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132-524: In cryptography , XTEA ( eXtended TEA ) is a block cipher designed to correct weaknesses in TEA . The cipher 's designers were David Wheeler and Roger Needham of the Cambridge Computer Laboratory , and the algorithm was presented in an unpublished technical report in 1997 (Needham and Wheeler, 1997). It is not subject to any patents . Like TEA, XTEA is a 64-bit block Feistel cipher with
264-445: A 128-bit key and a suggested 64 rounds. Several differences from TEA are apparent, including a somewhat more complex key-schedule and a rearrangement of the shifts, XORs , and additions. This standard C source code, adapted from the reference code released into the public domain by David Wheeler and Roger Needham, encrypts and decrypts using XTEA: The changes from the reference source code are minor: The recommended value for
396-468: 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
528-428: 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
660-410: A cryptographic hash of the password. If an attacker gets access to the file of hashed passwords guessing can be done offline, rapidly testing candidate passwords against the true password's hash value. In the example of a web-server, an online attacker can guess only at the rate at which the server will respond, while an off-line attacker (who gains access to the file) can guess at a rate limited only by
792-513: A mode of operation . An attack on the full Block TEA was described by Saarinen, which also details a weakness in Block TEA's successor, XXTEA . Cryptography Cryptography , or cryptology (from Ancient Greek : κρυπτός , romanized : kryptós "hidden, secret"; and γράφειν graphein , "to write", or -λογία -logia , "study", respectively ), is the practice and study of techniques for secure communication in
924-475: A passcode , is secret data, typically a string of characters, usually used to confirm a user's identity. Traditionally, passwords were expected to be memorized , but the large number of password-protected services that a typical individual accesses can make memorization of unique passwords for each service impractical. Using the terminology of the NIST Digital Identity Guidelines, the secret
1056-399: A polynomial , modulus , or an advanced hash function . Roger Needham invented the now-common approach of storing only a "hashed" form of the plaintext password. When a user types in a password on such a system, the password handling software runs through a cryptographic hash algorithm, and if the hash value generated from the user's entry matches the hash stored in the password database,
1188-599: A 12-bit salt and invoked a modified form of the DES algorithm 25 times to reduce the risk of pre-computed dictionary attacks . In modern times, user names and passwords are commonly used by people during a log in process that controls access to protected computer operating systems , mobile phones , cable TV decoders, automated teller machines (ATMs), etc. A typical computer user has passwords for many purposes: logging into accounts, retrieving e-mail , accessing applications, databases, networks, web sites, and even reading
1320-546: A LOGIN command that requested a user password. "After typing PASSWORD, the system turns off the printing mechanism, if possible, so that the user may type in his password with privacy." In the early 1970s, Robert Morris developed a system of storing login passwords in a hashed form as part of the Unix operating system. The system was based on a simulated Hagelin rotor crypto machine, and first appeared in 6th Edition Unix in 1974. A later version of his algorithm, known as crypt(3) , used
1452-624: 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
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#17330858067461584-400: A challenge because of the sheer number of passwords users of computers and the internet are expected to maintain. One survey concluded that the average user has around 100 passwords. To manage the proliferation of passwords, some users employ the same password for multiple accounts, a dangerous practice since a data breach in one account could compromise the rest. Less risky alternatives include
1716-400: A consistent theme to keep their passwords memorable. Because of these issues, there is some debate as to whether password aging is effective. Changing a password will not prevent abuse in most cases, since the abuse would often be immediately noticeable. However, if someone may have had access to the password through some means, such as sharing a computer or breaching a different site, changing
1848-430: 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
1980-484: A few important accounts, such as bank accounts. Similar arguments were made by Forbes in not change passwords as often as many "experts" advise, due to the same limitations in human memory. Historically, many security experts asked people to memorize their passwords: "Never write down a password". More recently, many security experts such as Bruce Schneier recommend that people use passwords that are too complicated to memorize, write them down on paper, and keep them in
2112-507: 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;
2244-486: 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
2376-428: 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
2508-440: 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
2640-537: A larger construction such as in PBKDF2 . The stored data—sometimes called the "password verifier" or the "password hash"—is often stored in Modular Crypt Format or RFC 2307 hash format, sometimes in the /etc/passwd file or the /etc/shadow file. The main storage methods for passwords are plain text, hashed, hashed and salted, and reversibly encrypted. If an attacker gains access to the password file, then if it
2772-662: A match, they know that their guess is the actual password for the associated user. Password cracking tools can operate by brute force (i.e. trying every possible combination of characters) or by hashing every word from a list; large lists of possible passwords in many languages are widely available on the Internet. The existence of password cracking tools allows attackers to easily recover poorly chosen passwords. In particular, attackers can quickly recover passwords that are short, dictionary words, simple variations on dictionary words, or that use easily guessable patterns. A modified version of
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#17330858067462904-414: 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
