is usually scrambled in...

 (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 machine
Rotor machine
In cryptography, a rotor machine is an electro-mechanical device used for encrypting and decrypting secret messages. Rotor machines were the cryptographic state-of-the-art for a prominent period of history; they were in widespread use in the 1920s–1970s...

s—famously including the Enigma machine
Enigma machine
An Enigma machine is any of a family of related electro-mechanical rotor cipher machines used for the encryption and decryption of secret messages. Enigma was invented by German engineer Arthur Scherbius at the end of World War I...

 used by the German government and military from the late '20s and during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

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

The computer era

The development of digital computers and electronics
Electronics
Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

 after WWII 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
Binary numeral system
The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

 bit
Bit
A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

 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.

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
Data Encryption Standard
The Data Encryption Standard is a block cipher that uses shared secret encryption. It was selected by the National Bureau of Standards as an official Federal Information Processing Standard for the United States in 1976 and which has subsequently enjoyed widespread use internationally. It is...

; Whitfield Diffie and Martin Hellman published their key agreement algorithm,; and the RSA algorithm was published in Martin Gardner
Martin Gardner
Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...

's Scientific American
Scientific American
Scientific American is a popular science magazine. It is notable for its long history of presenting science monthly to an educated but not necessarily scientific public, through its careful attention to the clarity of its text as well as the quality of its specially commissioned color graphics...

 column. Since then, cryptography has become a widely used tool in communications, computer network
Computer network
A computer network, often simply referred to as a network, is a collection of hardware components and computers interconnected by communication channels that allow sharing of resources and information....

s, and computer security generally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable, such as the integer factorization
Integer factorization
In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer....

 or the discrete logarithm
Discrete logarithm
In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga is a solution of the equation ax = b over the real or complex numbers...

 problems, so there are deep connections with abstract mathematics. There are no absolute proofs that a cryptographic technique is secure (but see one-time pad
One-time pad
In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...

); at best, there are proofs that some techniques are secure if some computational problem is difficult to solve, or this or that assumption about implementation or practical use is met.

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, thus 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; the announced imminence of small implementations of these machines may be making the need for this preemptive caution rather more than merely speculative.

Essentially, prior to the early 20th century, cryptography was chiefly concerned with linguistic
Language
Language may refer either to the specifically human capacity for acquiring and using complex systems of communication, or to a specific instance of such a system of complex communication...

 and lexicographic
Lexicographic code
Lexicographic codes or lexicodes are greedily generated error-correcting codes with remarkably good properties. They were produced independently byLevenshtein and Conway and Sloane and are known to be linear over some finite fields.- Construction :...

 patterns. Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

, computational complexity
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other...

, statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

, abstract algebra
Abstract algebra
Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras...

, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

, and finite mathematics generally. Cryptography is, also, a branch of engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...

, but an unusual one as it deals with active, intelligent, and malevolent opposition (see cryptographic engineering
Cryptographic engineering
Cryptographic engineering is the discipline of using cryptography to solve human problems. Cryptography is typically applied when trying to ensure data confidentiality, to authenticate people or devices, or to verify data integrity in risky environments....

 and security engineering
Security engineering
Security engineering is a specialized field of engineering that focuses on the security aspects in the design of systems that need to be able to deal robustly with possible sources of disruption, ranging from natural disasters to malicious acts...

); 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 (see quantum cryptography
Quantum cryptography
Quantum key distribution uses quantum mechanics to guarantee secure communication. It enables two parties to produce a shared random secret key known only to them, which can then be used to encrypt and decrypt messages...

 and quantum computing).

Modern cryptography

The modern field of cryptography can be divided into several areas of study. The chief ones are discussed here; see Topics in Cryptography for more.

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.

The Data Encryption Standard
Data Encryption Standard
The Data Encryption Standard is a block cipher that uses shared secret encryption. It was selected by the National Bureau of Standards as an official Federal Information Processing Standard for the United States in 1976 and which has subsequently enjoyed widespread use internationally. It is...

 (DES) and the Advanced Encryption Standard
Advanced Encryption Standard
Advanced Encryption Standard is a specification for the encryption of electronic data. It has been adopted by the U.S. government and is now used worldwide. It supersedes DES...

 (AES) are block cipher designs which have been designated cryptography standards
Cryptography standards
There are a number of standards related to cryptography. Standard algorithms and protocols provide a focus for study; standards for popular applications attract a large amount of cryptanalysis.-Encryption 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
E-mail privacy
The protection of email from unauthorized access and inspection is known as electronic privacy. In countries with a constitutional guarantee of the secrecy of correspondence, email is equated with letters and thus legally protected from all forms of eavesdropping.In the United States, privacy of...

 and secure remote access
Secure Shell
Secure Shell is a network protocol for secure data communication, remote shell services or command execution and other secure network services between two networked computers that it connects via a secure channel over an insecure network: a server and a client...

. Many other block ciphers have been designed and released, with considerable variation in quality. Many have been thoroughly broken, such as FEAL
FEAL
In cryptography, FEAL is a block cipher proposed as an alternative to the Data Encryption Standard , and designed to be much faster in software. The Feistel based algorithm was first published in 1987 by Akihiro Shimizu and Shoji Miyaguchi from NTT...

.

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 one-time pad
One-time pad
In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...

