The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages

Cryptography (or cryptology; derived from Greek κρύπτω krýpto "hidden" and the verb γράφω gráfo "to write" or λέγειν legein "to speak")^[1] is the practice and study of hiding information. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. "Tunny" redirects here For the fish see Tuna. The Lorenz SZ 40 and SZ 42 ( Schlüsselzusatz, meaning World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly In modern times, cryptography is considered to be a branch of both mathematics and computer science, and is affiliated closely with information theory, computer security, and engineering. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. This article describes how security can be achieved through design and engineering Engineering is the Discipline and Profession of applying technical and scientific Knowledge and Cryptography is used in applications present in technologically advanced societies; examples include the security of ATM cards, computer passwords, and electronic commerce, which all depend on cryptography. In computing a password is a Word or string of characters that is entered often along with a user name, in modern times usually into a computer system Electronic commerce, commonly known as e-commerce' or eCommerce, consists of the buying and selling of products or services over electronic

Terminology

Until modern times, cryptography referred almost exclusively to encryption, the process of converting ordinary information (plaintext) into unintelligible gibberish (i. In Cryptography, plaintext is the information which the sender wishes to transmit to the receiver(s e. , ciphertext). ^[2] Decryption is the reverse, moving from unintelligible ciphertext to plaintext. In Cryptography, plaintext is the information which the sender wishes to transmit to the receiver(s A cipher (or cypher) is a pair of algorithms which creates the encryption and the reversing decryption. In Cryptography, a cipher (or cypher) is an Algorithm for performing Encryption and Decryption &mdash a series of well-defined steps In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation The detailed operation of a cipher is controlled both by the algorithm and, in each instance, by a key. In Cryptography, a key is a piece of information (a Parameter) that determines the functional output of a cryptographic algorithm This is a secret parameter (ideally, known only to the communicants) for a specific message exchange context. Keys are important, as ciphers without variable keys are trivially breakable and therefore less than useful 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" is often used to mean any method of encryption or concealment of meaning. A colloquialism is an expression not used in formal speech, writing or Paralinguistics. 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 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 (for example, apple pie replaces attack at dawn). In Telecommunication, a code word is an element of a Code. Each code word is a Sequence of symbols assembled in accordance with the specific rules of 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 better adapted to computers as well.

Some use the terms cryptography and cryptology interchangeably in English, while others 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. ^[3][4]

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

History of cryptography and cryptanalysis

The Ancient Greek scytale (rhymes with Italy), probably much like this modern reconstruction, may have been one of the earliest devices used to implement a cipher. This article is about the encryption device for the Dune character see Scytale (Dune.

Main article: History of cryptography

Before the modern era, cryptography was concerned solely with message confidentiality (i. The history of Cryptography begins thousands of years ago Until recent decades it has been the story of what might be called classic cryptography — that is of e. , encryption) — conversion of messages from a comprehensible form into an incomprehensible one, and back again at the other end, rendering it unreadable by interceptors or eavesdroppers without secret knowledge (namely, the key needed for decryption of that message). Information as a concept has a diversity of meanings from everyday usage to technical settings In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication, digital signatures, interactive proofs, and secure computation, amongst others. Authentication (from Greek αυθεντικός real or genuine from authentes author is the act of establishing or confirming something (or someone as A digital signature or digital signature scheme is a type of asymmetric cryptography used to simulate the security properties of a handwritten Signature In Cryptography, secure multi-party computation is a problem that was initially suggested by Andrew C

The earliest forms of secret writing required little more than local pen and paper analogs, as most people could not read. More literacy, or opponent literacy, required actual cryptography. The main classical cipher types are transposition ciphers, which rearrange the order of letters in a message (e. In classical Cryptography, a transposition cipher changes one character from the Plaintext to another (to decrypt the reverse is done g. , 'help me' becomes 'ehpl em' in a trivially simple rearrangement scheme), and substitution ciphers, which systematically replace letters or groups of letters with other letters or groups of letters (e. In Cryptography, a substitution cipher is a method of Encryption by which units of plaintext are substituted with Ciphertext according to a regular system g. , 'fly at once' becomes 'gmz bu podf' by replacing each letter with the one following it in the English alphabet). Simple versions of either offered little confidentiality from enterprising opponents, and still don't. An early substitution cipher was the Caesar cipher, in which each letter in the plaintext was replaced by a letter some fixed number of positions further down the alphabet. 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 It was named after Julius Caesar who is reported to have used it, with a shift of 3, to communicate with his generals during his military campaigns, just like EXCESS-3 code in boolean algebra. Excess-3 Binary coded decimal (XS-3 also called biased representation or Excess-N, is a Numeral system used on some older computers that uses

Encryption attempts to ensure secrecy in communications, such as those of spies, military leaders, and diplomats. Diplomacy is the art and practice of conducting Negotiations between representatives of groups or states There is record of several early Hebrew ciphers as well. Cryptography is recommended in the Kama Sutra as a way for lovers to communicate without inconvenient discovery. The Kama Sutra ( Sanskrit: कामसूत्र (alternative spellings Kamasutram or simply Kamasutra) is an ancient Indian ^[5] Steganography (i. Steganography is the art and science of writing hidden messages in such a way that no one apart from the sender and intended recipient even realizes there is a hidden message 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, concealed a message - a tattoo on a slave's shaved head - under the regrown hair. Herodotus of Halicarnassus ( Greek: Hēródotos Halikarnāsseús) was a Greek Historian who lived in the 5th century BC ( 484 BC&ndash ^[2] More modern examples of steganography include the use of invisible ink, microdots, and digital watermarks to conceal information. Invisible ink is a substance used for writing which is either invisible on application or soon thereafter and which later on can be made visible by some means A microdot is text or an image substantially reduced in size onto a 1mm disc to prevent detection by unintended recipients Digital watermarking is the process of embedding information into a digital signal

