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130-564: In cryptography , RC4 (Rivest Cipher 4, also known as ARC4 or ARCFOUR , meaning Alleged RC4, see below) is a stream cipher . While it is remarkable for its simplicity and speed in software, multiple vulnerabilities have been discovered in RC4, rendering it insecure. It is especially vulnerable when the beginning of the output keystream is not discarded, or when nonrandom or related keys are used. Particularly problematic uses of RC4 have led to very insecure protocols such as WEP . As of 2015, there
260-468: 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
390-428: 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
520-584: A 2 attack against passwords encrypted with RC4, as used in TLS. At the Black Hat Asia 2015 Conference, Itsik Mantin presented another attack against SSL using RC4 cipher. In 2015, security researchers from KU Leuven presented new attacks against RC4 in both TLS and WPA-TKIP . Dubbed the Numerous Occurrence MOnitoring & Recovery Exploit (NOMORE) attack, it is the first attack of its kind that
650-624: 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
780-430: 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
910-507: 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;
1040-486: 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
1170-428: 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
1300-440: 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
1430-414: 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
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#17330855524541560-612: A paper on an updated redesign called Spritz . A hardware accelerator of Spritz was published in Secrypt, 2016 and shows that due to multiple nested calls required to produce output bytes, Spritz performs rather slowly compared to other hash functions such as SHA-3 and the best known hardware implementation of RC4. Cryptography Cryptography , or cryptology (from Ancient Greek : κρυπτός , romanized : kryptós "hidden, secret"; and γράφειν graphein , "to write", or -λογία -logia , "study", respectively ),
1690-468: A random bit XORed with a non-random bit will result in a random bit. Multiple sources of potentially random data can be combined using XOR, and the unpredictability of the output is guaranteed to be at least as good as the best individual source. XOR is used in RAID 3–6 for creating parity information. For example, RAID can "back up" bytes 10011100 2 and 01101100 2 from two (or more) hard drives by XORing
1820-476: 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
1950-516: 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
2080-464: 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
2210-486: A simple adder can be made with an XOR gate to add the numbers, and a series of AND, OR and NOT gates to create the carry output. On some computer architectures, it is more efficient to store a zero in a register by XOR-ing the register with itself (bits XOR-ed with themselves are always zero) than to load and store the value zero. In cryptography , XOR is sometimes used as a simple, self-inverse mixing function, such as in one-time pad or Feistel network systems. XOR
2340-406: 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
2470-588: 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
2600-535: A stream of K[0], K[1], ... which are XORed with the plaintext to obtain the ciphertext . So ciphertext[ l ] = plaintext[ l ] ⊕ K[ l ] . Several operating systems include arc4random , an API originating in OpenBSD providing access to a random number generator originally based on RC4. The API allows no seeding, as the function initializes itself using /dev/random . The use of RC4 has been phased out in most systems implementing this API. Man pages for
2730-490: A time, which is the square root of the exhaustive key search complexity. Subsequently, many other works have been performed on key reconstruction from RC4 internal states. Subhamoy Maitra and Goutam Paul also showed that the Roos-type biases still persist even when one considers nested permutation indices, like S[S[i]] or S[S[S[i]]] . These types of biases are used in some of the later key reconstruction methods for increasing
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#17330855524542860-465: 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
2990-446: 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