. In a stream cipher, the output stream is created based on a hidden internal state which changes as the cipher operates. That internal state is initially set up using the secret key material. RC4
RC4
In cryptography, RC4 is the most widely used software stream cipher and is used in popular protocols such as Secure Sockets Layer and WEP...

 is a widely used stream cipher; see :Category:Stream ciphers. Block ciphers can be used as stream ciphers; see Block cipher modes of operation
Block cipher modes of operation
In cryptography, modes of operation is the procedure of enabling the repeated and secure use of a block cipher under a single key.A block cipher by itself allows encryption only of a single data block of the cipher's block length. When targeting a variable-length message, the data must first be...

.

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
Hash function
A hash function is any algorithm or subroutine that maps large data sets to smaller data sets, called keys. For example, a single integer can serve as an index to an array...

 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
MD4
The MD4 Message-Digest Algorithm is a cryptographic hash function developed by Ronald Rivest in 1990. The digest length is 128 bits. The algorithm has influenced later designs, such as the MD5, SHA-1 and RIPEMD algorithms....

 is a long-used hash function which is now broken; MD5
MD5
The MD5 Message-Digest Algorithm is a widely used cryptographic hash function that produces a 128-bit hash value. Specified in RFC 1321, MD5 has been employed in a wide variety of security applications, and is also commonly used to check data integrity...

, a strengthened variant of MD4, is also widely used but broken in practice. The U.S. National Security Agency
National Security Agency
The National Security Agency/Central Security Service is a cryptologic intelligence agency of the United States Department of Defense responsible for the collection and analysis of foreign communications and foreign signals intelligence, as well as protecting U.S...

 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
SHA-2
In cryptography, SHA-2 is a set of cryptographic hash functions designed by the National Security Agency and published in 2001 by the NIST as a U.S. Federal Information Processing Standard. SHA stands for Secure Hash Algorithm. SHA-2 includes a significant number of changes from its predecessor,...

 family improves on SHA-1, but it isn't yet widely deployed, and the U.S. standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness of NIST's overall hash algorithm toolkit." Thus, a hash function design competition
NIST hash function competition
The NIST hash function competition is an open competition held by the US National Institute of Standards and Technology for a new SHA-3 function to replace the older SHA-1 and SHA-2, which was formally announced in the Federal Register on November 2, 2007...

 is underway and meant to select a new U.S. national standard, to be called SHA-3, by 2012.

Message authentication code
Message authentication code
In cryptography, a message authentication code is a short piece of information used to authenticate a message.A MAC algorithm, sometimes called a keyed hash function, accepts as input a secret key and an arbitrary-length message to be authenticated, and outputs a MAC...

s (MACs) are much like cryptographic hash functions, except that a secret key can be used to authenticate the hash value upon receipt.

Public-key cryptography

Symmetric-key cryptosystems use the same key for encryption and decryption of a message, though a message or group of messages may have a different key than others. A significant disadvantage of symmetric ciphers is the key management
Key management
Key management is the provisions made in a cryptography system design that are related to generation, exchange, storage, safeguarding, use, vetting, and replacement of keys. It includes cryptographic protocol design, key servers, user procedures, and other relevant protocols.Key management concerns...

 necessary to use them securely. Each distinct pair of communicating parties must, ideally, share a different key, and perhaps 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 straight and secret. The difficulty of securely establishing a secret key between two communicating parties, when a secure channel
Secure channel
In cryptography, a secure channel is a way of transferring data that is resistant to interception and tampering.A confidential channel is a way of transferring data that is resistant to interception, but not necessarily resistant to tampering....

 does not already exist between them, also presents a chicken-and-egg problem which is a considerable practical obstacle for cryptography users in the real world.

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. 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. The public key is typically used for encryption, while the private or secret key is used for decryption. Diffie and Hellman showed that public-key cryptography was possible by presenting the Diffie–Hellman key exchange protocol.

In 1978, Ronald Rivest, Adi Shamir
Adi Shamir
Adi Shamir is an Israeli cryptographer. He is a co-inventor of the RSA algorithm , a co-inventor of the Feige–Fiat–Shamir identification scheme , one of the inventors of differential cryptanalysis and has made numerous contributions to the fields of cryptography and computer...

, and Len Adleman invented RSA, another public-key system.

In 1997, it finally became publicly known that asymmetric key cryptography had been invented by James H. Ellis
James H. Ellis
James Henry Ellis was a British engineer and mathematician. In 1970, while working at the Government Communications Headquarters in Cheltenham he conceived of the possibility of "non-secret encryption", more commonly termed public-key cryptography.-Early life, education and career:Ellis was born...

 at GCHQ, a British
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

 intelligence organization, and that, in the early 1970s, both the Diffie–Hellman and RSA algorithms had been previously developed (by Malcolm J. Williamson
Malcolm J. Williamson
Malcolm John Williamson is a British mathematician and cryptographer. In 1974 he discovered what is now known as Diffie-Hellman key exchange. He was then working at GCHQ and was therefore unable to publicize his research as his work was classified...

 and Clifford Cocks
Clifford Cocks
Clifford Christopher Cocks, CB, is a British mathematician and cryptographer at GCHQ.He invented the widely-used encryption algorithm now commonly known as RSA, about three years before it was independently developed by Rivest, Shamir, and Adleman at MIT...