3036-453: A password and a counterpassword; for example in the opening days of the Battle of Normandy , paratroopers of the U.S. 101st Airborne Division used a password— flash —which was presented as a challenge, and answered with the correct response— thunder . The challenge and response were changed every three days. American paratroopers also famously used a device known as a "cricket" on D-Day in place of
3168-483: A password follow. The rate at which an attacker can submit guessed passwords to the system is a key factor in determining system security. Some systems impose a time-out of several seconds after a small number (e.g., three) of failed password entry attempts, also known as throttling. In the absence of other vulnerabilities, such systems can be effectively secure with relatively simple passwords if they have been well chosen and are not easily guessed. Many systems store
3300-411: A password system as a temporarily unique method of identification; one metallic click given by the device in lieu of a password was to be met by two clicks in reply. Passwords have been used with computers since the earliest days of computing. The Compatible Time-Sharing System (CTSS), an operating system introduced at MIT in 1961, was the first computer system to implement password login. CTSS had
3432-491: A precautionary measure. If a new password is passed to the system in unencrypted form, security can be lost (e.g., via wiretapping ) before the new password can even be installed in the password database and if the new password is given to a compromised employee, little is gained. Some websites include the user-selected password in an unencrypted confirmation e-mail message, with the obvious increased vulnerability. Identity management systems are increasingly used to automate
3564-466: A risk of alienating users, possibly decreasing security as a result. It is common practice amongst computer users to reuse the same password on multiple sites. This presents a substantial security risk, because an attacker needs to only compromise a single site in order to gain access to other sites the victim uses. This problem is exacerbated by also reusing usernames , and by websites requiring email logins, as it makes it easier for an attacker to track
3696-476: 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
3828-516: 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
3960-464: 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
4092-421: A single dictionary word is not. Having a personally designed algorithm for generating obscure passwords is another good method. However, asking users to remember a password consisting of a "mix of uppercase and lowercase characters" is similar to asking them to remember a sequence of bits: hard to remember, and only a little bit harder to crack (e.g. only 128 times harder to crack for 7-letter passwords, less if
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4224-579: A single user across multiple sites. Password reuse can be avoided or minimized by using mnemonic techniques , writing passwords down on paper , or using a password manager . It has been argued by Redmond researchers Dinei Florencio and Cormac Herley, together with Paul C. van Oorschot of Carleton University, Canada, that password reuse is inevitable, and that users should reuse passwords for low-security websites (which contain little personal data and no financial information, for example) and instead focus their efforts on remembering long, complex passwords for
4356-406: 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
4488-588: 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
4620-442: A wallet. Password manager software can also store passwords relatively safely, in an encrypted file sealed with a single master password. To facilitate estate administration, it is helpful for people to provide a mechanism for their passwords to be communicated to the persons who will administer their affairs in the event of their death. Should a record of accounts and passwords be prepared, care must be taken to ensure that
4752-470: A weak key assumption, which corresponds to 2 bytes of data and 2 operations, and 2 bytes of data and 2 operations respectively. Presented along with XTEA was a variable-width block cipher termed Block TEA , which uses the XTEA round function, but Block TEA applies it cyclically across an entire message for several iterations. Because it operates on the entire message, Block TEA has the property that it does not need
4884-465: 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
5016-446: 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
5148-472: Is a feature of some operating systems which forces users to change passwords frequently (e.g., quarterly, monthly or even more often). Such policies usually provoke user protest and foot-dragging at best and hostility at worst. There is often an increase in the number of people who note down the password and leave it where it can easily be found, as well as help desk calls to reset a forgotten password. Users may use simpler passwords or develop variation patterns on
5280-454: Is a wooden tablet with the word inscribed on it – takes his leave, and on returning to his quarters passes on the watchword and tablet before witnesses to the commander of the next maniple, who in turn passes it to the one next to him. All do the same until it reaches the first maniples, those encamped near the tents of the tribunes. These latter are obliged to deliver the tablet to the tribunes before dark. So that if all those issued are returned,
5412-417: 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
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5544-493: 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
5676-408: 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
5808-443: 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
5940-648: 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
6072-399: 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
6204-413: Is cracking both necessary and possible. If a cryptographic hash function is well designed, it is computationally infeasible to reverse the function to recover a plaintext password. An attacker can, however, use widely available tools to attempt to guess the passwords. These tools work by hashing possible passwords and comparing the result of each guess to the actual password hashes. If the attacker finds
6336-427: Is held by a party called the claimant while the party verifying the identity of the claimant is called the verifier . When the claimant successfully demonstrates knowledge of the password to the verifier through an established authentication protocol , the verifier is able to infer the claimant's identity. In general, a password is an arbitrary string of characters including letters, digits, or other symbols. If
