NationMaster - Encyclopedia: XSL attack

In cryptography, the XSL attack is a method of cryptanalysis for block ciphers. Block ciphers are a specific type of cipher (a "secret code" in more common speech). Cryptanalysis is the study of methods for obtaining the meaning of encrypted information without access to the secret information (the "key") which is normally required to do so. Cryptanalysis can loosely be thought of as "codebreaking", though that term is not entirely accurate. Image File history File links New-sci-xsl. ... Image File history File links New-sci-xsl. ... New Scientist cover - 18 December 2004 New Scientist is a weekly international science magazine covering recent developments in science and technology for a general English-speaking audience. ... 2003 : January - February - March - April - May - June - July - August - September - October - November - December A timeline of events in the news for June, 2003. ... Cryptography - Wikipedia, the free encyclopedia /**/ @import /skins-1. ... Cryptanalysis (from the Greek kryptÃ³s, hidden, and analÃ½ein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information without access to the secret information which is normally required to do so. ... In cryptography, a block cipher is a symmetric key cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation. ...

The attack was first published in 2002 by researchers Nicolas Courtois and Josef Pieprzyk. It has caused some controversy as it is claimed to have the potential to break the Advanced Encryption Standard (AES) cipher — also known as Rijndael — faster than an exhaustive search. Since AES is already widely used in commerce and government for the transmission of secret information, finding a technique that can shorten the amount of time it takes to retrieve the secret message without having the key would have wide implications. Opinions differ on whether the attack works because the method is heuristic and very technical, and so it has proved difficult to evaluate its complexity. In addition, the method is expected to have a high work-factor, which unless lessened, means the technique would not reduce the effort to break AES very much in comparison to an exhaustive search. Therefore, even if the attack has been analysed correctly, it is unlikely to affect the real-world security of block ciphers in the near future. Nonetheless, the attack has caused some experts to express greater unease at the algebraic simplicity of the current AES. 2002 (MMII) is a common year starting on Tuesday of the Gregorian calendar. ... Nicolas Courtois is a cryptographer who works on cryptosystems and cryptographic attacks based on multivariate polynomial equations over finite fields. ... Josef Pieprzyk is a professor at Macquarie University in Sydney, Australia. ... General Designer(s) Vincent Rijmen and Joan Daemen First published 1998 Derived from Square (cipher) Cipher(s) based on this design Crypton (cypher), Anubis (cipher), GRAND CRU Algorithm detail Block size(s) 128 bits note Key size(s) 128, 192 or 256 bits note Structure Substitution-permutation network Number of... This article is about algorithms for encryption and decryption. ... This article is about the block cipher. ... The EFFs US$250,000 DES cracking machine contained over 18,000 custom chips and could brute force a DES key in a matter of days â€” the photograph shows a DES Cracker circuit board fitted with several Deep Crack chips In cryptanalysis, a brute force attack is a method... In computer science, besides the common use as rule of thumb (see heuristic), the term heuristic has two well-defined technical meanings. ...

In overview, the XSL attack relies on first analysing the internals of a cipher and deriving a system of quadratic simultaneous equations. These systems of equations are typically very large, for example 8000 equations with 1600 variables for the 128-bit AES. Several methods for solving such systems are known. In the XSL attack, a specialised algorithm, termed XSL (eXtended Sparse Linearisation), is then applied to solve these equations and recover the key. f(x) = x2 - x - 2 In mathematics, a quadratic function is a polynomial function of the form , where a is nonzero. ... In mathematics, simultaneous equations are a set of equations where variables are shared. ... In computer science and mathematics, a variable is a symbol denoting a quantity or symbolic representation. ... A key is a piece of information that controls the operation of a cryptography algorithm. ...

The attack is notable for requiring only a handful of known plaintexts to perform; previous methods of cryptanalysis, such as linear and differential cryptanalysis, often require unrealistically large numbers of known or chosen plaintexts. The known-plaintext attack is a cryptanalytic attack in which the attacker has samples of both the plaintext and its encrypted version (ciphertext) and is at liberty to make use of them to reveal further secret information; typically this is the secret key. ... In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. ... Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. ... A chosen plaintext attack is any form of cryptanalysis which presumes that the attacker has the capability to choose arbitrary plaintexts to be encrypted and obtain the corresponding ciphertexts. ...