, respectively).

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. Others include the Cramer–Shoup cryptosystem, ElGamal encryption
ElGamal encryption
In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1984. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of...

, and various elliptic curve techniques
Elliptic curve cryptography
Elliptic curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor S...

. See :Category:Asymmetric-key cryptosystems.

In addition to encryption, public-key cryptography can be used to implement digital signature
Digital signature
A digital signature or digital signature scheme is a mathematical scheme for demonstrating the authenticity of a digital message or document. A valid digital signature gives a recipient reason to believe that the message was created by a known sender, and that it was not altered in transit...

 schemes. A digital signature is reminiscent of an ordinary signature
Signature
A signature is a handwritten depiction of someone's name, nickname, or even a simple "X" that a person writes on documents as a proof of identity and intent. The writer of a signature is a signatory. Similar to a handwritten signature, a signature work describes the work as readily identifying...

; they both have the characteristic that they are easy for a user to produce, but difficult for anyone else to forge
Forgery
Forgery is the process of making, adapting, or imitating objects, statistics, or documents with the intent to deceive. Copies, studio replicas, and reproductions are not considered forgeries, though they may later become forgeries through knowing and willful misrepresentations. Forging money or...

. 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
Digital Signature Algorithm
The Digital Signature Algorithm is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology in August 1991 for use in their Digital Signature Standard , specified in FIPS 186, adopted in 1993. A minor...

 are two of the most popular digital signature schemes. Digital signatures are central to the operation of public key infrastructure
Public key infrastructure
Public Key Infrastructure is a set of hardware, software, people, policies, and procedures needed to create, manage, distribute, use, store, and revoke digital certificates. In cryptography, a PKI is an arrangement that binds public keys with respective user identities by means of a certificate...

s and many network security schemes (e.g., SSL/TLS
Transport Layer Security
Transport Layer Security and its predecessor, Secure Sockets Layer , are cryptographic protocols that provide communication security over the Internet...

, many VPNs, etc.).

Public-key algorithms are most often based on the computational complexity
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other...

 of "hard" problems, often from number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

. For example, the hardness of RSA is related to the integer factorization
Integer factorization
In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer....

 problem, while Diffie–Hellman and DSA are related to the discrete logarithm
Discrete logarithm
In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga is a solution of the equation ax = b over the real or complex numbers...

 problem. More recently, elliptic curve cryptography
Elliptic curve cryptography
Elliptic curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor S...

has developed in which security is based on number theoretic problems involving elliptic curve
Elliptic curve
In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...

s. Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular
Modular arithmetic
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....

 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 cryptosystem
Hybrid cryptosystem
In cryptography, public-key cryptosystems are convenient in that they do not require the sender and receiver to share a common secret in order to communicate securely . However, they often rely on complicated mathematical computations and are thus generally much more inefficient than comparable...

s, 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.

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
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...

, Claude Shannon proved that the one-time pad
One-time pad
In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...

 cipher is unbreakable, provided the key material is truly random
Statistical randomness
A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal dice roll, or the digits of π exhibit statistical randomness....

, 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
Brute force attack
In cryptography, a brute-force attack, or exhaustive key search, is a strategy that can, in theory, be used against any encrypted data. Such an attack might be utilized when it is not possible to take advantage of other weaknesses in an encryption system that would make the task easier...

, 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.

There are a wide variety of cryptanalytic attacks, and they can be classified in any of several ways. A common distinction turns on what an attacker knows and what capabilities are available. In a ciphertext-only attack
Ciphertext-only attack
In cryptography, a ciphertext-only attack or known ciphertext attack is an attack model for cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts....

, the cryptanalyst has access only to the ciphertext (good modern cryptosystems are usually effectively immune to ciphertext-only attacks). In a known-plaintext attack
Known-plaintext attack
The known-plaintext attack is an attack model for cryptanalysis where the attacker has samples of both the plaintext , and its encrypted version . These can be used to reveal further secret information such as secret keys and code books...

, the cryptanalyst has access to a ciphertext and its corresponding plaintext (or to many such pairs). In a chosen-plaintext attack
Chosen-plaintext attack
A chosen-plaintext attack is an attack model for cryptanalysis which presumes that the attacker has the capability to choose arbitrary plaintexts to be encrypted and obtain the corresponding ciphertexts. The goal of the attack is to gain some further information which reduces the security of the...

, the cryptanalyst may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example is gardening
Gardening (cryptanalysis)
In cryptanalysis, gardening was a term used at Bletchley Park, England, during World War II for schemes to entice the Germans to include known plaintext, which the British called "cribs," in their encrypted messages...

, used by the British during WWII. Finally, in a chosen-ciphertext attack
Chosen-ciphertext attack
A chosen-ciphertext attack is an attack model for cryptanalysis in which the cryptanalyst gathers information, at least in part, by choosing a ciphertext and obtaining its decryption under an unknown key. In the attack, an adversary has a chance to enter one or more known ciphertexts into the...

, the cryptanalyst may be able to choose ciphertexts and learn their corresponding plaintexts. Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of the protocols
Cryptographic protocol
A security protocol is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods.A protocol describes how the algorithms should be used...

 involved; see Cryptanalysis of the Enigma for some historical examples of this).
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 255 decryptions, trying approximately half of the possible keys, to reach a point at which chances are better than even the key sought will have been found. But this may not be enough assurance; a linear cryptanalysis
Linear 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...

 attack against DES requires 243 known plaintexts and approximately 243 DES operations. This is a considerable improvement on brute force attacks.