Ciphertexts produced by classical ciphers (and some modern ones) always reveal statistical information about the plaintext, which can often be used to break them. After the discovery of frequency analysis (perhaps by the Arab polymath al-Kindi) in the 9th century, nearly all such ciphers became more or less readily breakable by an informed attacker. In Cryptanalysis, frequency analysis is the study of the frequency of letters or groups of letters in a Ciphertext. The araB gene Promoter is a bacterial promoter activated by e L-arabinose binding A polymath ( Greek polymathēs, πολυμαθής "having learned much" is a person whose knowledge is not restricted to one subject area ( أبو يوسف يعقوب إبن إسحاق الكندي) (c Such classical ciphers still enjoy popularity today, though mostly as puzzles (see cryptogram). A puzzle is a Problem or Enigma that challenges Ingenuity. In a basic puzzle one is intended to piece together objects in a logical way in order to A cryptogram is a type of puzzle which consists of a short piece of encrypted text Essentially all ciphers remained vulnerable to cryptanalysis using this technique until the invention of the polyalphabetic cipher, most clearly by Leon Battista Alberti around the year 1467 (though there is some indication of earlier Arab knowledge of them). A polyalphabetic cipher is any cipher based on substitution, using multiple substitution alphabets Leon Battista Alberti ( February 14, 1404 &ndash April 25, 1472) was an Italian author artist Architect, Poet Alberti's innovation was to use different ciphers (i. e. , substitution alphabets) for various parts of a message (perhaps for each successive plaintext letter in the limit). He also invented what was probably the first automatic cipher device, a wheel which implemented a partial realization of his invention. 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 In the polyalphabetic Vigenère cipher, encryption uses a key word, which controls letter substitution depending on which letter of the key word is used. 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 In the mid 1800s Babbage showed that polyalphabetic ciphers of this type remained partially vulnerable to frequency analysis techniques. ^[2]

The Enigma machine, used in several variants by the German military between the late 1920s and the end of World War II, implemented a complex electro-mechanical polyalphabetic cipher to protect sensitive communications. The Enigma machine is any one of a family of related electro-mechanical Rotor machines used to generate Ciphers for the Encryption and decryption of World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including In Cryptography, a cipher (or cypher) is an Algorithm for performing Encryption and Decryption &mdash a series of well-defined steps Breaking the Enigma cipher at the Biuro Szyfrów, and the subsequent large-scale decryption of Enigma traffic at Bletchley Park, was an important factor contributing to the Allied victory in WWII. The Enigma machines were a family of portable Cipher machines The Biuro Szyfrów ( Polish for " Cipher Bureau " was the Polish Interwar agency charged with both Cryptography (the Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes ^[2]

Although frequency analysis is a powerful and general technique, encryption was still often effective in practice; many a would-be cryptanalyst was unaware of the technique. Breaking a message without frequency analysis essentially required knowledge of the cipher used, thus encouraging espionage, bribery, burglary, defection, etc. to discover it. It was finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible or practical safeguard; in fact, it was further realized any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary fully understands the cipher algorithm itself. Secrecy of the key should alone be sufficient for a good cipher to maintain confidentiality under attack. This fundamental principle was first explicitly stated in 1883 by Auguste Kerckhoffs and is generally called Kerckhoffs' principle; alternatively and more bluntly, it was restated by Claude Shannon as Shannon's Maxim — 'the enemy knows the system'. Dr Auguste Kerckhoffs ( 19 January 1835 – 9 August 1903) was a Dutch linguist and Cryptographer who was In Cryptography, Kerckhoffs' principle (also called Kerckhoffs' assumption, axiom or law) was stated by Auguste Kerckhoffs in Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information

Various physical devices and aids have been used to assist with ciphers. One of the earliest may have been the scytale of ancient Greece, a rod supposedly used by the Spartans as an aid for a transposition cipher. This article is about the encryption device for the Dune character see Scytale (Dune. The term ancient Greece refers to the period of Greek history lasting from the Greek Dark Ages ca In medieval times, other aids were invented such as the cipher grille, also used for a kind of steganography. 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 (of paper With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's own cipher disk, Johannes Trithemius' tabula recta scheme, and Thomas Jefferson's multi-cylinder (reinvented independently by Bazeries around 1900). A cipher disk is an Enciphering and Deciphering tool developed in the 15th century by Leon Battista Alberti. Johannes Trithemius ( 1 February 1462 - 13 December 1516) was born Johann Heidenberg. 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 Thomas Jefferson (April 13 1743 – July 4 1826 was the third President of the United States (1801–1809 the principal author of the Declaration of Independence The Jefferson disk, or wheel cypher as Jefferson named it is a Cipher system using 26 wheels each with the letters of the alphabet arranged randomly around them Étienne Bazeries ( 21 August 1846 - 7 November 1931) was a French military Cryptanalyst Several mechanical encryption/decryption devices were invented early in the 20th century, and many patented, among them rotor machines — most famously the Enigma machine used by Germany from the late 20s and in World War II. In Cryptography, a rotor machine is an electro-mechanical device used for encrypting and decrypting secret messages The Enigma machine is any one of a family of related electro-mechanical Rotor machines used to generate Ciphers for the Encryption and decryption of World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including ^[6] The ciphers implemented by better quality examples of these designs brought about a substantial increase in cryptanalytic difficulty after WWI. ^[7]

The development of digital computers and electronics after WWII made possible much more complex ciphers. Electronics refers to the flow of charge (moving Electrons through Nonmetal conductors (mainly Semiconductors, whereas electrical Furthermore, computers allowed for the encryption of any kind of data represented by computers in any binary format, unlike classical ciphers which only encrypted written language texts, thus dissolving much of the utility of a linguistic approach to cryptanalysis. Many computer ciphers can be characterized by their operation on binary bit sequences (sometimes in groups or blocks), unlike classical and mechanical schemes, which generally manipulate traditional characters (i. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication 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), while breaking it requires an effort many orders of magnitude larger than before, making cryptanalysis so inefficient and impractical as to be effectively impossible.

A credit card with smart card capabilities. A smart card, chip card, or Integrated circuit card ( ICC) is any pocket-sized card with embedded integrated The 3 by 5 mm chip embedded in the card is shown enlarged in the insert. Smart cards attempt to combine portability with the power to compute modern cryptographic algorithms.