3120-557: Is a group . This unfortunately prevents the combination of these two systems into larger structures, such as a mathematical ring . However, the system using exclusive or ( { T , F } , ⊕ ) {\displaystyle (\{T,F\},\oplus )} is an abelian group . The combination of operators ∧ {\displaystyle \wedge } and ⊕ {\displaystyle \oplus } over elements { T , F } {\displaystyle \{T,F\}} produce
3250-429: Is a logical operator whose negation is the logical biconditional . With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd . It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR excludes that case. Some informal ways of describing XOR are "one or
3380-412: Is a modified version of RC4 with a more complex three-phase key schedule (taking about three times as long as RC4, or the same as RC4-drop512), and a more complex output function which performs four additional lookups in the S array for each byte output, taking approximately 1.7 times as long as basic RC4. This algorithm has not been analyzed significantly. In 2014, Ronald Rivest gave a talk and co-wrote
3510-417: 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
3640-557: Is also found in other languages. However, many languages have disjunctive constructions which are robustly exclusive such as French soit... soit . The symbol used for exclusive disjunction varies from one field of application to the next, and even depends on the properties being emphasized in a given context of discussion. In addition to the abbreviation "XOR", any of the following symbols may also be seen: If using binary values for true (1) and false (0), then exclusive or works exactly like addition modulo 2. Exclusive disjunction
3770-494: Is also heavily used in block ciphers such as AES (Rijndael) or Serpent and in block cipher implementation (CBC, CFB, OFB or CTR). In simple threshold-activated artificial neural networks , modeling the XOR function requires a second layer because XOR is not a linearly separable function. Similarly, XOR can be used in generating entropy pools for hardware random number generators . The XOR operation preserves randomness, meaning that
3900-493: 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
4030-405: Is another RC4 variant. It uses similar key schedule as RC4, with j := S[(j + S[i] + key[i mod keylength]) mod 256] iterating 3 × 256 = 768 times rather than 256, and with an optional additional 768 iterations to incorporate an initial vector. The output generation function operates as follows: This was attacked in the same papers as RC4A, and can be distinguished within 2 output bytes. RC4
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4160-408: 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
4290-443: 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
4420-478: Is called the function's algebraic normal form . Disjunction is often understood exclusively in natural languages . In English, the disjunctive word "or" is often understood exclusively, particularly when used with the particle "either". The English example below would normally be understood in conversation as implying that Mary is not both a singer and a poet. However, disjunction can also be understood inclusively, even in combination with "either". For instance,
4550-648: 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
4680-399: 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
4810-550: Is equivalent to the disjunction of the negation of its antecedent and its consequence) and material equivalence . In summary, we have, in mathematical and in engineering notation: By applying the spirit of De Morgan's laws , we get: ¬ ( p ↮ q ) ⇔ ¬ p ↮ q ⇔ p ↮ ¬ q . {\displaystyle \lnot (p\nleftrightarrow q)\Leftrightarrow \lnot p\nleftrightarrow q\Leftrightarrow p\nleftrightarrow \lnot q.} Although
4940-456: Is famous for breaking the WEP standard). Because RC4 is a stream cipher , it is more malleable than common block ciphers . If not used together with a strong message authentication code (MAC), then encryption is vulnerable to a bit-flipping attack . The cipher is also vulnerable to a stream cipher attack if not implemented correctly. It is noteworthy, however, that RC4, being a stream cipher,
5070-560: 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
5200-461: Is incremented, two bytes are generated: Thus, the algorithm is: Although the algorithm required the same number of operations per output byte, there is greater parallelism than RC4, providing a possible speed improvement. Although stronger than RC4, this algorithm has also been attacked, with Alexander Maximov and a team from NEC developing ways to distinguish its output from a truly random sequence. Variably Modified Permutation Composition (VMPC)