Solving multivariate quadratic equations

Solving multivariate quadratic equations (MQ) is an NP-hard problem (in the general case) with several applications in cryptography. The XSL attack requires an efficient algorithm for tackling MQ. In 1999, Kipnis and Shamir showed that a particular public key algorithm — known as the Hidden Field Equations scheme (HFE) — could be reduced to a system of overdefined quadratic equations ("overdefined" means that there are more equations than unknowns). One technique for solving such systems is linearisation, which involves replacing each quadratic term with an independent variable and solving the resultant linear system using an algorithm such as Gaussian elimination. To succeed, linearisation requires enough linearly independent equations (approximately as many as the number of terms). However, for the cryptanalysis of HFE there were too few equations, so Kipnis and Shamir proposed relinearisation, a technique where extra non-linear equations are added after linearisation, and the resultant system is solved by a second application of linearisation. Relinearisation proved general enough to be applicable to other schemes. Multivariate is a concept from statistics. ... In computational complexity theory, NP-hard (Non-deterministic Polynomial-time hard) refers to the class of decision problems that contains all problems H such that for all decision problems L in NP there is a polynomial-time many-one reduction to H. Informally this class can be described as containing... 1999 (MCMXCIX) is a common year starting on Friday, and was designated the International Year of Older Persons by the United Nations. ... Adi Shamir at the CRYPTO 2003 conference. ... In cryptography, an asymmetric key algorithm uses a pair of different, though related, cryptographic keys to encrypt and decrypt. ... HFE stands for Hidden Fields Equations. ... In mathematics, Gaussian elimination or Gauss-Jordan elimination, named after Carl Friedrich Gauss and Wilhelm Jordan (for many, Gaussian elimination is regarded as the front half of the complete Gauss-Jordan elimination), is an algorithm in linear algebra for determining the solutions of a system of linear equations, for determining... In linear algebra, a set of elements of a vector space is linearly independent if none of the vectors in the set can be written as a linear combination of finitely many other vectors in the set. ...

In 2000, Courtois et al. proposed an improved algorithm for MQ known as XL (for eXtended Linearisation), which increases the number of equations by multiplying them with all monomials of a certain degree. Complexity estimates showed that the XL attack would not work against the equations derived from block ciphers such as AES. However, the systems of equations produced had a special structure, and the XSL algorithm was developed as a refinement of XL which could take advantage of this structure. In XSL, the equations are multiplied only by carefully selected monomials, and several variants have been proposed. This article is about the year 2000. ... In mathematics, a monomial is a particular kind of polynomial, having just one term. ... This article is about the term degree as used in mathematics. ...

Research into the efficiency of XL and its derivative algorithms remains ongoing (Yang and Chen, 2004). In 2005 Cid and Leurent gave strong evidence that, in its proposed form, the XSL algorithm does not provide an efficient method for solving the AES system of equations.

Application to block ciphers

Courtois and Pieprzyk (2002) observed that Rijndael and Serpent could be expressed as a system of quadratic equations. The variables represent not just the plaintext, ciphertext and key bits, but also various intermediate values within the algorithm. The S-box of Rijndael seems especially vulnerable to this type of analysis, as it is based on the algebraically simple inverse function. Subsequently, other ciphers have been studied to see what of systems of equations can be produced (Biryukov and De Cannière, 2003), including Camellia, KHAZAD, MISTY-1 and KASUMI. Unlike other forms of cryptanalysis, such as differential and linear cryptanalysis, only one or two known plaintexts are required. This article is about the block cipher. ... Serpent is a symmetric key block cipher which was a finalist in the Advanced Encryption Standard contest, where it came second to Rijndael. ... The plain text term has a different meaning. ... This article is about algorithms for encryption and decryption. ... In cryptography, a substitution box (or S-box) is a basic component of symmetric key algorithms. ... In mathematics, an inverse function is in simple terms a function which does the reverse of a given function. ... In cryptography, Camellia is a block cipher that has been evaluated favorably by several organisations, including the European Unions NESSIE project (a selected algorithm), and the Japanese CRYPTREC project (a recommended algorithm). ... In cryptography, KHAZAD is a block cipher designed by Paulo S. L. M. Barreto together with Vincent Rijmen, one of the designers of the Advanced Encryption Standard (Rijndael). ... In cryptography, MISTY1 (or MISTY-1) is a block cipher designed in 1995 by Mitsuru Matsui for Mitsubishi Electric. ... In cryptography, KASUMI, also termed A5/3, is a block cipher used in the confidentiality (f8) and integrity algorithms (f9) for 3GPP mobile communications. ... Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. ... In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. ... The known-plaintext attack is a cryptanalytic attack in which the attacker has samples of both the plaintext and its encrypted version (ciphertext) and is at liberty to make use of them to reveal further secret information; typically this is the secret key. ...