Extensive open academic research into cryptography is relatively recent — it began only in the mid-1970s with the public specification of DES (the Data Encryption Standard) by the US Government's National Bureau of Standards, the Diffie-Hellman paper,^[8] and the public release of the RSA algorithm. The Data Encryption Standard ( DES) is a Cipher (a method for Encrypting information selected by NBS as an official Federal Information Diffie-Hellman key exchange ( D-H) is a Cryptographic protocol that allows two parties that have no prior knowledge of each other to jointly establish a shared secret In Cryptography, RSA is an Algorithm for Public-key cryptography. Since then, cryptography has become a widely used tool in communications, computer networks, and computer security generally. A computer network is a group of interconnected Computers. Networks may be classified according to a wide variety of characteristics The present security level of many modern cryptographic techniques is based on the difficulty of certain computational problems, such as the integer factorisation or the discrete logarithm problems. In Mathematics, specifically in Abstract algebra and its applications discrete logarithms are group-theoretic analogues of ordinary Logarithms In many cases, there are proofs that cryptographic techniques are secure if a certain computational problem cannot be solved efficiently. ^[3] With one notable exception -— the one-time pad —- these proofs are contingent, and thus not definitive, but are currently the best available for cryptographic algorithms and protocols. In Cryptography, the one-time pad (OTP is an Encryption Algorithm where the Plaintext is combined with a random key or "pad"

As well as being aware of cryptographic history, cryptographic algorithm and system designers must also sensibly consider probable future developments in their designs. For instance, continuous improvements in computer processing power have increased the scope of brute-force attacks, thus when specifying key lengths, the standard is similarly advancing. In Cryptanalysis, a brute force attack is a method of defeating a Cryptographic scheme by trying a large number of possibilities for example possible keys In Cryptography, key size or key length is the size (usually measured in bits or bytes of the key used in a cryptographic algorithm (such as a Cipher The potential effects of quantum computing are already being considered by some cryptographic system designers; the announced imminence of small implementations of these machines is making the need for this preemptive caution fully explicit. A quantum computer is a device for Computation that makes direct use of distinctively Quantum mechanical Phenomena, such as superposition ^[9]

Essentially, prior to the early 20th century, cryptography was chiefly concerned with linguistic patterns. A language is a dynamic set of visual auditory or tactile Symbols of Communication and the elements used to manipulate them Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory, computational complexity, statistics, combinatorics, abstract algebra, and number theory. Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. Computational complexity theory, as a branch of the Theory of computation in Computer science, investigates the problems related to the amounts of resources Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. Combinatorics is a branch of Pure mathematics concerning the study of discrete (and usually finite) objects Abstract algebra is the subject area of Mathematics that studies Algebraic structures such as groups, rings, fields, modules Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes Cryptography is also a branch of engineering, but an unusual one as it deals with active, intelligent, and malevolent opposition (see cryptographic engineering and security engineering); most other kinds of engineering need deal only with neutral natural forces. Engineering is the Discipline and Profession of applying technical and scientific Knowledge and Cryptographic Engineering is the discipline of using cryptography to solve human problems Security engineering is a specialized field of Engineering that deals with the development of detailed engineering plans and designs for security features controls and systems There is also active research examining the relationship between cryptographic problems and quantum physics (see quantum cryptography and quantum computing). Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Quantum cryptography, or quantum key distribution (QKD uses Quantum mechanics to guarantee secure communication A quantum computer is a device for Computation that makes direct use of distinctively Quantum mechanical Phenomena, such as superposition

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. This article is intended to be an 'analytic glossary' or alternatively an organized collection of annotated pointers

Symmetric-key cryptography

Main article: Symmetric key algorithm

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). Symmetric-key algorithms are a class of Algorithms for Cryptography that use trivially related often identical Cryptographic keys for both decryption This was the only kind of encryption publicly known until June 1976. ^[8]

One round (out of 8. 5) of the patented IDEA cipher, used in some versions of PGP for high-speed encryption of, for instance, e-mail

The modern study of symmetric-key ciphers relates mainly to the study of block ciphers and stream ciphers and to their applications. A patent is a set of Exclusive rights granted by a State to an inventor or his assignee for a fixed period of time in exchange for a disclosure of an In Cryptography, the International Data Encryption Algorithm ( IDEA) is a Block cipher designed by Xuejia Lai and James Massey Pretty Good Privacy (PGP is a Computer program that provides Cryptographic Privacy and Authentication. Electronic mail, often abbreviated to e-mail, email, or originally eMail, is a Store-and-forward method of writing sending receiving In Cryptography, a block cipher is a symmetric key Cipher which operates on fixed-length groups of Bits termed blocks, with an In Cryptography, a stream cipher is a symmetric key Cipher where plaintext bits are combined with a Pseudorandom cipher bit stream ( Keystream A block cipher is, in a sense, a modern embodiment of Alberti's polyalphabetic cipher: block ciphers take as input a block of plaintext and a key, and output a block of ciphertext of the same size. Since messages are almost always longer than a single block, some method of knitting together successive blocks is required. Several have been developed, some with better security in one aspect or another than others. They are the mode of operations and must be carefully considered when using a block cipher in a cryptosystem.

The Data Encryption Standard (DES) and the Advanced Encryption Standard (AES) are block cipher designs which have been designated cryptography standards by the US government (though DES's designation was finally withdrawn after the AES was adopted). The Data Encryption Standard ( DES) is a Cipher (a method for Encrypting information selected by NBS as an official Federal Information In Cryptography, the Advanced Encryption Standard ( AES) also known as Rijndael, is a Block cipher adopted as an Encryption There are a number of standards related to Cryptography. Standard algorithms and protocols provide a focus for study standards for popular applications attract a ^[10] 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^[11] to e-mail privacy^[12] and secure remote access. In Cryptography, Triple DES is a Block cipher formed from the Data Encryption Standard (DES Cipher by using it three times The protection of electronic mail from unauthorized access and inspection is known as electronic privacy. ^[13] Many other block ciphers have been designed and released, with considerable variation in quality. Many have been thoroughly broken. See Category:Block ciphers. ^[9][14]

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. In Cryptography, the one-time pad (OTP is an Encryption Algorithm where the Plaintext is combined with a random key or "pad" In a stream cipher, the output stream is created based on an internal state which changes as the cipher operates. That state change is controlled by the key, and, in some stream ciphers, by the plaintext stream as well. RC4 is an example of a well-known, and widely used, stream cipher; see Category:Stream ciphers. In Cryptography, RC4 (also known as ARC4 or ARCFOUR meaning Alleged RC4 see below is the most widely-used software ^[9]

Cryptographic hash functions (often called message digest functions) do not necessarily use keys, but are a related and important class of cryptographic algorithms. A cryptographic Hash function is a transformation that takes an input (or 'message' and returns a fixed-size string which is called the hash value (sometimes They take input data (often an entire message), and output a short, fixed length hash, and do so as a one-way function. A hash function is any well-defined procedure or mathematical function for turning some kind of Data into a relatively small integer, that may For good ones, collisions (two plaintexts which produce the same hash) are extremely difficult to find.

Message authentication codes (MACs) are much like cryptographic hash functions, except that a secret key is used to authenticate the hash value^[9] on receipt. A cryptographic message authentication code (MAC is a short piece of information used to Authenticate a message These block an attack against plain hash functions.