5330-574: Is officially termed "Rivest Cipher 4", the RC acronym is alternatively understood to stand for "Ron's Code" (see also RC2 , RC5 and RC6 ). RC4 was initially a trade secret , but in September 1994, a description of it was anonymously posted to the Cypherpunks mailing list. It was soon posted on the sci.crypt newsgroup , where it was broken within days by Bob Jenkins . From there, it spread to many sites on
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5460-469: Is often used for bitwise operations. Examples: As noted above, since exclusive disjunction is identical to addition modulo 2, the bitwise exclusive disjunction of two n -bit strings is identical to the standard vector of addition in the vector space ( Z / 2 Z ) n {\displaystyle (\mathbb {Z} /2\mathbb {Z} )^{n}} . In computer science, exclusive disjunction has several uses: In logical circuits,
5590-617: 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
5720-422: Is performed the same way (since exclusive or with given data is an involution ). This is similar to the one-time pad , except that generated pseudorandom bits , rather than a prepared stream, are used. To generate the keystream, the cipher makes use of a secret internal state which consists of two parts: The permutation is initialized with a variable-length key , typically between 40 and 2048 bits, using
5850-559: Is plausible that some state cryptologic agencies may already have better attacks that render RC4 insecure. Given that, as of 2013, a large amount of TLS traffic uses RC4 to avoid attacks on block ciphers that use cipher block chaining , if these hypothetical better attacks exist, then this would make the TLS-with-RC4 combination insecure against such attackers in a large number of practical scenarios. In March 2015, researcher to Royal Holloway announced improvements to their attack, providing
5980-515: Is prohibited by RFC 7465 published in February 2015. In 1995, Andrew Roos experimentally observed that the first byte of the keystream is correlated with the first three bytes of the key, and the first few bytes of the permutation after the KSA are correlated with some linear combination of the key bytes. These biases remained unexplained until 2007, when Goutam Paul, Siddheshwar Rathi and Subhamoy Maitra proved
6110-733: 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
6240-398: Is sometimes useful to write p ↮ q {\displaystyle p\nleftrightarrow q} in the following way: or: This equivalence can be established by applying De Morgan's laws twice to the fourth line of the above proof. The exclusive or is also equivalent to the negation of a logical biconditional , by the rules of material implication (a material conditional
6370-464: Is speculation that some state cryptologic agencies may possess the capability to break RC4 when used in the TLS protocol . IETF has published RFC 7465 to prohibit the use of RC4 in TLS; Mozilla and Microsoft have issued similar recommendations. A number of attempts have been made to strengthen RC4, notably Spritz, RC4A, VMPC , and RC4. RC4 was designed by Ron Rivest of RSA Security in 1987. While it
6500-454: 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
6630-405: Is the number of initial keystream bytes that are dropped. The SCAN default is n = 768 bytes, but a conservative value would be n = 3072 bytes. The Fluhrer, Mantin and Shamir attack does not apply to RC4-based SSL, since SSL generates the encryption keys it uses for RC4 by hashing, meaning that different SSL sessions have unrelated keys. In 2005, Andreas Klein presented an analysis of
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#17330855524546760-827: 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
6890-499: 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
7020-439: 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
7150-434: 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
7280-419: 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
7410-415: Is zero, and the second byte is not equal to 2, then the second output byte is always zero. Such bias can be detected by observing only 256 bytes. Souradyuti Paul and Bart Preneel of COSIC showed that the first and the second bytes of the RC4 were also biased. The number of required samples to detect this bias is 2 bytes. Scott Fluhrer and David McGrew also showed attacks that distinguished
7540-435: The key-scheduling algorithm (KSA). Once this has been completed, the stream of bits is generated using the pseudo-random generation algorithm (PRGA). The key-scheduling algorithm is used to initialize the permutation in the array "S". "keylength" is defined as the number of bytes in the key and can be in the range 1 ≤ keylength ≤ 256, typically between 5 and 16, corresponding to a key length of 40–128 bits. First,
