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108-536: The CPRM / CPPM specification defines a renewable cryptographic method for restricting content when recorded on physical media. The currently implemented method utilizes the Cryptomeria cipher (C2) algorithm for symmetric encryption. The types of physical media supported include, but are not limited to, recordable DVD media and flash memory . The most widespread use of CPRM is arguably in Secure Digital cards such as

216-468: A chosen-plaintext attack , Eve may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example is gardening , used by the British during WWII. In a chosen-ciphertext attack , Eve may be able to choose ciphertexts and learn their corresponding plaintexts. Finally in a man-in-the-middle attack Eve gets in between Alice (the sender) and Bob (the recipient), accesses and modifies

324-428: A classical cipher (and some modern ciphers) will reveal statistical information about the plaintext, and that information can often be used to break the cipher. After the discovery of frequency analysis , nearly all such ciphers could be broken by an informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzles (see cryptogram ). The Arab mathematician and polymath Al-Kindi wrote

432-399: A plaintext letter in the cipher: if this is not the case, deciphering the message is more difficult. For many years, cryptographers attempted to hide the telltale frequencies by using several different substitutions for common letters, but this technique was unable to fully hide patterns in the substitutions for plaintext letters. Such schemes were being widely broken by the 16th century. In

540-558: A rotor machine is an electro-mechanical stream cipher device used for encrypting and decrypting messages. Rotor machines were the cryptographic state-of-the-art for much of the 20th century; they were in widespread use from the 1920s to the 1970s. The most famous example is the German Enigma machine , the output of which was deciphered by the Allies during World War II, producing intelligence code-named Ultra . The primary component of

648-565: A 'long' key could be generated from a simple pattern (ideally automatically), producing a cipher in which there are so many substitution alphabets that frequency counting and statistical attacks would be effectively impossible. Enigma, and the rotor machines generally, were just what was needed since they were seriously polyalphabetic, using a different substitution alphabet for each letter of plaintext, and automatic, requiring no extraordinary abilities from their users. Their messages were, generally, much harder to break than any previous ciphers. It

756-624: A book on cryptography entitled Risalah fi Istikhraj al-Mu'amma ( Manuscript for the Deciphering Cryptographic Messages ), which described the first known use of frequency analysis cryptanalysis techniques. Language letter frequencies may offer little help for some extended historical encryption techniques such as homophonic cipher that tend to flatten the frequency distribution. For those ciphers, language letter group (or n-gram) frequencies may provide an attack. Essentially all ciphers remained vulnerable to cryptanalysis using

864-430: A cryptographic hash function is computed, and only the resulting hash is digitally signed. Cryptographic hash functions are functions that take a variable-length input and return a fixed-length output, which can be used in, for example, a digital signature. For a hash function to be secure, it must be difficult to compute two inputs that hash to the same value ( collision resistance ) and to compute an input that hashes to

972-459: A different substitution for every letter, but this usually meant a very long key, which was a problem in several ways. A long key takes longer to convey (securely) to the parties who need it, and so mistakes are more likely in key distribution. Also, many users do not have the patience to carry out lengthy, letter-perfect evolutions, and certainly not under time pressure or battlefield stress. The 'ultimate' cipher of this type would be one in which such

1080-507: A given output ( preimage resistance ). MD4 is a long-used hash function that is now broken; MD5 , a strengthened variant of MD4, is also widely used but broken in practice. The US National Security Agency developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1 is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it;

1188-486: A good cipher to maintain confidentiality under an attack. This fundamental principle was first explicitly stated in 1883 by Auguste Kerckhoffs and is generally called Kerckhoffs's Principle ; alternatively and more bluntly, it was restated by Claude Shannon , the inventor of information theory and the fundamentals of theoretical cryptography, as Shannon's Maxim —'the enemy knows the system'. Different physical devices and aids have been used to assist with ciphers. One of

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1296-463: A handful of different alphabets could be used; anything more complex would be impractical. However, using only a few alphabets left the ciphers vulnerable to attack. The invention of rotor machines mechanised polyalphabetic encryption, providing a practical way to use a much larger number of alphabets. The earliest cryptanalytic technique was frequency analysis , in which letter patterns unique to every language could be used to discover information about

1404-428: A hashed output that cannot be used to retrieve the original input data. Cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security. Symmetric-key cryptosystems use the same key for encryption and decryption of a message, although a message or group of messages can have a different key than others. A significant disadvantage of symmetric ciphers