Public-key cryptography

Main article: 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. Public-key cryptography, also known as asymmetric cryptography, is a form of Cryptography in which the key used to encrypt a message differs from the key A significant disadvantage of symmetric ciphers is the key management necessary to use them securely. Key management is a term used to describe two different fields (1 Cryptography, and (2 physical key management (or Electronic key management) within building or 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. In Algebra, the square of a number is that number multiplied by itself The difficulty of securely establishing a secret key between two communicating parties, when a secure channel doesn't 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 Cryptography, a secure channel is a way of transferring data that is resistant to interception and tampering The chicken or the egg Causality dilemma is commonly stated as "which came first the Chicken or the egg ?" Chickens hatch from eggs

Whitfield Diffie and Martin Hellman, publishers of the first paper on public-key cryptography

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. Bailey Whitfield 'Whit' Diffie (born June 5 1944) is a US Cryptographer and one of the pioneers of Public-key cryptography. Martin Edward Hellman (born October 2, 1945) is a cryptologist, famous for his invention of Public key cryptography in cooperation with Bailey Whitfield 'Whit' Diffie (born June 5 1944) is a US Cryptographer and one of the pioneers of Public-key cryptography. Martin Edward Hellman (born October 2, 1945) is a cryptologist, famous for his invention of Public key cryptography in cooperation with ^[15] 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. ^[16] The historian David Kahn described public-key cryptography as "the most revolutionary new concept in the field since polyalphabetic substitution emerged in the Renaissance". David Kahn (b February 7, 1930) is a US Historian, Journalist and Writer. ^[17]

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. Diffie-Hellman key exchange ( D-H) is a Cryptographic protocol that allows two parties that have no prior knowledge of each other to jointly establish a shared secret ^[8]

In 1978, Ronald Rivest, Adi Shamir, and Len Adleman invented RSA, another public-key system. Ronald Linn Rivest (born 1947, Schenectady, New York) is a cryptographer. Adi Shamir (עדי שמיר born 1952 is an Israeli cryptographer. Leonard Max Adleman (born December 31, 1945) is a theoretical computer scientist and professor of Computer science and Molecular biology In Cryptography, RSA is an Algorithm for Public-key cryptography. ^[18]

In 1997, it finally became publicly known that asymmetric key cryptography had been invented by James H. Ellis at GCHQ, a British intelligence organization, and that, in the early 1970s, both the Diffie-Hellman and RSA algorithms had been previously developed (by Malcolm J. Williamson and Clifford Cocks, respectively). James H Ellis (1924&ndashNovember 1997 was an Engineer and Mathematician. The Government Communications Headquarters (GCHQ is a British Intelligence agency responsible for providing Signals intelligence (SIGINT and Information The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located Malcolm J Williamson discovered in 1974 what is now known as Diffie-Hellman key exchange. Clifford Christopher Cocks, CB, (born 1951 is a British Mathematician and Cryptographer at GCHQ who invented the widely-used encryption algorithm ^[19]

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. In Cryptography, RSA is an Algorithm for Public-key cryptography. Others include the Cramer-Shoup cryptosystem, ElGamal encryption, and various elliptic curve techniques. The Cramer-Shoup system is an Asymmetric key encryption algorithm, and was the first efficient scheme proven to be secure against Adaptive chosen ciphertext attack In Cryptography, the ElGamal encryption system is an Asymmetric key encryption algorithm for Public-key cryptography which is based on the Diffie-Hellman Elliptic curve cryptography (ECC is an approach to Public-key cryptography based on the algebraic structure of Elliptic curves over Finite fields The use See Category:Asymmetric-key cryptosystems.

Padlock icon from the Firefox Web browser, meant to indicate a page has been sent in SSL or TLS-encrypted protected form. However, such an icon is not a guarantee of security; any subverted browser might mislead a user by displaying such an icon when a transmission is not actually being protected by SSL or TLS.

In addition to encryption, public-key cryptography can be used to implement digital signature schemes. A digital signature or digital signature scheme is a type of asymmetric cryptography used to simulate the security properties of a handwritten Signature A digital signature is reminiscent of an ordinary signature; they both have the characteristic that they are easy for a user to produce, but difficult for anyone else to forge. A signature (from Latin signare, " Sign " is a handwritten (and sometimes stylized depiction of someone's name nickname or even a simple Forgery is the process of making adapting or imitating objects statistics or documents (see False document) with the intent to deceive. Digital signatures can also be permanently tied to the content of the message being signed; they cannot then be 'moved' from one document to another, for any attempt will be detectable. In digital signature schemes, there are two algorithms: one for signing, in which a secret key is used to process the message (or a hash of the message, or both), and one for verification, in which the matching public key is used with the message to check the validity of the signature. RSA and DSA are two of the most popular digital signature schemes. In Cryptography, RSA is an Algorithm for Public-key cryptography. The Digital Signature Algorithm (DSA is a United States Federal Government standard or FIPS for Digital signatures It was proposed by the Digital signatures are central to the operation of public key infrastructures and many network security schemes (eg, SSL/TLS, many VPNs, etc). In Cryptography, a public key infrastructure ( PKI) is an arrangement that binds Public keys with respective user identities by means of a Certificate Transport Layer Security ( TLS) and its predecessor Secure Sockets Layer ( SSL) are Cryptographic protocols that provide secure ^[14]

Public-key algorithms are most often based on the computational complexity of "hard" problems, often from number theory. Computational complexity theory, as a branch of the Theory of computation in Computer science, investigates the problems related to the amounts of resources Number theory is the branch of Pure mathematics concerned with the properties of Numbers in general and Integers in particular as well as the wider classes For example, the hardness of RSA is related to the integer factorization problem, while Diffie-Hellman and DSA are related to the discrete logarithm problem. In Mathematics, specifically in Abstract algebra and its applications discrete logarithms are group-theoretic analogues of ordinary Logarithms More recently, elliptic curve cryptography has developed in which security is based on number theoretic problems involving elliptic curves. Elliptic curve cryptography (ECC is an approach to Public-key cryptography based on the algebraic structure of Elliptic curves over Finite fields The use In Mathematics, an elliptic curve is a smooth, projective Algebraic curve of genus one on which there is a specified point O Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular multiplication and exponentiation, which are much more computationally expensive than the techniques used in most block ciphers, especially with typical key sizes. In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers As a result, public-key cryptosystems are commonly hybrid cryptosystems, in which a fast high-quality symmetric-key encryption algorithm is used for the message itself, while the relevant symmetric key is sent with the message, but encrypted using a public-key algorithm. 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 (among Similarly, hybrid signature schemes are often used, in which a cryptographic hash function is computed, and only the resulting hash is digitally signed. ^[9]