7670-467: The English Misplaced Pages article on RC4 in his own course notes in 2008 and confirmed the history of RC4 and its code in a 2014 paper by him. RC4 became part of some commonly used encryption protocols and standards, such as WEP in 1997 and WPA in 2003/2004 for wireless cards; and SSL in 1995 and its successor TLS in 1999, until it was prohibited for all versions of TLS by RFC 7465 in 2015, due to
7800-548: The RC4 attacks weakening or breaking RC4 used in SSL/TLS. The main factors in RC4's success over such a wide range of applications have been its speed and simplicity: efficient implementations in both software and hardware were very easy to develop. RC4 generates a pseudorandom stream of bits (a keystream ). As with any stream cipher, these can be used for encryption by combining it with the plaintext using bitwise exclusive or ; decryption
7930-442: 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
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#17330855524548060-450: The WEP ("wired equivalent privacy") encryption used with 802.11 wireless networks . This caused a scramble for a standards-based replacement for WEP in the 802.11 market and led to the IEEE ;802.11i effort and WPA . Protocols can defend against this attack by discarding the initial portion of the keystream. Such a modified algorithm is traditionally called "RC4-drop[ n ]", where n
8190-557: 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
8320-423: The logical conjunction ("logical and", ∧ {\displaystyle \wedge } ), the disjunction ("logical or", ∨ {\displaystyle \lor } ), and the negation ( ¬ {\displaystyle \lnot } ) as follows: The exclusive disjunction p ↮ q {\displaystyle p\nleftrightarrow q} can also be expressed in
8450-501: 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
8580-529: The operators ∧ {\displaystyle \wedge } ( conjunction ) and ∨ {\displaystyle \lor } ( disjunction ) are very useful in logic systems, they fail a more generalizable structure in the following way: The systems ( { T , F } , ∧ ) {\displaystyle (\{T,F\},\wedge )} and ( { T , F } , ∨ ) {\displaystyle (\{T,F\},\lor )} are monoids , but neither
8710-619: 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
8840-550: 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
8970-488: 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
9100-481: The Internet. The leaked code was confirmed to be genuine, as its output was found to match that of proprietary software using licensed RC4. Because the algorithm is known, it is no longer a trade secret. The name RC4 is trademarked, so RC4 is often referred to as ARCFOUR or ARC4 (meaning alleged RC4 ) to avoid trademark problems. RSA Security has never officially released the algorithm; Rivest has, however, linked to
9230-567: 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
9360-402: 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
9490-549: The RC4 stream cipher, showing more correlations between the RC4 keystream and the key. Erik Tews , Ralf-Philipp Weinmann , and Andrei Pychkine used this analysis to create aircrack-ptw, a tool that cracks 104-bit RC4 used in 128-bit WEP in under a minute. Whereas the Fluhrer, Mantin, and Shamir attack used around 10 million messages, aircrack-ptw can break 104-bit keys in 40,000 frames with 50% probability, or in 85,000 frames with 95% probability. A combinatorial problem related to
9620-642: 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
9750-532: The above have motivated analyses of the exclusivity inference as pragmatic conversational implicatures calculated on the basis of an inclusive semantics . Implicatures are typically cancellable and do not arise in downward entailing contexts if their calculation depends on the Maxim of Quantity . However, some researchers have treated exclusivity as a bona fide semantic entailment and proposed nonclassical logics which would validate it. This behavior of English "or"
9880-469: 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 ,
10010-531: The array "S" is initialized to the identity permutation . S is then processed for 256 iterations in a similar way to the main PRGA, but also mixes in bytes of the key at the same time. For as many iterations as are needed, the PRGA modifies the state and outputs a byte of the keystream. In each iteration, the PRGA: Each element of S is swapped with another element at least once every 256 iterations. Thus, this produces
10140-453: 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.)