1512-440: A keystream (in place of a Pseudorandom number generator ) and applying an XOR operation to each bit of the plaintext with each bit of the keystream. Message authentication codes (MACs) are much like cryptographic hash functions , except that a secret key can be used to authenticate the hash value upon receipt; this additional complication blocks an attack scheme against bare digest algorithms , and so has been thought worth

1620-414: A more specific meaning: the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a code word (for example, "wallaby" replaces "attack at dawn"). A cypher, in contrast, is a scheme for changing or substituting an element below such a level (a letter, a syllable, or a pair of letters, etc.) to produce a cyphertext. Cryptanalysis is the term used for the study of methods for obtaining

1728-402: A rotor machine is a set of rotors , also termed wheels or drums , which are rotating disks with an array of electrical contacts on either side. The wiring between the contacts implements a fixed substitution of letters, replacing them in some complex fashion. On its own, this would offer little security; however, before or after encrypting each letter, the rotors advance positions, changing

1836-476: A secret key is used to process the message (or a hash of the message, or both), and one for verification , in which the matching public key is used with the message to check the validity of the signature. RSA and DSA are two of the most popular digital signature schemes. Digital signatures are central to the operation of public key infrastructures and many network security schemes (e.g., SSL/TLS , many VPNs , etc.). Public-key algorithms are most often based on

1944-516: 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 was meant to select a new U.S. national standard, to be called SHA-3 , by 2012. The competition ended on October 2, 2012, when the NIST announced that Keccak would be the new SHA-3 hash algorithm. Unlike block and stream ciphers that are invertible, cryptographic hash functions produce

2052-464: A shared secret key. In practice, asymmetric systems are used to first exchange a secret key, and then secure communication proceeds via a more efficient symmetric system using that key. Examples of asymmetric systems include Diffie–Hellman key exchange , RSA ( Rivest–Shamir–Adleman ), ECC ( Elliptic Curve Cryptography ), and Post-quantum cryptography . Secure symmetric algorithms include the commonly used AES ( Advanced Encryption Standard ) which replaced

2160-406: A story by Edgar Allan Poe . Until modern times, cryptography referred almost exclusively to "encryption", which is the process of converting ordinary information (called plaintext ) into an unintelligible form (called ciphertext ). Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A cipher (or cypher) is a pair of algorithms that carry out

2268-588: A stream cipher. The Data Encryption Standard (DES) and the Advanced Encryption Standard (AES) are block cipher designs that have been designated cryptography standards by the US government (though DES's designation was finally withdrawn after the AES was adopted). Despite its deprecation as an official standard, DES (especially its still-approved and much more secure triple-DES variant) remains quite popular; it

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2376-465: A wide variety of cryptanalytic attacks, and they can be classified in any of several ways. A common distinction turns on what Eve (an attacker) knows and what capabilities are available. In a ciphertext-only attack , Eve has access only to the ciphertext (good modern cryptosystems are usually effectively immune to ciphertext-only attacks). In a known-plaintext attack , Eve has access to a ciphertext and its corresponding plaintext (or to many such pairs). In

2484-446: A widely used tool in communications, computer networks , and computer security generally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable , such as the integer factorization or the discrete logarithm problems, so there are deep connections with abstract mathematics . There are very few cryptosystems that are proven to be unconditionally secure. The one-time pad

2592-417: Is also active research examining the relationship between cryptographic problems and quantum physics . Just as the development of digital computers and electronics helped in cryptanalysis, it made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this

2700-493: Is also widely used but broken in practice. The US National Security Agency developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1 is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2 family improves on SHA-1, but is vulnerable to clashes as of 2011; and the US standards authority thought it "prudent" from

2808-408: Is beyond the ability of any adversary. This means it must be shown that no efficient method (as opposed to the time-consuming brute force method) can be found to break the cipher. Since no such proof has been found to date, the one-time-pad remains the only theoretically unbreakable cipher. Although well-implemented one-time-pad encryption cannot be broken, traffic analysis is still possible. There are

2916-443: Is called cryptolinguistics . Cryptolingusitics is especially used in military intelligence applications for deciphering foreign communications. Before the modern era, cryptography focused on message confidentiality (i.e., encryption)—conversion of messages from a comprehensible form into an incomprehensible one and back again at the other end, rendering it unreadable by interceptors or eavesdroppers without secret knowledge (namely