Cryptanalysis

Main article: Cryptanalysis

The goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion. Cryptanalysis (from the Greek kryptós, "hidden" and analýein, "to loosen" or "to untie" is the study of methods for

It is a commonly held misconception that every encryption method can be broken. In connection with his WWII work at Bell Labs, Claude Shannon proved that the one-time pad cipher is unbreakable, provided the key material is truly random, never reused, kept secret from all possible attackers, and of equal or greater length than the message. Bell Laboratories (also known as Bell Labs and formerly known as AT&T Bell Laboratories and Bell Telephone Laboratories) is the Research organization Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information In Cryptography, the one-time pad (OTP is an Encryption Algorithm where the Plaintext is combined with a random key or "pad" Random number may refer to A number generated for or part of a set exhibiting Statistical randomness. ^[20] Most ciphers, apart from the one-time pad, can be broken with enough computational effort by brute force attack, but the amount of effort needed may be exponentially dependent on the key size, as compared to the effort needed to use the cipher. In Cryptanalysis, a brute force attack is a method of defeating a Cryptographic scheme by trying a large number of possibilities for example possible keys In complexity theory, exponential time is the Computation time of a problem where the time to complete the computation m ( n) is bounded by an 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 showing can be made currently, as of today, 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, the cryptanalyst has access only to the ciphertext (good modern cryptosystems are usually effectively immune to ciphertext-only attacks). In Cryptography, a ciphertext-only attack (COA or known ciphertext attack is an Attack model for Cryptanalysis where the attacker is assumed In a known-plaintext attack, the cryptanalyst has access to a ciphertext and its corresponding plaintext (or to many such pairs). The known-plaintext attack (KPA is an Attack model for Cryptanalysis where the attacker has samples of both the Plaintext and its encrypted In a chosen-plaintext attack, the cryptanalyst may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example is gardening, used by the British during WWII. A chosen-plaintext attack (CPA is an Attack model for Cryptanalysis which presumes that the attacker has the capability to choose arbitrary Plaintexts In Cryptanalysis, gardening was a term used at Bletchley Park during World War II for schemes to entice the Germans to include Known plaintext Bletchley Park, also known as Station X, is an estate located in the town of Bletchley, in Buckinghamshire, and (since 1967 part of Milton Keynes Finally, in a chosen-ciphertext attack, the cryptanalyst may be able to choose ciphertexts and learn their corresponding plaintexts. A chosen-ciphertext attack (CCA is an Attack model for Cryptanalysis in which the cryptanalyst gathers information at least in part by choosing a Ciphertext ^[9] Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of the protocols involved; see Cryptanalysis of the Enigma for some historical examples of this). A security protocol ( cryptographic protocol or encryption protocol) is an abstract or concrete protocol that performs a security -related function The Enigma machines were a family of portable Cipher machines

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 attack against DES requires 2⁴³ known plaintexts and approximately 2⁴³ DES operations. In Cryptography, linear cryptanalysis is a general form of Cryptanalysis based on finding affine approximations to the action of a Cipher. ^[21] 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 (e. g. , the RSA algorithm is based on a problem related to integer factoring), but the discrete logarithm problem is also important. In Mathematics, specifically in Abstract algebra and its applications discrete logarithms are group-theoretic analogues of ordinary Logarithms Much public-key cryptanalysis concerns numerical algorithms for solving these computational problems, or some of them, efficiently (ie, in a practical time). For instance, the best known algorithms for solving the elliptic curve-based version of discrete logarithm are much more time-consuming than the best known algorithms for factoring, at least for problems of more or less equivalent size. Elliptic curve cryptography (ECC is an approach to Public-key cryptography based on the algebraic structure of Elliptic curves over Finite fields The use 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. In Cryptography, a side channel attack is any attack based on information gained from the physical Implementation of a Cryptosystem, rather than brute If a cryptanalyst has access to, say, the amount of time the device took to encrypt a number of plaintexts or report an error in a password or PIN character, he may be able to use a timing attack to break a cipher that is otherwise resistant to analysis. 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 An attacker might also study the pattern and length of messages to derive valuable information; this is known as traffic analysis,^[22] and can be quite useful to an alert adversary. Traffic analysis is the process of intercepting and examining messages in order to deduce information from patterns in Communication. Poor administration of a crypotsystem, such as permitting too short keys, will make any system vulnerable, regardless of other virtues. And, of course, social engineering, and other attacks against the personnel who work with cryptosystems or the messages they handle (e. Social engineering is the art of manipulating people into performing actions or divulging confidential information g. , bribery, extortion, blackmail, espionage, torture, . Bribery, a form of pecuniary corruption is an act usually implying money or gift given that alters the behaviour of the recipient in ways not consistent with the duties of that person Extortion, outwresting, or exaction is a criminal offense, which occurs when a person Unlawfully obtains either money property or services Blackmail is the crime of threatening to reveal substantially true information about a person to the public a family member or associates unless a demand made upon the Torture, according to the United Nations Convention Against Torture, is "any act by which severe pain or suffering, whether physical or mental is intentionally . . ) may be the most productive attacks of all.

Cryptographic primitives

Much of the theoretical work in cryptography concerns cryptographic primitives — algorithms with basic cryptographic properties — and their relationship to other cryptographic problems. Cryptographic primitives are well-established low-level cryptographic algorithms that are frequently used to build Computer security systems More complicated cryptographic tools are then built from these basic primitives. Complex functionality in an application must be built in using combinations of these algorithms and assorted protocols. Such combinations are called cryptosystems and it is they which users actually encounter. 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 Examples include PGP and its variants, ssh, SSL/TLS, all PKIs, digital signatures, etc For example, a one-way function is a function intended to be easy to compute but hard to invert. Pretty Good Privacy (PGP is a Computer program that provides Cryptographic Privacy and Authentication. Secure Shell or SSH is a Network protocol that allows data to be exchanged using a Secure channel between two networked devices Transport Layer Security ( TLS) and its predecessor Secure Sockets Layer ( SSL) are Cryptographic protocols that provide secure Transport Layer Security ( TLS) and its predecessor Secure Sockets Layer ( SSL) are Cryptographic protocols that provide secure In Cryptography, a public key infrastructure ( PKI) is an arrangement that binds Public keys with respective user identities by means of a Certificate A digital signature or digital signature scheme is a type of asymmetric cryptography used to simulate the security properties of a handwritten Signature A one-way function is a function that is easy to compute but "hard to invert" (in the sense defined below The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function