6468-560: 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
6600-431: Is made, possibly supplying a code that must be entered in addition to a password. More sophisticated factors include such things as hardware tokens and biometric security. Password rotation is a policy that is commonly implemented with the goal of enhancing computer security . In 2019, Microsoft stated that the practice is "ancient and obsolete". Most organizations specify a password policy that sets requirements for
6732-617: 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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#17330858067466864-733: 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
6996-424: Is sometimes called a passphrase . A passphrase is similar to a password in usage, but the former is generally longer for added security. Passwords have been used since ancient times. Sentries would challenge those wishing to enter an area to supply a password or watchword , and would only allow a person or group to pass if they knew the password. Polybius describes the system for the distribution of watchwords in
7128-612: Is sometimes used to distribute passwords but this is generally an insecure method. Since most email is sent as plaintext , a message containing a password is readable without effort during transport by any eavesdropper. Further, the message will be stored as plaintext on at least two computers: the sender's and the recipient's. If it passes through intermediate systems during its travels, it will probably be stored on there as well, at least for some time, and may be copied to backup , cache or history files on any of these systems. Using client-side encryption will only protect transmission from
7260-450: Is stored as plain text, no cracking is necessary. If it is hashed but not salted then it is vulnerable to rainbow table attacks (which are more efficient than cracking). If it is reversibly encrypted then if the attacker gets the decryption key along with the file no cracking is necessary, while if he fails to get the key cracking is not possible. Thus, of the common storage formats for passwords only when passwords have been salted and hashed
7392-481: Is the Transport Layer Security (TLS, previously called SSL ) feature built into most current Internet browsers . Most browsers alert the user of a TLS/SSL-protected exchange with a server by displaying a closed lock icon, or some other sign, when TLS is in use. There are several other techniques in use. There is a conflict between stored hashed-passwords and hash-based challenge–response authentication ;
7524-454: 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
7656-499: 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
7788-439: 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
7920-601: Is to prevent bystanders from reading the password; however, some argue that this practice may lead to mistakes and stress, encouraging users to choose weak passwords. As an alternative, users should have the option to show or hide passwords as they type them. Effective access control provisions may force extreme measures on criminals seeking to acquire a password or biometric token. Less extreme measures include extortion , rubber hose cryptanalysis , and side channel attack . Some specific password management issues that must be considered when thinking about, choosing, and handling,
8052-434: 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
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#17330858067468184-419: 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
8316-499: The DES algorithm was used as the basis for the password hashing algorithm in early Unix systems. The crypt algorithm used a 12-bit salt value so that each user's hash was unique and iterated the DES algorithm 25 times in order to make the hash function slower, both measures intended to frustrate automated guessing attacks. The user's password was used as a key to encrypt a fixed value. More recent Unix or Unix-like systems (e.g., Linux or
8448-456: The Roman military as follows: The way in which they secure the passing round of the watchword for the night is as follows: from the tenth maniple of each class of infantry and cavalry, the maniple which is encamped at the lower end of the street, a man is chosen who is relieved from guard duty, and he attends every day at sunset at the tent of the tribune , and receiving from him the watchword—that
8580-442: 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
8712-557: 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
8844-501: 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
8976-619: 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
9108-577: The "num_rounds" parameter is 32, not 64, as each iteration of the loop does two Feistel-cipher rounds. To additionally improve speed, the loop can be unrolled by pre-computing the values of sum+key[]. In 2004, Ko et al. presented a related-key differential attack on 27 out of 64 rounds of XTEA, requiring 2 chosen plaintexts and a time complexity of 2. In 2009, Lu presented a related-key rectangle attack on 36 rounds of XTEA, breaking more rounds than any previously published cryptanalytic results for XTEA. The paper presents two attacks, one without and with
9240-550: 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
9372-488: 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
9504-567: 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
9636-402: 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
9768-642: 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
9900-469: 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 ,
10032-431: The attacker. Some systems, such as PGP and Wi-Fi WPA , apply a computation-intensive hash to the password to slow such attacks, in a technique known as key stretching . An alternative to limiting the rate at which an attacker can make guesses on a password is to limit the total number of guesses that can be made. The password can be disabled, requiring a reset, after a small number of consecutive bad guesses (say 5); and
10164-436: The authenticating machine or person. If the password is carried as electrical signals on unsecured physical wiring between the user access point and the central system controlling the password database, it is subject to snooping by wiretapping methods. If it is carried as packeted data over the Internet, anyone able to watch the packets containing the logon information can snoop with a very low probability of detection. Email
10296-453: 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.)