Public-key algorithms are based on the computational difficulty of various problems. The most famous of these is integer factorization
Integer factorization
In number theory, integer factorization or prime factorization is the decomposition of a composite number into smaller non-trivial divisors, which when multiplied together equal the original integer....

 (e.g., the RSA algorithm is based on a problem related to integer factoring), but the discrete logarithm
Discrete logarithm
In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga is a solution of the equation ax = b over the real or complex numbers...

 problem is also important. Much public-key cryptanalysis concerns numerical algorithms for solving these computational problems, or some of them, efficiently (i.e., in a practical time). For instance, the best known algorithms for solving the elliptic curve-based
Elliptic curve cryptography
Elliptic curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. The use of elliptic curves in cryptography was suggested independently by Neal Koblitz and Victor S...

 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
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...

 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
Traffic analysis
Traffic analysis is the process of intercepting and examining messages in order to deduce information from patterns in communication. It can be performed even when the messages are encrypted and cannot be decrypted. In general, the greater the number of messages observed, or even intercepted and...

, 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. And, of course, social engineering
Social engineering (security)
Social engineering is commonly understood to mean the art of manipulating people into performing actions or divulging confidential information...

, and other attacks against the personnel who work with cryptosystems or the messages they handle (e.g., bribery
Bribery
Bribery, a form of corruption, is an act implying money or gift giving that alters the behavior of the recipient. Bribery constitutes a crime and is defined by Black's Law Dictionary as the offering, giving, receiving, or soliciting of any item of value to influence the actions of an official or...

, extortion
Extortion
Extortion is a criminal offence which occurs when a person unlawfully obtains either money, property or services from a person, entity, or institution, through coercion. Refraining from doing harm is sometimes euphemistically called protection. Extortion is commonly practiced by organized crime...

, blackmail
Blackmail
In common usage, blackmail is a crime involving threats to reveal substantially true or false information about a person to the public, a family member, or associates unless a demand is met. It may be defined as coercion involving threats of physical harm, threat of criminal prosecution, or threats...

, espionage
Espionage
Espionage or spying involves an individual obtaining information that is considered secret or confidential without the permission of the holder of the information. Espionage is inherently clandestine, lest the legitimate holder of the information change plans or take other countermeasures once it...

, torture
Torture
Torture is the act of inflicting severe pain as a means of punishment, revenge, forcing information or a confession, or simply as an act of cruelty. Throughout history, torture has often been used as a method of political re-education, interrogation, punishment, and coercion...

, ...) may be the most productive attacks of all.

Cryptographic primitives

Much of the theoretical work in cryptography concerns cryptographic primitives
Cryptographic primitive
Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions.- Rationale :...

—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 function
Pseudorandom function
In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can distinguish between a function chosen randomly from the PRF family and a random oracle...

s, one-way function
One-way function
In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here "easy" and "hard" are to be understood in the sense of computational complexity theory, specifically the theory of polynomial time problems...

s, 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
ElGamal encryption
In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1984. ElGamal encryption is used in the free GNU Privacy Guard software, recent versions of...

) are designed to provide particular functionality (e.g. public key encryption) while guaranteeing certain security properties (e.g. chosen-plaintext attack (CPA)
Chosen-plaintext attack
A chosen-plaintext attack is an attack model for cryptanalysis which presumes that the attacker has the capability to choose arbitrary plaintexts to be encrypted and obtain the corresponding ciphertexts. The goal of the attack is to gain some further information which reduces the security of the...

 security in the random oracle model). Cryptosystems use the properties of the underlying cryptographic primitives to support the system's security properties. Of course, 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
Backup
In information technology, a backup or the process of backing up is making copies of data which may be used to restore the original after a data loss event. The verb form is back up in two words, whereas the noun is backup....

 data). Such cryptosystems are sometimes called cryptographic protocol
Cryptographic protocol
A security protocol is an abstract or concrete protocol that performs a security-related function and applies cryptographic methods.A protocol describes how the algorithms should be used...

s
.

Some widely known cryptosystems include RSA encryption, Schnorr signature
Schnorr signature
In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm. Its security is based on the intractability of certain discrete logarithm problems. It is considered the simplest digital signature scheme to be provably secure in a random oracle model . It is...

, El-Gamal encryption, PGP
Pretty Good Privacy
Pretty Good Privacy is a data encryption and decryption computer program that provides cryptographic privacy and authentication for data communication. PGP is often used for signing, encrypting and decrypting texts, E-mails, files, directories and whole disk partitions to increase the security...

, etc. More complex cryptosystems include electronic cash
Electronic cash
Electronic cash is the debit card system of the German Central Credit Committee, the association which represents the top German financial interest groups. Usually paired with a checking account, cards with an Electronic Cash logo are only handed out by proper credit institutions...

 systems, signcryption
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 confidentiality, integrity, and non-repudiation...

 systems, etc. Some more 'theoretical' cryptosystems include interactive proof system
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. The parties, the verifier and the prover, interact by exchanging messages in order to ascertain whether a given string belongs to a...

s, (like zero-knowledge proof
Zero-knowledge proof
In cryptography, a zero-knowledge proof or zero-knowledge protocol is an interactive method for one party to prove to another that a statement is true, without revealing anything other than the veracity of the statement....

s,), systems for secret sharing
Secret sharing
Secret sharing refers to method for distributing a secret amongst a group of participants, each of whom is allocated a share of the secret. The secret can be reconstructed only when a sufficient number of shares are combined together; individual shares are of no use on their own.More formally, in a...