But note that, in a very general sense, for any cryptographic application to be secure (if based on computational feasibility assumptions), one-way functions must exist. However, if one-way functions exist, this implies that P ≠ NP. The relationship between the Complexity classes P and NP is an unsolved question in Theoretical computer science. ^[3] Since the P versus NP problem is currently unsolved, it is not known if one-way functions really do exist. For instance, if one-way functions exist, then secure pseudorandom generators and secure pseudorandom functions exist. A cryptographically secure pseudo-random number generator ( CSPRNG) is a Pseudo-random number generator (PRNG with properties that make it suitable for use in ^[23]

Other cryptographic primitives include the encryption algorithms themselves, one-way permutations, trapdoor permutations, etc. A one-way function is a function that is easy to compute but "hard to invert" (in the sense defined below A trapdoor function is a function that is easy to compute in one direction yet believed to be difficult to compute in the opposite direction (finding its inverse)

Cryptographic protocols

In many cases, cryptographic techniques involve back and forth communication among two or more parties in space (e. g. , between the home office and a branch office) or across time (e. g. , cryptographically protected backup data). In Information technology, backup refers to making copies of Data so that these additional copies may be used to restore the original after a The term cryptographic protocol captures this general idea. A security protocol ( cryptographic protocol or encryption protocol) is an abstract or concrete protocol that performs a security -related function

Cryptographic protocols have been developed for a wide range of problems, including relatively simple ones like interactive proof systems,^[24] secret sharing,^[25][26] and zero-knowledge proofs,^[27] and much more complex ones like electronic cash^[28] and secure multiparty computation. In Computational complexity theory, an interactive proof system is an Abstract machine that models Computation as the exchange of messages between two parties Secret sharing refers to any method for distributing a secret amongst a group of participants each of which is allocated a share of the secret In Cryptography, a zero-knowledge proof or zero-knowledge protocol is an interactive method for one party to prove to another that a (usually mathematical statement Electronic money (also known as e-money, electronic cash, electronic currency, digital money, digital cash or digital currency In Cryptography, secure multi-party computation is a problem that was initially suggested by Andrew C ^[29]

When the security of a good cryptographic system fails, it is rare that the vulnerability leading to the breach will have been in a quality cryptographic primitive. Instead, weaknesses are often mistakes in the protocol design (often due to inadequate design procedures, or less than thoroughly informed designers), in the implementation (e. g. , a software bug), in a failure of the assumptions on which the design was based (e. A software bug (or just “bug” is an error flaw mistake Failure, fault or “undocumented feature” in a Computer program that prevents it g. , proper training of those who will be using the system), or some other human error.

Many cryptographic protocols have been designed and analyzed using ad hoc methods, but they rarely have any proof of security, leaving aside the effects of humans in their operations. Methods for formally analyzing the security of protocols, based on techniques from mathematical logic (see for example BAN logic), and more recently from concrete security principles, have been the subject of research for the past few decades. Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. Burrows-Abadi-Needham logic (also known as the BAN logic) is a set of rules for defining and analyzing information exchange protocols In Cryptography, concrete security or exact security is a practice-oriented approach that aims to give more precise estimates of the computational complexities of ^[30][31][32] Unfortunately, to date these tools have been cumbersome and are not widely used for complex designs.

The study of how best to implement and integrate cryptography in applications is itself a distinct field, see: cryptographic engineering and security engineering. Cryptographic Engineering is the discipline of using cryptography to solve human problems Security engineering is a specialized field of Engineering that deals with the development of detailed engineering plans and designs for security features controls and systems

Legal issues involving cryptography

Prohibitions

Cryptography has long been of interest to intelligence gathering and law enforcement agencies. Law enforcement agency ( LEA) is a term used to describe either an organisation that enforces the laws of one or more governing bodies or an organisation that actively and directly Actually secret communications may be criminal or even treasonous; those whose communications are open to inspection may be less likely to be either. Because of its facilitation of privacy, and the diminution of privacy attendant on its prohibition, cryptography is also of considerable interest to civil rights supporters. Privacy is the ability of an individual or group to seclude themselves or information about themselves and thereby reveal themselves selectively Accordingly, there has been a history of controversial legal issues surrounding cryptography, especially since the advent of inexpensive computers has made possible widespread access to high quality cryptography.

In some countries, even the domestic use of cryptography is, or has been, restricted. Until 1999, France significantly restricted the use of cryptography domestically. This article is about the country For a topic outline on this subject see List of basic France topics. In China, a license is still required to use cryptography. Talk People's Republic of China) PEOPLE'S REPUBLIC OF CHINA ARTICLE GUIDELINES Many countries have tight restrictions on the use of cryptography. Among the more restrictive are laws in Belarus, Kazakhstan, Mongolia, Pakistan, Russia, Singapore, Tunisia, Venezuela, and Vietnam. Belarus ( Belarusian Беларусь / Biełaruś is a Landlocked country in Eastern Europe, bordered by Russia to the north and east Kazakhstan, also Kazakstan ( Қазақстан, Qazaqstan, qɑzɑqˈstɑn Казахстан, Kazakhstán,) officially the Mongolia (mɒŋˈɡoʊliə, literally Mongol country/nation,) is a Landlocked Country in East Pakistan () officially the Islamic Republic of Pakistan, is a country located in South Asia, Southwest Asia, Middle East and Russia (Россия Rossiya) or the Russian Federation ( Rossiyskaya Federatsiya) is a transcontinental Country extending Singapore Tunisia (تونس Tūnis officially the Tunisian Republic ( is a country located in North Africa. Venezuela (ˌvɛnəˈzweɪlə) officially the Bolivarian Republic of Venezuela (Spanish República Bolivariana de Venezuela) is a country on the Vietnam (ˌviːɛtˈnɑːm Việt Nam) officially ^[33]

In the United States, cryptography is legal for domestic use, but there has been much conflict over legal issues related to cryptography. The United States of America —commonly referred to as the One particularly important issue has been the export of cryptography and cryptographic software and hardware. The export of cryptography is the transfer from one country to another of devices and technology related to Cryptography. Because of the importance of cryptanalysis in World War II and an expectation that cryptography would continue to be important for national security, many western governments have, at some point, strictly regulated export of cryptography. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including After World War II, it was illegal in the US to sell or distribute encryption technology overseas; in fact, encryption was defined legally to be a munition. Ammunition, often referred to as ammo, is a generic term derived from the French language la munition which ^[34] Until the advent of the personal computer and the Internet, this was not especially problematic. A personal computer ( PC) is any Computer whose original sales price size and capabilities make it useful for individuals and which is intended to be operated The Internet is a global system of interconnected Computer networks Good cryptography is indistinguishable from bad cryptography for nearly all users, and in any case, most of the cryptographic techniques generally available were slow and error prone whether good or bad. 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