3024-648: Is claimed to have developed the Diffie–Hellman key exchange. Public-key cryptography is also used for implementing digital signature schemes. A digital signature is reminiscent of an ordinary signature; they both have the characteristic of being easy for a user to produce, but difficult for anyone else to forge . Digital signatures can also be permanently tied to the content of the message being signed; they cannot then be 'moved' from one document to another, for any attempt will be detectable. In digital signature schemes, there are two algorithms: one for signing , in which

3132-399: Is combined with the plaintext bit-by-bit or character-by-character, somewhat like the one-time pad . In a stream cipher, the output stream is created based on a hidden internal state that changes as the cipher operates. That internal state is initially set up using the secret key material. RC4 is a widely used stream cipher. Block ciphers can be used as stream ciphers by generating blocks of

3240-560: Is impossible; it is quite unusable in practice. The discrete logarithm problem is the basis for believing some other cryptosystems are secure, and again, there are related, less practical systems that are provably secure relative to the solvability or insolvability discrete log problem. 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

3348-617: Is one, and was proven to be so by Claude Shannon. There are a few important algorithms that have been proven secure under certain assumptions. For example, the infeasibility of factoring extremely large integers is the basis for believing that RSA is secure, and some other systems, but even so, proof of unbreakability is unavailable since the underlying mathematical problem remains open. In practice, these are widely used, and are believed unbreakable in practice by most competent observers. There are systems similar to RSA, such as one by Michael O. Rabin that are provably secure provided factoring n = pq

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3456-733: Is relatively recent, beginning in the mid-1970s. In the early 1970s IBM personnel designed the Data Encryption Standard (DES) algorithm that became the first federal government cryptography standard in the United States. In 1976 Whitfield Diffie and Martin Hellman published the Diffie–Hellman key exchange algorithm. In 1977 the RSA algorithm was published in Martin Gardner 's Scientific American column. Since then, cryptography has become

3564-417: Is straightforward to create a machine for performing simple substitution. In an electrical system with 26 switches attached to 26 light bulbs, any one of the switches will illuminate one of the bulbs. If each switch is operated by a key on a typewriter , and the bulbs are labelled with letters, then such a system can be used for encryption by choosing the wiring between the keys and the bulb: for example, typing

3672-454: Is the key management necessary to use them securely. Each distinct pair of communicating parties must, ideally, share a different key, and perhaps for each ciphertext exchanged as well. The number of keys required increases as the square of the number of network members, which very quickly requires complex key management schemes to keep them all consistent and secret. In a groundbreaking 1976 paper, Whitfield Diffie and Martin Hellman proposed

3780-827: Is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science , information security , electrical engineering , digital signal processing , physics, and others. Core concepts related to information security ( data confidentiality , data integrity , authentication , and non-repudiation ) are also central to cryptography. Practical applications of cryptography include electronic commerce , chip-based payment cards , digital currencies , computer passwords , and military communications . Cryptography prior to

3888-499: Is theoretically possible to break into a well-designed system, it is infeasible in actual practice to do so. Such schemes, if well designed, are therefore termed "computationally secure". Theoretical advances (e.g., improvements in integer factorization algorithms) and faster computing technology require these designs to be continually reevaluated and, if necessary, adapted. Information-theoretically secure schemes that provably cannot be broken even with unlimited computing power, such as

3996-439: Is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion. It is a common misconception that every encryption method can be broken. In connection with his WWII work at Bell Labs , Claude Shannon proved that 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

4104-434: 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. Symmetric-key cryptography refers to encryption methods in which both

4212-419: Is used across a wide range of applications, from ATM encryption to e-mail privacy and secure remote access . Many other block ciphers have been designed and released, with considerable variation in quality. Many, even some designed by capable practitioners, have been thoroughly broken, such as FEAL . Stream ciphers, in contrast to the 'block' type, create an arbitrarily long stream of key material, which

4320-789: The Battle of the Atlantic . During World War II (WWII), both the Germans and Allies developed additional rotor machines. The Germans used the Lorenz SZ 40/42 and Siemens and Halske T52 machines to encipher teleprinter traffic which used the Baudot code ; this traffic was known as Fish to the Allies. The Allies developed the Typex (British) and the SIGABA (American). During the War

4428-783: The German Army began to use a different variant around 1928. The Enigma (in several variants) was the rotor machine that Scherbius's company and its successor, Heimsoth & Reinke, supplied to the German military and to such agencies as the Nazi party security organization, the SD . The Poles broke the German Army Enigma beginning in December 1932, not long after it had been put into service. On July 25, 1939, just five weeks before Hitler's invasion of Poland,