, etc.

Until recently, most security properties of most cryptosystems were demonstrated using empirical techniques, or using ad hoc reasoning. Recently, there has been considerable effort to develop formal techniques for establishing the security of cryptosystems; this has been generally called provable security
Provable security
In cryptography, a system has provable security if its security requirements can be stated formally in an adversarial model, as opposed to heuristically, with clear assumptions that the adversary has access to the system as well as enough computational resources...

. The general idea of provable security is to give arguments about the computational difficulty needed to compromise some security aspect of the cryptosystem (i.e., to any adversary).

The study of how best to implement and integrate cryptography in software applications is itself a distinct field; see: Cryptographic engineering
Cryptographic engineering
Cryptographic engineering is the discipline of using cryptography to solve human problems. Cryptography is typically applied when trying to ensure data confidentiality, to authenticate people or devices, or to verify data integrity in risky environments....

 and Security engineering
Security engineering
Security engineering is a specialized field of engineering that focuses on the security aspects in the design of systems that need to be able to deal robustly with possible sources of disruption, ranging from natural disasters to malicious acts...

.

Prohibitions

Cryptography has long been of interest to intelligence gathering and law enforcement agencies
Law enforcement agency
In North American English, a law enforcement agency is a government agency responsible for the enforcement of the laws.Outside North America, such organizations are called police services. In North America, some of these services are called police while others have other names In North American...

. Secret communications may be criminal or even treason
Treason
In law, treason is the crime that covers some of the more extreme acts against one's sovereign or nation. Historically, treason also covered the murder of specific social superiors, such as the murder of a husband by his wife. Treason against the king was known as high treason and treason against a...

ous. Because of its facilitation of privacy
Privacy
Privacy is the ability of an individual or group to seclude themselves or information about themselves and thereby reveal themselves selectively...

, 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
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 significantly restricted the use of cryptography domestically, though it has relaxed many of these. In China
People's Republic of China
China , officially the People's Republic of China , is the most populous country in the world, with over 1.3 billion citizens. Located in East Asia, the country covers approximately 9.6 million square kilometres...

, 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
Belarus , officially the Republic of Belarus, is a landlocked country in Eastern Europe, bordered clockwise by Russia to the northeast, Ukraine to the south, Poland to the west, and Lithuania and Latvia to the northwest. Its capital is Minsk; other major cities include Brest, Grodno , Gomel ,...

, Kazakhstan
Kazakhstan
Kazakhstan , officially the Republic of Kazakhstan, is a transcontinental country in Central Asia and Eastern Europe. Ranked as the ninth largest country in the world, it is also the world's largest landlocked country; its territory of is greater than Western Europe...

, Mongolia
Mongolia
Mongolia is a landlocked country in East and Central Asia. It is bordered by Russia to the north and China to the south, east and west. Although Mongolia does not share a border with Kazakhstan, its western-most point is only from Kazakhstan's eastern tip. Ulan Bator, the capital and largest...

, Pakistan
Pakistan
Pakistan , officially the Islamic Republic of Pakistan is a sovereign state in South Asia. It has a coastline along the Arabian Sea and the Gulf of Oman in the south and is bordered by Afghanistan and Iran in the west, India in the east and China in the far northeast. In the north, Tajikistan...

, Singapore
Singapore
Singapore , officially the Republic of Singapore, is a Southeast Asian city-state off the southern tip of the Malay Peninsula, north of the equator. An island country made up of 63 islands, it is separated from Malaysia by the Straits of Johor to its north and from Indonesia's Riau Islands by the...

, Tunisia
Tunisia
Tunisia , officially the Tunisian RepublicThe long name of Tunisia in other languages used in the country is: , is the northernmost country in Africa. It is a Maghreb country and is bordered by Algeria to the west, Libya to the southeast, and the Mediterranean Sea to the north and east. Its area...

, and Vietnam
Vietnam
Vietnam – sometimes spelled Viet Nam , officially the Socialist Republic of Vietnam – is the easternmost country on the Indochina Peninsula in Southeast Asia. It is bordered by China to the north, Laos to the northwest, Cambodia to the southwest, and the South China Sea –...

.

In the United States
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...

, 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
Export of cryptography
The export of cryptography in the United States is the transfer from the United States to another country of devices and technology related to cryptography....

 and cryptographic software and hardware. Probably because of the importance of cryptanalysis in World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

 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
United States Munitions List
The United States Munitions List is a list of articles, services, and related technology designated as defense-related by the United States federal government. This designation is pursuant to sections 38 and 47 of the Arms Export Control Act...

. Until the development of the personal computer
Personal computer
A personal computer is any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator...

, asymmetric key algorithms (i.e., public key techniques), and the Internet
Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

, 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. As a result, export controls came to be seen to be an impediment to commerce and to research.