Main article: Export of cryptography

In the 1990s, there were several challenges to US export regulations of cryptography. The export of cryptography is the transfer from one country to another of devices and technology related to Cryptography. One involved Philip Zimmermann's Pretty Good Privacy (PGP) encryption program; it was released in the US, together with its source code, and found its way onto the Internet in June of 1991. Philip R "Phil" Zimmermann Jr (born February 12, 1954) is the creator of Pretty Good Privacy (PGP the most widely used Email Pretty Good Privacy (PGP is a Computer program that provides Cryptographic Privacy and Authentication. In Computer science, source code (commonly just source or code) is any sequence of statements or declarations written in some Human-readable After a complaint by RSA Security (then called RSA Data Security, Inc. RSA The Security Division of EMC Corporation, is headquartered in Bedford Massachusetts, United States and maintains offices in Ireland, Israel , or RSADSI), Zimmermann was criminally investigated by the Customs Service and the FBI for several years. No charges were ever filed, however. ^[35][36] 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. Daniel Julius Bernstein (sometimes known simply as djb; born October 29, 1971) is a Professor at the University of Illinois at Chicago The University of California Berkeley (also referred to as Cal, Berkeley and UC Berkeley) is a major research university located in Berkeley The First Amendment to the United States Constitution is part of the United States Bill of Rights that expressly prohibits the United States Congress The 1995 case Bernstein v. United States which ultimately resulted in a 1999 decision that printed source code for cryptographic algorithms and systems was protected as free speech by the United States Constitution. Bernstein v United States is a set of court cases brought by Daniel J Freedom of speech is the freedom to speak freely without Censorship or Limitation. ^[37]

In 1996, thirty-nine countries signed the Wassenaar Arrangement, an arms control treaty that deals with the export of arms and "dual-use" technologies such as cryptography. The Wassenaar Arrangement (full name "The Wassenaar Arrangement on Export Controls for Conventional Arms and Dual-Use Goods and Technologies" is a Multilateral export control 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. ^[38] Cryptography exports from the US are now much less strictly regulated than in the past as a consequence of a major relaxation in 2000;^[33] there are no longer very many restrictions on key sizes in US-exported mass-market software. The export of cryptography is the transfer from one country to another of devices and technology related to Cryptography. In practice today, since the relaxation in US export restrictions, and because almost every personal computer connected to the Internet, everywhere in the world, includes US-sourced web browsers such as Mozilla Firefox or Microsoft Internet Explorer, almost every Internet user worldwide has access to quality cryptography (i. A personal computer ( PC) is any Computer whose original sales price size and capabilities make it useful for individuals and which is intended to be operated The Internet is a global system of interconnected Computer networks A web browser is a software application which enables a user to display and interact with text images videos music games and other information typically located on a Windows Internet Explorer (formerly Microsoft Internet Explorer abbreviated MSIE) commonly abbreviated to IE, is a series of graphical e. , when using sufficiently long keys with properly operating and unsubverted software, etc) in their browsers; examples are Transport Layer Security or SSL stack. Transport Layer Security ( TLS) and its predecessor Secure Sockets Layer ( SSL) are Cryptographic protocols that provide secure Transport Layer Security ( TLS) and its predecessor Secure Sockets Layer ( SSL) are Cryptographic protocols that provide secure The Mozilla Thunderbird and Microsoft Outlook E-mail client programs similarly can connect to IMAP or POP servers via TLS, and can send and receive email encrypted with S/MIME. Mozilla Thunderbird is a free, Open source, Cross-platform e-mail and News client developed by the Mozilla Foundation. Microsoft Outlook or Outlook (full name Microsoft Office Outlook since Outlook 2003 is a Personal information manager from Microsoft, and is An e-mail client, aka Mail User Agent (MUA aka e-mail reader is a frontend Computer program used to manage E-mail. The Internet Message Access Protocol or IMAP is one of the two most prevalent Internet standard protocols for E-mail retrieval the other being POP3 In Computing, local E-mail clients use the Post Office Protocol version 3 ( POP3) an application-layer Internet standard protocol S/MIME ( Secure / Multipurpose Internet Mail Extensions) is a standard for Public key Encryption and signing of E-mail encapsulated Many Internet users don't realize that their basic application software contains such extensive cryptosystems. 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 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

See also: Clipper chip

Another contentious issue connected to cryptography in the United States is the influence of the National Security Agency on cipher development and policy. The Clipper chip is a Chipset that was developed and promoted by the U The National Security Agency/ Central Security Service ( NSA/CSS) is a cryptologic intelligence agency of the United States government NSA was involved with the design of DES during its development at IBM and its consideration by the National Bureau of Standards as a possible Federal Standard for cryptography. The Data Encryption Standard ( DES) is a Cipher (a method for Encrypting information selected by NBS as an official Federal Information International Business Machines Corporation abbreviated IBM and nicknamed "Big Blue", is a multinational Computer Technology ^[39] DES was designed to be resistant to differential cryptanalysis,^[40] a powerful and general cryptanalytic technique known to NSA and IBM, that became publicly known only when it was rediscovered in the late 1980s. Differential cryptanalysis is a general form of Cryptanalysis applicable primarily to Block ciphers but also to Stream ciphers and Cryptographic hash ^[41] According to Steven Levy, IBM rediscovered differential cryptanalysis,^[42] but kept the technique secret at NSA's request. Steven Levy (born 1951 is an American Journalist who has written several books on computers technology Cryptography, the Internet cybersecurity 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 affair, an encryption microchip intended to be part of the Capstone cryptography-control initiative. The Clipper chip is a Chipset that was developed and promoted by the U Capstone is the name of a United States government long-term project to develop Cryptography standards for public and government use Clipper was widely criticized by cryptographers for two reasons. The cipher algorithm was then classified (the cipher, called Skipjack, though it was declassified in 1998 long after the Clipper initiative lapsed). In Cryptography, Skipjack is a Block cipher &mdash an Algorithm for Encryption &mdash developed by the U 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' principle, as the scheme included a special escrow key held by the government for use by law enforcement, for example in wiretaps. In Cryptography, Kerckhoffs' principle (also called Kerckhoffs' assumption, axiom or law) was stated by Auguste Kerckhoffs in Key escrow (also known as a fair cryptosystem) is an arrangement in which the keys needed to decrypt encrypted data are held in Escrow so that under certain ^[36]