10428-418: The conflict and limitation of hash-based methods. An augmented system allows a client to prove knowledge of the password to a server, where the server knows only a (not exactly) hashed password, and where the un-hashed password is required to gain access. Usually, a system must provide a way to change a password, either because a user believes the current password has been (or might have been) compromised, or as
10560-428: 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
10692-650: 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
10824-612: 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
10956-412: The effect of advice given to users about a good choice of password. They found that passwords based on thinking of a phrase and taking the first letter of each word are just as memorable as naively selected passwords, and just as hard to crack as randomly generated passwords. Combining two or more unrelated words and altering some of the letters to special characters or numbers is another good method, but
11088-409: 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,
11220-549: 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,
11352-506: 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
11484-481: 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
11616-406: 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
11748-415: 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
11880-524: The hardware on which the attack is running and the strength of the algorithm used to create the hash. Passwords that are used to generate cryptographic keys (e.g., for disk encryption or Wi-Fi security) can also be subjected to high rate guessing, known as password cracking . Lists of common passwords are widely available and can make password attacks very efficient. Security in such situations depends on using passwords or passphrases of adequate complexity, making such an attack computationally infeasible for
12012-510: The hash is used as a shared secret, an attacker does not need the original password to authenticate remotely; they only need the hash. Rather than transmitting a password, or transmitting the hash of the password, password-authenticated key agreement systems can perform a zero-knowledge password proof , which proves knowledge of the password without exposing it. Moving a step further, augmented systems for password-authenticated key agreement (e.g., AMP , B-SPEKE , PAK-Z , SRP-6 ) avoid both
12144-492: The issuance of replacements for lost passwords, a feature called self-service password reset . The user's identity is verified by asking questions and comparing the answers to ones previously stored (i.e., when the account was opened). Some password reset questions ask for personal information that could be found on social media, such as mother's maiden name. As a result, some security experts recommend either making up one's own questions or giving false answers. "Password aging"
12276-497: 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
12408-427: The latter requires a client to prove to a server that they know what the shared secret (i.e., password) is, and to do this, the server must be able to obtain the shared secret from its stored form. On many systems (including Unix -type systems) doing remote authentication, the shared secret usually becomes the hashed form and has the serious limitation of exposing passwords to offline guessing attacks. In addition, when
12540-459: The like. Physical security issues are also a concern, from deterring shoulder surfing to more sophisticated physical threats such as video cameras and keyboard sniffers. Passwords should be chosen so that they are hard for an attacker to guess and hard for an attacker to discover using any of the available automatic attack schemes. Nowadays, it is a common practice for computer systems to hide passwords as they are typed. The purpose of this measure
12672-421: The mail handling system server to the client machine. Previous or subsequent relays of the email will not be protected and the email will probably be stored on multiple computers, certainly on the originating and receiving computers, most often in clear text. The risk of interception of passwords sent over the Internet can be reduced by, among other approaches, using cryptographic protection. The most widely used
12804-488: 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
12936-457: 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)
13068-417: 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
13200-402: The morning newspaper online. The easier a password is for the owner to remember generally means it will be easier for an attacker to guess. However, passwords that are difficult to remember may also reduce the security of a system because (a) users might need to write down or electronically store the password, (b) users will need frequent password resets and (c) users are more likely to re-use
13332-674: 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
13464-553: 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
13596-448: 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
13728-432: 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
13860-539: 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
13992-466: The password limits the window for abuse. Allotting separate passwords to each user of a system is preferable to having a single password shared by legitimate users of the system, certainly from a security viewpoint. This is partly because users are more willing to tell another person (who may not be authorized) a shared password than one exclusively for their use. Single passwords are also much less convenient to change because many people need to be told at
14124-411: The permissible characters are constrained to be numeric, the corresponding secret is sometimes called a personal identification number (PIN). Despite its name, a password does not need to be an actual word; indeed, a non-word (in the dictionary sense) may be harder to guess, which is a desirable property of passwords. A memorized secret consisting of a sequence of words or other text separated by spaces