Export controls

In the 1990s, there were several challenges to US export regulations of cryptography. One involved Philip Zimmermann's Pretty Good Privacy
Pretty Good Privacy
Pretty Good Privacy is a data encryption and decryption computer program that provides cryptographic privacy and authentication for data communication. PGP is often used for signing, encrypting and decrypting texts, E-mails, files, directories and whole disk partitions to increase the security...

 (PGP) encryption program; it was released in the US, together with its source code
Source code
In computer science, source code is text written using the format and syntax of the programming language that it is being written in. Such a language is specially designed to facilitate the work of computer programmers, who specify the actions to be performed by a computer mostly by writing source...

, and found its way onto the Internet in June 1991. After a complaint by RSA Security
RSA Security
RSA, the security division of EMC Corporation, is headquartered in Bedford, Massachusetts, United States, and maintains offices in Australia, Ireland, Israel, the United Kingdom, Singapore, India, China, Hong Kong and Japan....

 (then called RSA Data Security, Inc., or RSADSI), Zimmermann was criminally investigated by the Customs Service and the FBI
Federal Bureau of Investigation
The Federal Bureau of Investigation is an agency of the United States Department of Justice that serves as both a federal criminal investigative body and an internal intelligence agency . The FBI has investigative jurisdiction over violations of more than 200 categories of federal crime...

 for several years. No charges were ever filed, however.
Also, Daniel Bernstein, then a graduate student at UC Berkeley, brought a lawsuit against the US government challenging some aspects of the restrictions based on free speech grounds. The 1995 case Bernstein v. United States
Bernstein v. United States
Bernstein v. United States is a set of court cases brought by Daniel J. Bernstein challenging restrictions on the export of cryptography from the 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
Freedom of speech is the freedom to speak freely without censorship. The term freedom of expression is sometimes used synonymously, but includes any act of seeking, receiving and imparting information or ideas, regardless of the medium used...

 by the United States Constitution.

In 1996, thirty-nine countries signed the Wassenaar Arrangement
Wassenaar Arrangement
The Wassenaar Arrangement is a multilateral export control regime with 40 participating states including many former COMECON countries.It is the successor to the Cold war-era Coordinating Committee for Multilateral Export Controls , and was...

, 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 are now much less strictly regulated than in the past as a consequence of a major relaxation in 2000; there are no longer very many restrictions on key sizes in US-exported
Export of cryptography
The export of cryptography in the United States is the transfer from the United States to another country of devices and technology related to cryptography....

 mass-market software. In practice today, since the relaxation in US export restrictions, and because almost every personal computer connected to the Internet
Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

, everywhere in the world, includes US-sourced web browser
Web browser
A web browser is a software application for retrieving, presenting, and traversing information resources on the World Wide Web. An information resource is identified by a Uniform Resource Identifier and may be a web page, image, video, or other piece of content...

s such as Firefox or Internet Explorer
Internet Explorer
Windows Internet Explorer is a series of graphical web browsers developed by Microsoft and included as part of the Microsoft Windows line of operating systems, starting in 1995. It was first released as part of the add-on package Plus! for Windows 95 that year...

, almost every Internet user worldwide has access to quality cryptography (i.e., when using sufficiently long keys with properly operating and unsubverted software, etc.) in their browsers; examples are Transport Layer Security
Transport Layer Security
Transport Layer Security and its predecessor, Secure Sockets Layer , are cryptographic protocols that provide communication security over the Internet...

 or SSL stack. The Mozilla Thunderbird
Mozilla Thunderbird
Mozilla Thunderbird is a free, open source, cross-platform e-mail and news client developed by the Mozilla Foundation. The project strategy is modeled after Mozilla Firefox, a project aimed at creating a web browser...

 and Microsoft Outlook
Microsoft Outlook
Microsoft Outlook is a personal information manager from Microsoft, available both as a separate application as well as a part of the Microsoft Office suite...

 E-mail client
E-mail client
An email client, email reader, or more formally mail user agent , is a computer program used to manage a user's email.The term can refer to any system capable of accessing the user's email mailbox, regardless of it being a mail user agent, a relaying server, or a human typing on a terminal...

 programs similarly can connect to IMAP or POP
Post Office Protocol
In computing, the Post Office Protocol is an application-layer Internet standard protocol used by local e-mail clients to retrieve e-mail from a remote server over a TCP/IP connection. POP and IMAP are the two most prevalent Internet standard protocols for e-mail retrieval. Virtually all modern...

 servers via TLS, and can send and receive email encrypted with S/MIME
S/MIME
S/MIME 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 RFCs. S/MIME was originally developed by RSA Data Security Inc...

. Many Internet users don't realize that their basic application software contains such extensive cryptosystem
Cryptosystem
There are two different meanings of the word cryptosystem. One is used by the cryptographic community, while the other is the meaning understood by the public.- General meaning :...

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
National Security Agency
The National Security Agency/Central Security Service is a cryptologic intelligence agency of the United States Department of Defense responsible for the collection and analysis of foreign communications and foreign signals intelligence, as well as protecting U.S...

 on cipher development and policy. NSA was involved with the design of DES
Data Encryption Standard
The Data Encryption Standard is a block cipher that uses shared secret encryption. It was selected by the National Bureau of Standards as an official Federal Information Processing Standard for the United States in 1976 and which has subsequently enjoyed widespread use internationally. It is...

 during its development at IBM
IBM
International Business Machines Corporation or IBM is an American multinational technology and consulting corporation headquartered in Armonk, New York, United States. IBM manufactures and sells computer hardware and software, and it offers infrastructure, hosting and consulting services in areas...