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4536-523: The Latin alphabet ) before the key repeats, and yet it still only requires you to communicate a key of two letters/numbers to set things up. If a key of 676 length is not long enough, another rotor can be added, resulting in a period 17,576 letters long. In order to be as easy to decipher as encipher, some rotor machines, most notably the Enigma machine , embodied a symmetric-key algorithm , i.e., encrypting twice with

4644-779: The Polish General Staff 's Cipher Bureau shared its Enigma-decryption methods and equipment with the French and British as the Poles' contribution to the common defense against Nazi Germany. Dilly Knox had already broken Spanish Nationalist messages on a commercial Enigma machine in 1937 during the Spanish Civil War . A few months later, using the Polish techniques, the British began reading Enigma ciphers in collaboration with Polish Cipher Bureau cryptologists who had escaped Poland, overrun by

4752-568: The SD-Audio standard. Note that the available 0.9 revision includes only the portions of the specification covering DVD media. The CPRM / CPPM specification was designed to meet the requirements of intellectual property owners while balancing the implementation requirements of manufacturers. To accomplish these requirements, the system defined by the specification relies on public-key cryptography 's key management for interchangeable media, content encryption, and "media-based renewability." The use of

4860-442: The SHA-2 family improves on SHA-1, but is vulnerable to clashes as of 2011; and the US standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness of NIST 's overall hash algorithm toolkit." Thus, a hash function design competition was meant to select a new U.S. national standard, to be called SHA-3 , by 2012. The competition ended on October 2, 2012, when

4968-595: The Swiss began development on an Enigma improvement which became the NEMA machine which was put into service after World War II. There was even a Japanese developed variant of the Enigma in which the rotors sat horizontally; it was apparently never put into service. The Japanese PURPLE machine was not a rotor machine, being built around electrical stepping switches , but was conceptually similar. Rotor machines continued to be used even in

5076-502: The US Army 's SIS promptly demonstrated a flaw in the system that allowed the ciphers from it, and from any machine with similar design features, to be cracked with enough work. Another early rotor machine inventor was Dutchman Hugo Koch , who filed a patent on a rotor machine in 1919. At about the same time in Sweden , Arvid Gerhard Damm invented and patented another rotor design. However,

5184-399: The ciphertext , which provide clues about the length of the key. Once this is known, the message essentially becomes a series of messages, each as long as the length of the key, to which normal frequency analysis can be applied. Charles Babbage , Friedrich Kasiski , and William F. Friedman are among those who did most to develop these techniques. Cipher designers tried to get users to use

5292-557: The computational complexity of "hard" problems, often from number theory . 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. The security of elliptic curve cryptography is based on number theoretic problems involving elliptic curves . Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular multiplication and exponentiation, which are much more computationally expensive than

5400-501: The one-time pad , are much more difficult to use in practice than the best theoretically breakable but computationally secure schemes. The growth of cryptographic technology has raised a number of legal issues in the Information Age . Cryptography's potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or even prohibit its use and export. In some jurisdictions where

5508-619: The rāz-saharīya which was used to communicate secret messages with other countries. David Kahn notes in The Codebreakers that modern cryptology originated among the Arabs , the first people to systematically document cryptanalytic methods. Al-Khalil (717–786) wrote the Book of Cryptographic Messages , which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels. Ciphertexts produced by

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5616-471: The 1920s. He sold a small number of machines to the US Navy in 1931. In Hebern's machines the rotors could be opened up and the wiring changed in a few minutes, so a single mass-produced system could be sold to a number of users who would then produce their own rotor keying. Decryption consisted of taking out the rotor(s) and turning them around to reverse the circuitry. Unknown to Hebern, William F. Friedman of

5724-453: The 20th century, and several patented, among them rotor machines —famously including the Enigma machine used by the German government and military from the late 1920s and during World War II . The ciphers implemented by better quality examples of these machine designs brought about a substantial increase in cryptanalytic difficulty after WWI. Cryptanalysis of the new mechanical ciphering devices proved to be both difficult and laborious. In

5832-457: The CPRM specification and access to the cryptographic materials required to implement it requires a license from 4C Entity , LLC. The license includes a facsimile key for the product which uses CPRM / CPPM technology. A controversial proposal to add generic key exchange commands (that could be utilized by CPRM and other content restriction technologies) to ATA specifications for removable hard drives