14256-418: 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. Password A password , sometimes called
14388-757: 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
14520-399: The records are secure, to prevent theft or fraud. Multi-factor authentication schemes combine passwords (as "knowledge factors") with one or more other means of authentication, to make authentication more secure and less vulnerable to compromised passwords. For example, a simple two-factor login might send a text message, e-mail, automated phone call, or similar alert whenever a login attempt
14652-461: The same password across different accounts. Similarly, the more stringent the password requirements, such as "have a mix of uppercase and lowercase letters and digits" or "change it monthly", the greater the degree to which users will subvert the system. Others argue longer passwords provide more security (e.g., entropy ) than shorter passwords with a wide variety of characters. In The Memorability and Security of Passwords , Jeff Yan et al. examine
14784-420: The same password for accounts on different systems, those will be compromised as well. More secure systems store each password in a cryptographically protected form, so access to the actual password will still be difficult for a snooper who gains internal access to the system, while validation of user access attempts remains possible. The most secure do not store passwords at all, but a one-way derivation, such as
14916-401: The same time, and they make removal of a particular user's access more difficult, as for instance on graduation or resignation. Separate logins are also often used for accountability, for example to know who changed a piece of data. Common techniques used to improve the security of computer systems protected by a password include: Some of the more stringent policy enforcement measures can pose
15048-551: 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
15180-410: 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
15312-412: 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
15444-508: 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
15576-405: The tribune knows that the watchword has been given to all the maniples, and has passed through all on its way back to him. If any one of them is missing, he makes inquiry at once, as he knows by the marks from what quarter the tablet has not returned, and whoever is responsible for the stoppage meets with the punishment he merits. Passwords in military use evolved to include not just a password, but
15708-473: The use of password managers , single sign-on systems and simply keeping paper lists of less critical passwords. Such practices can reduce the number of passwords that must be memorized, such as the password manager's master password, to a more manageable number. The security of a password-protected system depends on several factors. The overall system must be designed for sound security, with protection against computer viruses , man-in-the-middle attacks and
15840-431: 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 ",
15972-519: The user is permitted access. The hash value is created by applying a cryptographic hash function to a string consisting of the submitted password and, in many implementations, another value known as a salt . A salt prevents attackers from easily building a list of hash values for common passwords and prevents password cracking efforts from scaling across all users. MD5 and SHA1 are frequently used cryptographic hash functions, but they are not recommended for password hashing unless they are used as part of
16104-408: The user may be required to change the password after a larger cumulative number of bad guesses (say 30), to prevent an attacker from making an arbitrarily large number of bad guesses by interspersing them between good guesses made by the legitimate password owner. Attackers may conversely use knowledge of this mitigation to implement a denial of service attack against the user by intentionally locking
16236-421: The user out of their own device; this denial of service may open other avenues for the attacker to manipulate the situation to their advantage via social engineering . Some computer systems store user passwords as plaintext , against which to compare user logon attempts. If an attacker gains access to such an internal password store, all passwords—and so all user accounts—will be compromised. If some users employ
16368-615: The user simply capitalises one of the letters). Asking users to use "both letters and digits" will often lead to easy-to-guess substitutions such as 'E' → '3' and 'I' → '1', substitutions that are well known to attackers. Similarly typing the password one keyboard row higher is a common trick known to attackers. In 2013, Google released a list of the most common password types, all of which are considered insecure because they are too easy to guess (especially after researching an individual on social media), which includes: Traditional advice to memorize passwords and never write them down has become
16500-422: The various BSD systems) use more secure password hashing algorithms such as PBKDF2 , bcrypt , and scrypt , which have large salts and an adjustable cost or number of iterations. A poorly designed hash function can make attacks feasible even if a strong password is chosen. LM hash is a widely deployed and insecure example. Passwords are vulnerable to interception (i.e., "snooping") while being transmitted to
16632-525: 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
16764-542: 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
16896-499: 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
17028-488: 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
17160-570: 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
17292-508: 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
17424-525: 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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