 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
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 an input can affect the resultant difference at the output...

, a powerful and general cryptanalytic technique known to NSA and IBM, that became publicly known only when it was rediscovered in the late 1980s. According to Steven Levy
Steven Levy
Steven Levy is an American journalist who has written several books on computers, technology, cryptography, the Internet, cybersecurity, and privacy.-Career:...

, IBM rediscovered differential cryptanalysis, but kept the technique secret at NSA's request. The technique became publicly known only when Biham and Shamir re-rediscovered 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 NSA's involvement was the 1993 Clipper chip
Clipper chip
The Clipper chip was a chipset that was developed and promoted by the U.S. National Security Agency as an encryption device to be adopted by telecommunications companies for voice transmission...

 affair, an encryption microchip intended to be part of the Capstone
Capstone (cryptography)
Capstone is the name of a United States government long-term project to develop cryptography standards for public and government use. Capstone was driven by the NIST and the NSA; the project began in 1993...

 cryptography-control initiative. Clipper was widely criticized by cryptographers for two reasons. The cipher algorithm was then classified (the cipher, called Skipjack
Skipjack (cipher)
In cryptography, Skipjack is a block cipher—an algorithm for encryption—developed by the U.S. National Security Agency . Initially classified, it was originally intended for use in the controversial Clipper chip...

, though it was declassified in 1998 long after the Clipper initiative lapsed). The secret cipher caused concerns that 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
Key escrow
Key escrow is an arrangement in which the keys needed to decrypt encrypted data are held in escrow so that, under certain circumstances, an authorized third party may gain access to those keys...

 held by the government for use by law enforcement, for example in wiretaps.

Digital rights management

Cryptography is central to digital rights management (DRM), a group of techniques for technologically controlling use of copyright
Copyright
Copyright is a legal concept, enacted by most governments, giving the creator of an original work exclusive rights to it, usually for a limited time...

ed material, being widely implemented and deployed at the behest of some copyright holders. In 1998, American President Bill Clinton
Bill Clinton
William Jefferson "Bill" Clinton is an American politician who served as the 42nd President of the United States from 1993 to 2001. Inaugurated at age 46, he was the third-youngest president. He took office at the end of the Cold War, and was the first president of the baby boomer generation...

 signed the Digital Millennium Copyright Act
Digital Millennium Copyright Act
The Digital Millennium Copyright Act is a United States copyright law that implements two 1996 treaties of the World Intellectual Property Organization . It criminalizes production and dissemination of technology, devices, or services intended to circumvent measures that control access to...

 (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, or might violate, 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
World Intellectual Property Organization
The World Intellectual Property Organization is one of the 17 specialized agencies of the United Nations. WIPO was created in 1967 "to encourage creative activity, to promote the protection of intellectual property throughout the world"....

 member-states.

The United States Department of Justice
United States Department of Justice
The United States Department of Justice , is the United States federal executive department responsible for the enforcement of the law and administration of justice, equivalent to the justice or interior ministries of other countries.The Department is led by the Attorney General, who is nominated...

 and FBI
Federal Bureau of Investigation
The Federal Bureau of Investigation is an agency of the United States Department of Justice that serves as both a federal criminal investigative body and an internal intelligence agency . The FBI has investigative jurisdiction over violations of more than 200 categories of federal crime...

 have not enforced the DMCA as rigorously as had been feared by some, but the law, nonetheless, remains a controversial one. Niels Ferguson
Niels Ferguson
Niels T. Ferguson is a Dutch cryptographer and consultant who currently works for Microsoft. He has worked with others, including Bruce Schneier, designing cryptographic algorithms, testing algorithms and protocols, and writing papers and books...

, a well-respected cryptography researcher, has publicly stated that he will not release some of his research into an Intel
Intel Corporation
Intel Corporation is an American multinational semiconductor chip maker corporation headquartered in Santa Clara, California, United States and the world's largest semiconductor chip maker, based on revenue. It is the inventor of the x86 series of microprocessors, the processors found in most...

 security design for fear of prosecution under the DMCA. Both Alan Cox
Alan Cox
Alan Cox is a British computer programmer who formerly maintained the 2.2 branch of the Linux kernel and continues to be heavily involved in the development of the Linux kernel, an association that dates back to 1991...

 (longtime number 2 in Linux kernel
Linux kernel
The Linux kernel is an operating system kernel used by the Linux family of Unix-like operating systems. It is one of the most prominent examples of free and open source software....

 development) and Professor Edward Felten
Edward Felten
Edward William Felten is a professor of computer science and public affairs at Princeton University. On November 4, 2010 he was named the Chief Technologist for the United States Federal Trade Commission, a position he officially assumed January 3, 2011.Felten has done a variety of computer...

 (and some of his students at Princeton) have encountered problems related to the Act. Dmitry Sklyarov
Dmitry Sklyarov
Dmitry Vitalevich Sklyarov is a Russian computer programmer known for his 2001 arrest by American law enforcement over software copyright restrictions under the DMCA anti-circumvention provision...