5940-612: The Enigma .) Scherbius joined forces with a mechanical engineer named Ritter and formed Chiffriermaschinen AG in Berlin before demonstrating Enigma to the public in Bern in 1923, and then in 1924 at the World Postal Congress in Stockholm . In 1927 Scherbius bought Koch's patents, and in 1928 they added a plugboard , essentially a non-rotating manually rewireable fourth rotor, on the front of

6048-498: The Germans, to reach Paris . The Poles continued breaking German Army Enigma—along with Luftwaffe Enigma traffic—until work at Station PC Bruno in France was shut down by the German invasion of May–June 1940. The British continued breaking Enigma and, assisted eventually by the United States, extended the work to German Naval Enigma traffic (which the Poles had been reading before the war), most especially to and from U-boats during

6156-488: The Government Communications Headquarters ( GCHQ ), a British intelligence organization, revealed that cryptographers at GCHQ had anticipated several academic developments. Reportedly, around 1970, James H. Ellis had conceived the principles of asymmetric key cryptography. In 1973, Clifford Cocks invented a solution that was very similar in design rationale to RSA. In 1974, Malcolm J. Williamson

6264-567: The Kautiliyam, the cipher letter substitutions are based on phonetic relations, such as vowels becoming consonants. In the Mulavediya, the cipher alphabet consists of pairing letters and using the reciprocal ones. In Sassanid Persia , there were two secret scripts, according to the Muslim author Ibn al-Nadim : the šāh-dabīrīya (literally "King's script") which was used for official correspondence, and

6372-402: The NIST announced that Keccak would be the new SHA-3 hash algorithm. Unlike block and stream ciphers that are invertible, cryptographic hash functions produce a hashed output that cannot be used to retrieve the original input data. Cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security. The goal of cryptanalysis

6480-642: The United Kingdom, cryptanalytic efforts at Bletchley Park during WWII spurred the development of more efficient means for carrying out repetitive tasks, such as military code breaking (decryption) . This culminated in the development of the Colossus , the world's first fully electronic, digital, programmable computer, which assisted in the decryption of ciphers generated by the German Army's Lorenz SZ40/42 machine. Extensive open academic research into cryptography

6588-469: The amusement of literate observers rather than as a way of concealing information. The Greeks of Classical times are said to have known of ciphers (e.g., the scytale transposition cipher claimed to have been used by the Spartan military). Steganography (i.e., hiding even the existence of a message so as to keep it confidential) was also first developed in ancient times. An early example, from Herodotus ,

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6696-453: 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. RFC   2828 advises that steganography is sometimes included in cryptology. The study of characteristics of languages that have some application in cryptography or cryptology (e.g. frequency data, letter combinations, universal patterns, etc.)

6804-507: The computer age. The KL-7 (ADONIS), an encryption machine with 8 rotors, was widely used by the U.S. and its allies from the 1950s until the 1980s. The last Canadian message encrypted with a KL-7 was sent on June 30, 1983. The Soviet Union and its allies used a 10-rotor machine called Fialka well into the 1970s. A unique rotor machine called the Cryptograph was constructed in 2002 by Netherlands -based Tatjana van Vark. This unusual device

6912-496: The course of a single plaintext. The idea is simple and effective, but proved more difficult to use than might have been expected. Many ciphers were only partial implementations of Alberti's, and so were easier to break than they might have been (e.g. the Vigenère cipher ). Not until the 1840s (Babbage) was any technique known which could reliably break any of the polyalphabetic ciphers. His technique also looked for repeating patterns in

7020-428: 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

7128-650: The earliest may have been the scytale of ancient Greece, a rod supposedly used by the Spartans as an aid for a transposition cipher. In medieval times, other aids were invented such as the cipher grille , which was also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's own cipher disk , Johannes Trithemius ' tabula recta scheme, and Thomas Jefferson 's wheel cypher (not publicly known, and reinvented independently by Bazeries around 1900). Many mechanical encryption/decryption devices were invented early in

7236-612: The early 20th century, cryptography was mainly concerned with linguistic and lexicographic patterns. Since then cryptography has broadened in scope, and now makes extensive use of mathematical subdisciplines, including information theory, computational complexity , statistics, combinatorics , abstract algebra , number theory , and finite mathematics . Cryptography is also a branch of engineering, but an unusual one since it deals with active, intelligent, and malevolent opposition; other kinds of engineering (e.g., civil or chemical engineering) need deal only with neutral natural forces. There