Digital Rights Management

Main article: Digital Rights Management

Cryptography is central to digital rights management (DRM), a group of techniques for technologically controlling use of copyrighted material, being widely implemented and deployed at the behest of some copyright holders. Digital rights management ( DRM) is a generic term that refers to Access control technologies used by hardware manufacturers publishers and Copyright holders Copyright is a legal concept enacted by Governments, giving the creator of an original work of authorship Exclusive rights to control its distribution usually for Copyright is a legal concept enacted by Governments, giving the creator of an original work of authorship Exclusive rights to control its distribution usually for In 1998, American President Bill Clinton signed the Digital Millennium Copyright Act (DMCA), which criminalized all production, dissemination, and use of certain cryptanalytic techniques and technology (now known or later discovered); specifically, those that could be used to circumvent DRM technological schemes. William Jefferson "Bill" Clinton (born William Jefferson Blythe III, August 19 1946 served as the forty-second President of the United States The Digital Millennium Copyright Act (DMCA is a United States Copyright Law which implements two 1996 treaties of the World Intellectual Property ^[43] 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. The Directive 2001/29/EC of the European Parliament and of the Council of 22 May 2001 on the harmonisation of certain aspects of copyright and related rights in the information society Similar restrictions are called for by treaties signed by World Intellectual Property Organization member-states. The World Intellectual Property Organization ( WIPO) is one of the 16 specialized agencies of the United Nations.

The United States Department of Justice and FBI have not enforced the DMCA as rigorously as had been feared by some, but the law, nonetheless, remains a controversial one. For animal rights group see Justice Department (JD The United States Department of Justice ( DOJ) is a Cabinet department One well-respected cryptography researcher, Niels Ferguson, has publicly stated that he will not release some of his research into an Intel security design for fear of prosecution under the DMCA, and both Alan Cox (longtime number 2 in Linux kernel development) and Professor Edward Felten (and some of his students at Princeton) have encountered problems related to the Act. Niels Ferguson is a Dutch cryptographic Engineer and consultant who currently works for Microsoft. Alan Cox (born July 22, 1968 in Solihull, England) is a British Computer programmer heavily involved in the development Linux is an operating system kernel used by a family of Unix-like Operating systems These are popularly termed Linux operating systems and Edward William Felten (born March 25, 1963) is a professor of Computer science and public affairs at Princeton University. Dmitry Sklyarov was arrested during a visit to the US from Russia, and jailed for some months for alleged violations of the DMCA which had occurred in Russia, where the work for which he was arrested and charged was then, and when he was arrested, legal. Dmitry Sklyarov (Дмитрий Скляров (born December 18, 1974) is a Russian Computer programmer known for his 2001 arrest In 2007, the cryptographic keys responsible for DVD and HD DVD content scrambling were discovered and released onto the internet. DVD (also known as " Digital Versatile Disc " or " Digital Video Disc " - see Etymology)is not insert the publicly disclosed HD DVD key into this article for the time being The Internet is a global system of interconnected Computer networks Both times, the MPAA sent out numerous DMCA takedown notices, and there was a massive internet backlash as a result of the implications of such notices on fair use and free speech both legally protected in the US and in some other jurisdictions. Before editing this article or commenting on this article's talk page please read the Electronic Frontier Foundation's legal primer on this issue http//www Fair use is a doctrine in United States copyright law that allows limited use of copyrighted material without requiring permission from the rights holders such as use for Freedom of speech is the freedom to speak freely without Censorship or Limitation.

See also

Cryptography Portal

• Topics in cryptography
• List of cryptographers
• Category:Cryptographers
• Books on cryptography
• List of important publications in computer science#Cryptography
• List of open problems in computer science#Cryptography

References

Further reading

• 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.
• Introduction to Modern Cryptography by Jonathan Katz and Yehuda Lindell. [1].
• Introduction to Modern Cryptography by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs. Phillip Rogaway is a professor of Computer science at the University of California Davis. Mihir Bellare is a cryptographer at the University of California San Diego. PDF download.
• Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century, by James Gannon. Cryptography (or cryptology; from Greek grc κρυπτός kryptos, "hidden secret" and grc γράφω gráphō, "I write" The twentieth century of the Common Era began on James Gannon is a Freelance writer and producer of documentaries for NBC News.
• Cryptonomicon by Neal Stephenson (novel, WW2 Enigma cryptanalysis figures into the story, though not always realistically). Cryptonomicon is a 1999 novel by Neal Stephenson. It concurrently follows the exploits of World War II -era Cryptographers affiliated with Neal Town Stephenson (born October 31, 1959) is an American writer known primarily for his Science fiction works in the Postcyberpunk genre The Enigma machine is any one of a family of related electro-mechanical Rotor machines used to generate Ciphers for the Encryption and decryption of
• Alvin's Secret Code by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis). Clifford B Hicks is an American writer and magazine editor best known for his children's books chronicling the adventures of Alvin Fernald
• In Code: A Mathematical Journey by Sarah Flannery (with David Flannery). Sarah Flannery (born 1982 County Cork, Ireland) was at sixteen years old the winner of the 1999 Esat Young Scientist Exhibition for development of the Popular account of Sarah's award-winning project on public-key cryptography, co-written with her father.
• Cryptography and Mathematics by Bernhard Esslinger, 200 pages, part of the free open-source package Cryptool, http://www.cryptool.com. CrypTool is a Free software illustrating the cryptographic concepts.
• Ibrahim A. Al-Kadi ,"The origins of cryptology: The Arab contributions”, Cryptologia, 16(2) (April 1992) pp. 97–126.
• Andreas Pfitzmann: Security in IT Networks: Multilateral Security in Distributed and by Distributed Systems

• Becket, B (1988). Introduction to Cryptology. Blackwell Scientific Publications. ISBN 0-632-01836-4.   Excellent coverage of many classical ciphers and cryptograpy concepts and of the "modern" DES and RSA systems.

External links

• AttackPrevention Resource for Cryptography Whitepapers, Tools, Videos, and Podcasts.
• Handbook of Applied Cryptography by A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone (PDF download available), somewhat more mathematical than Schneier's book.
• Cryptography: The Ancient Art of Secret Messages by Monica Pawlan - February 1998
• sci.crypt mini-FAQ
• NSA's CryptoKids.
• RSA Laboratories' Frequently Asked Questions About Today's Cryptography