 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
HD DVD
HD DVD is a discontinued high-density optical disc format for storing data and high-definition video.Supported principally by Toshiba, HD DVD was envisioned to be the successor to the standard DVD format...

 content scrambling were discovered and released
AACS encryption key controversy
A controversy surrounding the AACS cryptographic key arose in April 2007 when the Motion Picture Association of America and the Advanced Access Content System Licensing Administrator, LLC began issuing demand letters to websites publishing a 128-bit number, represented in hexadecimal as 09 F9 11...

 onto the Internet
Internet
The Internet is a global system of interconnected computer networks that use the standard Internet protocol suite to serve billions of users worldwide...

. In both cases, the MPAA 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
Fair use is a limitation and exception to the exclusive right granted by copyright law to the author of a creative work. In United States copyright law, fair use is a doctrine that permits limited use of copyrighted material without acquiring permission from the rights holders...

 and free speech.

See also

  • Steganography
    Steganography
    Steganography is the art and science of writing hidden messages in such a way that no one, apart from the sender and intended recipient, suspects the existence of the message, a form of security through obscurity...

  • Encyclopedia of Cryptography and Security
    Encyclopedia of Cryptography and Security
    The Encyclopedia of Cryptography and Security is a comprehensive work on Cryptography for both information security professionals and experts in the fields of Computer Science, Applied Mathematics, Engineering, Information Theory, Data Encryption, etc . It consists of 460 articles in alphabetical...

  • Intypedia
    Intypedia
    Intypedia is an educational non-profit project developed by the Technical University of Madrid. It’s a visual encyclopedia on information security. The aim of this Project is to spread knowledge of this topic through a series of videos created by renowned experts, while using a language that is...

  • Outline of cryptography
    Outline of cryptography
    The following outline is provided as an overview of and topical guide to cryptography:Cryptography – practice and study of hiding information. Modern cryptography intersects the disciplines of mathematics, computer science, and engineering...

  • Strong secrecy
    Strong secrecy
    Strong secrecy is a term used in cryptography. Bruno Blanchet provides the following definition:For example if a process encrypts a message m an attacker can differentiate between different messages, since their ciphertexts will be different. Thus m is not a strong secret. If however, probabilistic...

    , a term used in cryptography
  • Cryptography laws in different nations
    Cryptography laws in different nations
    Cryptography is the practice and study of hiding information. There are many different cryptography laws in different nations. Some countries prohibit export of cryptography software and/or encryption algorithms or cryptoanalysis methods. In some countries a license is required to use encryption...


  • Books on cryptography
    Books on cryptography
    Books on cryptography have been published sporadically and with highly variable quality for a long time. This is despite the tempting, though superficial, paradox that secrecy is of the essence in sending confidential messages — see Kerckhoffs' principle....


:Category:Cryptographers
  • List of cryptographers
  • List of important publications in networks and security
  • List of multiple discoveries (see "RSA")
  • List of unsolved problems in computer science

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
    CrypTool is an open source e-learning tool illustrating cryptographic concepts.-Features:The graphical interface, online documentation, analytic tools and algorithms of CrypTool introduce users to the field of cryptography...

    , PDF download. CyrpTool is the most widespread e-learning program about cryptography and cryptanalysis, open source.
  • In Code: A Mathematical Journey by Sarah Flannery
    Sarah Flannery
    Sarah Flannery was, at sixteen years old, the winner of the 1999 Esat Young Scientist Exhibition for development of the Cayley–Purser algorithm, based on work she had done with researchers at Baltimore Technologies during a brief internship there...

     (with David Flannery). Popular account of Sarah's award-winning project on public-key cryptography, co-written with her father.
  • James Gannon
    James Gannon
    James Gannon is a freelance writer and producer of documentaries for NBC News. He has published articles in a variety of subjects and venues....

    , Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century, Washington, D.C., Brassey's, 2001, ISBN 1-57488-367-4.
  • Oded Goldreich
    Oded Goldreich
    Oded Goldreich is a professor of Computer Science at the Faculty of Mathematics and Computer Science of Weizmann Institute of Science, Israel. His research interests lie within the theory of computation...

    , Foundations of Cryptography, in two volumes, Cambridge University Press, 2001 and 2004.
  • Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell.
  • Alvin's Secret Code by Clifford B. Hicks
    Clifford B. Hicks
    Clifford B. Hicks was an American writer and magazine editor, best known for his children's books chronicling the adventures of Alvin Fernald.-Biography:...

     (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.
  • Handbook of Applied Cryptography by A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone CRC Press, (PDF download available), somewhat more mathematical than Schneier's Applied Cryptography.
  • 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
    Phillip Rogaway
    Phillip Rogaway is a professor of computer science at the University of California, Davis. He graduated with an BA in computer science from UC Berkeley and completed his PhD in cryptography at MIT, in the Theory of Computation group. He has taught at UC Davis since 1994.Dr...

     and Mihir Bellare
    Mihir Bellare
    Mihir Bellare is a cryptographer and professor at the University of California, San Diego. He has published several seminal papers in the field of cryptography , many coauthored with Phillip Rogaway. Bellare has published a number of papers in the field of Format-Preserving Encryption...

    , 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 ISBN 978-1-907934-01-8.


External links

The source of this article is wikipedia, the free encyclopedia.  The text of this article is licensed under the GFDL.
 
x
OK