7344-409: The effort. Cryptographic hash functions are a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed-length hash , which can be used in (for example) a digital signature. For good hash functions, an attacker cannot find two messages that produce the same hash. MD4 is a long-used hash function that is now broken; MD5 , a strengthened variant of MD4,

7452-549: The encryption and decryption algorithms that correspond to each key. Keys are important both formally and in actual practice, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless (or even counter-productive) for most purposes. Historically, ciphers were often used directly for encryption or decryption without additional procedures such as authentication or integrity checks. There are two main types of cryptosystems: symmetric and asymmetric . In symmetric systems,

7560-506: The encryption and the reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and, in each instance, by a "key". The key is a secret (ideally known only to the communicants), usually a string of characters (ideally short so it can be remembered by the user), which is needed to decrypt the ciphertext. In formal mathematical terms, a " cryptosystem " is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, and

7668-481: The field since polyalphabetic substitution emerged in the Renaissance". In public-key cryptosystems, the public key may be freely distributed, while its paired private key must remain secret. In a public-key encryption system, the public key is used for encryption, while the private or secret key is used for decryption. While Diffie and Hellman could not find such a system, they showed that public-key cryptography

7776-406: The foundations of modern cryptography and provided a mathematical basis for future cryptography. His 1949 paper has been noted as having provided a "solid theoretical basis for cryptography and for cryptanalysis", and as having turned cryptography from an "art to a science". As a result of his contributions and work, he has been described as the "founding father of modern cryptography". Prior to

7884-415: 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

7992-497: The key needed for decryption of that message). Encryption attempted to ensure secrecy in communications, such as those of spies , military leaders, and diplomats. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication, digital signatures , interactive proofs and secure computation , among others. The main classical cipher types are transposition ciphers , which rearrange

8100-428: The keyboard increments the rotor position and get a new substitution, implementing a polyalphabetic substitution cipher. Depending on the size of the rotor, this may, or may not, be more secure than hand ciphers. If the rotor has only 26 positions on it, one for each letter, then all messages will have a (repeating) key 26 letters long. Although the key itself (mostly hidden in the wiring of the rotor) might not be known,

8208-417: The letter A would make the bulb labelled Q light up. However, the wiring is fixed, providing little security. Rotor machines change the interconnecting wiring with each key stroke. The wiring is placed inside a rotor, and then rotated with a gear every time a letter is pressed. So while pressing A the first time might generate a Q , the next time it might generate a J . Every letter pressed on

8316-429: The machine. After the death of Scherbius in 1929, Willi Korn was in charge of further technical development of Enigma. As with other early rotor machine efforts, Scherbius had limited commercial success. However, the German armed forces, responding in part to revelations that their codes had been broken during World War I, adopted the Enigma to secure their communications. The Reichsmarine adopted Enigma in 1926, and

8424-488: 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

8532-457: The message. Most ciphers , apart from the one-time pad, can be broken with enough computational effort by brute force attack , but the amount of effort needed may be 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)

8640-457: The methods for attacking these types of ciphers don't need that information. So while such a single rotor machine is certainly easy to use, it is no more secure than any other partial polyalphabetic cipher system. But this is easy to correct. Simply stack more rotors next to each other, and gear them together. After the first rotor spins "all the way", make the rotor beside it spin one position. Now you would have to type 26 × 26 = 676 letters (for

8748-501: The mid-15th century, a new technique was invented by Alberti , now known generally as polyalphabetic ciphers , which recognised the virtue of using more than a single substitution alphabet; he also invented a simple technique for "creating" a multitude of substitution patterns for use in a message. Two parties exchanged a small amount of information (referred to as the key ) and used it to create many substitution alphabets, and so many different substitutions for each plaintext letter over

8856-417: The modern age was effectively synonymous with encryption , converting readable information ( plaintext ) to unintelligible nonsense text ( ciphertext ), which can only be read by reversing the process ( decryption ). The sender of an encrypted (coded) message shares the decryption (decoding) technique only with the intended recipients to preclude access from adversaries. The cryptography literature often uses

8964-674: The names "Alice" (or "A") for the sender, "Bob" (or "B") for the intended recipient, and "Eve" (or "E") for the eavesdropping adversary. Since the development of rotor cipher machines in World War ;I and the advent of computers in World War II , cryptography methods have become increasingly complex and their applications more varied. Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions , making such algorithms hard to break in actual practice by any adversary. While it