10270-428: 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
10400-650: 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
10530-612: 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
10660-409: 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,
10790-549: 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,
10920-506: 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
11050-481: 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
11180-406: The first example below shows that "either" can be felicitously used in combination with an outright statement that both disjuncts are true. The second example shows that the exclusive inference vanishes away under downward entailing contexts. If disjunction were understood as exclusive in this example, it would leave open the possibility that some people ate both rice and beans. Examples such as
11310-399: The following way: This representation of XOR may be found useful when constructing a circuit or network, because it has only one ¬ {\displaystyle \lnot } operation and small number of ∧ {\displaystyle \land } and ∨ {\displaystyle \lor } operations. A proof of this identity is given below: It
11440-406: 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
11570-415: 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
11700-596: The inputs differ: Exclusive disjunction essentially means 'either one, but not both nor none'. In other words, the statement is true if and only if one is true and the other is false. For example, if two horses are racing, then one of the two will win the race, but not both of them. The exclusive disjunction p ↮ q {\displaystyle p\nleftrightarrow q} , also denoted by p ? q {\displaystyle p\operatorname {?} q} or J p q {\displaystyle Jpq} , can be expressed in terms of
11830-406: The just mentioned bytes, resulting in ( 11110000 2 ) and writing it to another drive. Under this method, if any one of the three hard drives are lost, the lost byte can be re-created by XORing bytes from the remaining drives. For instance, if the drive containing 01101100 2 is lost, 10011100 2 and 11110000 2 can be XORed to recover the lost byte. XOR is also used to detect an overflow in
11960-497: 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
12090-400: The keystream of the RC4 from a random stream given a gigabyte of output. The complete characterization of a single step of RC4 PRGA was performed by Riddhipratim Basu, Shirshendu Ganguly, Subhamoy Maitra, and Goutam Paul. Considering all the permutations, they proved that the distribution of the output is not uniform given i and j, and as a consequence, information about j is always leaked into
12220-405: The keystream–key correlation and, in another work, Goutam Paul and Subhamoy Maitra proved the permutation–key correlations. The latter work also used the permutation–key correlations to design the first algorithm for complete key reconstruction from the final permutation after the KSA, without any assumption on the key or initialization vector . This algorithm has a constant probability of success in
12350-404: The logical "AND" operation as multiplication on F 2 {\displaystyle \mathbb {F} _{2}} and the "XOR" operation as addition on F 2 {\displaystyle \mathbb {F} _{2}} : The description of a Boolean function as a polynomial in F 2 {\displaystyle \mathbb {F} _{2}} , using this basis,
12480-488: 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
12610-457: 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)
12740-417: 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
12870-674: 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
13000-497: The new arc4random include the backronym "A Replacement Call for Random" for ARC4 as a mnemonic, as it provides better random data than rand() does. Proposed new random number generators are often compared to the RC4 random number generator. Several attacks on RC4 are able to distinguish its output from a random sequence . Many stream ciphers are based on linear-feedback shift registers (LFSRs), which, while efficient in hardware, are less so in software. The design of RC4 avoids
13130-553: 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
13260-399: The number of inputs and outputs of the RC4 cipher was first posed by Itsik Mantin and Adi Shamir in 2001, whereby, of the total 256 elements in the typical state of RC4, if x number of elements ( x ≤ 256) are only known (all other elements can be assumed empty), then the maximum number of elements that can be produced deterministically is also x in the next 256 rounds. This conjecture
13390-448: 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
13520-432: 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
13650-539: 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
13780-961: The other but not both", "either one or the other", and "A or B, but not A and B". It is symbolized by the prefix operator J {\displaystyle J} and by the infix operators XOR ( / ˌ ɛ k s ˈ ɔː r / , / ˌ ɛ k s ˈ ɔː / , / ˈ k s ɔː r / or / ˈ k s ɔː / ), EOR , EXOR , ∨ ˙ {\displaystyle {\dot {\vee }}} , ∨ ¯ {\displaystyle {\overline {\vee }}} , ∨ _ {\displaystyle {\underline {\vee }}} , ⩛ , ⊕ {\displaystyle \oplus } , ↮ {\displaystyle \nleftrightarrow } , and ≢ {\displaystyle \not \equiv } . The truth table of A ⊕ B {\displaystyle A\oplus B} shows that it outputs true whenever
13910-405: The output stream. This is known as RC4-drop N , where N is typically a multiple of 256, such as 768 or 1024. A number of attempts have been made to strengthen RC4, notably Spritz, RC4A, VMPC , and RC4. Souradyuti Paul and Bart Preneel have proposed an RC4 variant, which they call RC4A. RC4A uses two state arrays S1 and S2 , and two indexes j1 and j2 . Each time i