9072-553: 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

9180-448: The older DES ( Data Encryption Standard ). Insecure symmetric algorithms include children's language tangling schemes such as Pig Latin or other cant , and all historical cryptographic schemes, however seriously intended, prior to the invention of the one-time pad early in the 20th century. In colloquial use, the term " code " is often used to mean any method of encryption or concealment of meaning. However, in cryptography, code has

9288-432: The only ones known until the 1970s, the same secret key encrypts and decrypts a message. Data manipulation in symmetric systems is significantly faster than in asymmetric systems. Asymmetric systems use a "public key" to encrypt a message and a related "private key" to decrypt it. The advantage of asymmetric systems is that the public key can be freely published, allowing parties to establish secure communication without having

9396-492: The order of letters in a message (e.g., 'hello world' becomes 'ehlol owrdl' in a trivially simple rearrangement scheme), and substitution ciphers , which systematically replace letters or groups of letters with other letters or groups of letters (e.g., 'fly at once' becomes 'gmz bu podf' by replacing each letter with the one following it in the Latin alphabet ). Simple versions of either have never offered much confidentiality from enterprising opponents. An early substitution cipher

9504-408: The possible keys, to reach a point at which chances are better than even that the key sought will have been found. But this may not be enough assurance; a linear cryptanalysis attack against DES requires 2 known plaintexts (with their corresponding ciphertexts) and approximately 2 DES operations. This is a considerable improvement over brute force attacks. Rotor machine In cryptography ,

9612-411: The rotor machine was ultimately made famous by Arthur Scherbius , who filed a rotor machine patent in 1918. Scherbius later went on to design and market the Enigma machine . The most widely known rotor cipher device is the German Enigma machine used during World War II, of which there were a number of variants. The standard Enigma model, Enigma I, used three rotors. At the end of the stack of rotors

9720-438: The same settings recovers the original message (see involution ). The concept of a rotor machine occurred to a number of inventors independently at a similar time. In 2003, it emerged that the first inventors were two Dutch naval officers , Theo A. van Hengel (1875–1939) and R. P. C. Spengler (1875–1955) in 1915 (De Leeuw, 2003). Previously, the invention had been ascribed to four inventors working independently and at much

9828-549: The same time: Edward Hebern , Arvid Damm , Hugo Koch and Arthur Scherbius . In the United States Edward Hugh Hebern built a rotor machine using a single rotor in 1917. He became convinced he would get rich selling such a system to the military, the Hebern Rotor Machine , and produced a series of different machines with one to five rotors. His success was limited, however, and he went bankrupt in

9936-551: The scope of brute-force attacks , so when specifying key lengths , the required key lengths are similarly advancing. The potential impact of quantum computing are already being considered by some cryptographic system designers developing post-quantum cryptography. The announced imminence of small implementations of these machines may be making the need for preemptive caution rather more than merely speculative. Claude Shannon 's two papers, his 1948 paper on information theory , and especially his 1949 paper on cryptography, laid

10044-410: 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

10152-565: The substitution alphabet(s) in use in a mono-alphabetic substitution cipher . For instance, in English, the plaintext letters E, T, A, O, I, N and S, are usually easy to identify in ciphertext on the basis that since they are very frequent, their corresponding ciphertext letters will also be as frequent. In addition, bigram combinations like NG, ST and others are also very frequent, while others are rare indeed (Q followed by anything other than U for instance). The simplest frequency analysis relies on one ciphertext letter always being substituted for

10260-662: The substitution. By this means, a rotor machine produces a complex polyalphabetic substitution cipher, which changes with every key press. In classical cryptography , one of the earliest encryption methods was the simple substitution cipher , where letters in a message were systematically replaced using some secret scheme. Monoalphabetic substitution ciphers used only a single replacement scheme — sometimes termed an "alphabet"; this could be easily broken, for example, by using frequency analysis . Somewhat more secure were schemes involving multiple alphabets, polyalphabetic ciphers . Because such schemes were implemented by hand, only

10368-412: The techniques used in most block ciphers, especially with typical key sizes. As a result, public-key cryptosystems are commonly hybrid cryptosystems , in which a fast high-quality symmetric-key encryption algorithm is used for the message itself, while the relevant symmetric key is sent with the message, but encrypted using a public-key algorithm. Similarly, hybrid signature schemes are often used, in which

10476-508: The traffic and then forward it to the recipient. Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of the protocols involved). Cryptanalysis of symmetric-key ciphers typically involves looking for attacks against the block ciphers or stream ciphers that are more efficient than any attack that could be against a perfect cipher. For example, a simple brute force attack against DES requires one known plaintext and 2 decryptions, trying approximately half of

10584-431: The use of cryptography is legal, laws permit investigators to compel the disclosure of encryption keys for documents relevant to an investigation. Cryptography also plays a major role in digital rights management and copyright infringement disputes with regard to digital media . The first use of the term "cryptograph" (as opposed to " cryptogram ") dates back to the 19th century—originating from " The Gold-Bug ",

10692-431: Was "reflected" back through the disks before going to the lamps. The advantage of this was that there was nothing that had to be done to the setup in order to decipher a message; the machine was "symmetrical". The Enigma's reflector guaranteed that no letter could be enciphered as itself, so an A could never turn back into an A . This helped Polish and, later, British efforts to break the cipher. ( See Cryptanalysis of

10800-525: Was a message tattooed on a slave's shaved head and concealed under the regrown hair. Other steganography methods involve 'hiding in plain sight,' such as using a music cipher to disguise an encrypted message within a regular piece of sheet music. More modern examples of steganography include the use of invisible ink , microdots , and digital watermarks to conceal information. In India, the 2000-year-old Kama Sutra of Vātsyāyana speaks of two different kinds of ciphers called Kautiliyam and Mulavediya. In

10908-427: Was abandoned after outcry in 2001. CPRM is widely deployed in the popular Secure Digital card consumer-electronics flash memory format. Cryptography This is an accepted version of this page Cryptography , or cryptology (from Ancient Greek : κρυπτός , romanized :  kryptós "hidden, secret"; and γράφειν graphein , "to write", or -λογία -logia , "study", respectively ),

11016-403: Was an additional, non-rotating disk, the "reflector," wired such that the input was connected electrically back out to another contact on the same side and thus was "reflected" back through the three-rotor stack to produce the ciphertext . When current was sent into most other rotor cipher machines, it would travel through the rotors and out the other side to the lamps. In the Enigma, however, it

11124-542: Was finally won in 1978 by Ronald Rivest , Adi Shamir , and Len Adleman , whose solution has since become known as the RSA algorithm . The Diffie–Hellman and RSA algorithms , in addition to being the first publicly known examples of high-quality public-key algorithms, have been among the most widely used. Other asymmetric-key algorithms include the Cramer–Shoup cryptosystem , ElGamal encryption , and various elliptic curve techniques . A document published in 1997 by

11232-499: Was first published about ten years later by Friedrich Kasiski . Although frequency analysis can be a powerful and general technique against many ciphers, encryption has still often been effective in practice, as many a would-be cryptanalyst was unaware of the technique. Breaking a message without using frequency analysis essentially required knowledge of the cipher used and perhaps of the key involved, thus making espionage, bribery, burglary, defection, etc., more attractive approaches to

11340-488: Was indeed possible by presenting the Diffie–Hellman key exchange protocol, a solution that is now widely used in secure communications to allow two parties to secretly agree on a shared encryption key . The X.509 standard defines the most commonly used format for public key certificates . Diffie and Hellman's publication sparked widespread academic efforts in finding a practical public-key encryption system. This race

11448-570: Was new and significant. Computer use has thus supplanted linguistic cryptography, both for cipher design and cryptanalysis. Many computer ciphers can be characterized by their operation on binary bit sequences (sometimes in groups or blocks), unlike classical and mechanical schemes, which generally manipulate traditional characters (i.e., letters and digits) directly. However, computers have also assisted cryptanalysis, which has compensated to some extent for increased cipher complexity. Nonetheless, good modern ciphers have stayed ahead of cryptanalysis; it

11556-458: Was probably the first automatic cipher device , a wheel that implemented a partial realization of his invention. In the Vigenère cipher , a polyalphabetic cipher , encryption uses a key word , which controls letter substitution depending on which letter of the key word is used. In the mid-19th century Charles Babbage showed that the Vigenère cipher was vulnerable to Kasiski examination , but this

11664-525: Was the Caesar cipher , in which each letter in the plaintext was replaced by a letter three positions further down the alphabet. Suetonius reports that Julius Caesar used it with a shift of three to communicate with his generals. Atbash is an example of an early Hebrew cipher. The earliest known use of cryptography is some carved ciphertext on stone in Egypt ( c.  1900 BCE ), but this may have been done for

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