14040-481: The output. In 2001, a new and surprising discovery was made by Fluhrer , Mantin and Shamir : over all the possible RC4 keys, the statistics for the first few bytes of output keystream are strongly non-random, leaking information about the key. If the nonce and long-term key are simply concatenated to generate the RC4 key, this long-term key can be discovered by analysing a large number of messages encrypted with this key. This and related effects were then used to break
14170-504: 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. Exclusive or Exclusive or , exclusive disjunction , exclusive alternation , logical non-equivalence , or logical inequality
14300-462: The protocol must specify how to combine the nonce and the long-term key to generate the stream key for RC4. One approach to addressing this is to generate a "fresh" RC4 key by hashing a long-term key with a nonce . However, many applications that use RC4 simply concatenate key and nonce; RC4's weak key schedule then gives rise to related-key attacks , like the Fluhrer, Mantin and Shamir attack (which
14430-774: The result of a signed binary arithmetic operation. If the leftmost retained bit of the result is not the same as the infinite number of digits to the left, then that means overflow occurred. XORing those two bits will give a "1" if there is an overflow. XOR can be used to swap two numeric variables in computers, using the XOR swap algorithm ; however this is regarded as more of a curiosity and not encouraged in practice. XOR linked lists leverage XOR properties in order to save space to represent doubly linked list data structures. In computer graphics , XOR-based drawing methods are often used to manage such items as bounding boxes and cursors on systems without alpha channels or overlay planes. It
14560-551: 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
14690-410: 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
14820-417: The success probability. The keystream generated by the RC4 is biased to varying degrees towards certain sequences, making it vulnerable to distinguishing attacks . The best such attack is due to Itsik Mantin and Adi Shamir , who showed that the second output byte of the cipher was biased toward zero with probability 1/128 (instead of 1/256). This is due to the fact that if the third byte of the original state
14950-412: 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
15080-508: 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
15210-411: The use of LFSRs and is ideal for software implementation, as it requires only byte manipulations. It uses 256 bytes of memory for the state array, S[0] through S[255], k bytes of memory for the key, key[0] through key[k−1], and integer variables, i, j, and K. Performing a modular reduction of some value modulo 256 can be done with a bitwise AND with 255 (which is equivalent to taking the low-order byte of
15340-431: 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 ",
15470-419: The value in question). These test vectors are not official, but convenient for anyone testing their own RC4 program. The keys and plaintext are ASCII , the keystream and ciphertext are in hexadecimal . Unlike a modern stream cipher (such as those in eSTREAM ), RC4 does not take a separate nonce alongside the key. This means that if a single long-term key is to be used to securely encrypt multiple streams,
15600-520: The well-known two-element field F 2 {\displaystyle \mathbb {F} _{2}} . This field can represent any logic obtainable with the system ( ∧ , ∨ ) {\displaystyle (\land ,\lor )} and has the added benefit of the arsenal of algebraic analysis tools for fields. More specifically, if one associates F {\displaystyle F} with 0 and T {\displaystyle T} with 1, one can interpret
15730-525: 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
15860-464: Was demonstrated in practice. Their attack against TLS can decrypt a secure HTTP cookie within 75 hours. The attack against WPA-TKIP can be completed within an hour and allows an attacker to decrypt and inject arbitrary packets. As mentioned above, the most important weakness of RC4 comes from the insufficient key schedule; the first bytes of output reveal information about the key. This can be corrected by simply discarding some initial portion of
15990-542: 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
16120-499: 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
16250-575: Was for a period of time the only common cipher that was immune to the 2011 BEAST attack on TLS 1.0 . The attack exploits a known weakness in the way cipher-block chaining mode is used with all of the other ciphers supported by TLS 1.0, which are all block ciphers. In March 2013, there were new attack scenarios proposed by Isobe, Ohigashi, Watanabe and Morii, as well as AlFardan, Bernstein, Paterson, Poettering and Schuldt that use new statistical biases in RC4 key table to recover plaintext with large number of TLS encryptions. The use of RC4 in TLS
16380-488: 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
16510-570: 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
16640-508: 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
16770-486: Was put to rest in 2004 with a formal proof given by Souradyuti Paul and Bart Preneel . In 2013, a group of security researchers at the Information Security Group at Royal Holloway, University of London reported an attack that can become effective using only 2 encrypted messages. While yet not a practical attack for most purposes, this result is sufficiently close to one that it has led to speculation that it
16900-525: 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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