The XSL algorithm is tailored to solve the type of equation systems that are produced. Courtois and Pieprzyk estimate that an "optimistic evaluation shows that the XSL attack might be able to break Rijndael [with] 256 bits and Serpent for key lengths [of] 192 and 256 bits." Their analysis, however, is not universally accepted. For example:

One of the inventors of Rijndael, Vincent Rijmen, commented, "The XSL attack is not an attack. It is a dream." [2] Don Coppersmith is a cryptographer and mathematician who was involved in the design of the Data Encryption Standard block cipher at IBM. He has also worked on algorithms for computing discrete logarithms, the cryptanalysis of RSA, methods for rapid matrix multiplication and IBMs MARS cipher, In 1972, Coppersmith obtained... Together with Joan Daemen, Vincent Rijmen designed the Rijndael block cipher, which was selected as the Advanced Encryption Standard in 2000. ...

In 2003, Murphy and Robshaw discovered an alternative description of AES, embedding it in a larger cipher called "BES", which can be described using very simple operations over a single field, GF(2⁸). An XSL attack mounted on this system yields a simpler set of equations which would break AES with complexity of around 2¹⁰⁰, if the Courtois and Pieprzyk analysis is correct. 2003 (MMIII) is a common year starting on Wednesday of the Gregorian calendar. ... In abstract algebra, a field is an algebraic structure in which the operations of addition, subtraction, multiplication and division (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers. ...

Even if XSL works against some modern algorithms, the attack currently poses little danger in terms of practical security. Like many modern cryptanalytic results, it would be a so-called "certificational weakness": while faster than a brute force attack, the resources required are still huge, and it is very unlikely that real-world systems could be compromised by using it. Future improvements could increase the practicality of an attack, however. Because this type of attack is new and unexpected, some cryptographers have expressed unease at the algebraic simplicity of ciphers like Rijndael. Bruce Schneier and Niels Ferguson write, "We have one criticism of AES: we don't quite trust the security...What concerns us the most about AES is its simple algebraic structure....No other block cipher we know of has such a simple algebraic representation. We have no idea whether this leads to an attack or not, but not knowing is reason enough to be skeptical about the use of AES." (Practical Cryptography, 2003, pp56-57) The EFFs US$250,000 DES cracking machine contained over 18,000 custom chips and could brute force a DES key in a matter of days â€” the photograph shows a DES Cracker circuit board fitted with several Deep Crack chips In cryptanalysis, a brute force attack is a method... Pre-19th century Leone Battista Alberti, polymath/universal genius, inventor of polyalphabetic substitution (see frequency analysis for the significance of this -- missed by most for a long time and dumbed down in the Vigenère cipher), and what may have been the first mechanical encryption aid. ... Bruce Schneier Bruce Schneier (born January 15, 1963) is an American cryptographer, computer security specialist, and writer. ...

References

New Scientist cover - 18 December 2004 New Scientist is a weekly international science magazine covering recent developments in science and technology for a general English-speaking audience. ...

External links

Category: Cryptographic attacks In cryptography, a block cipher is a symmetric key cipher which operates on fixed-length groups of bits, termed blocks, with an unvarying transformation. ... In cryptography, 3-Way is a block cipher designed in 1994 by Joan Daemen, who also (with Vincent Rijmen) designed Rijndael, the winner of NISTs Advanced Encryption Standard (AES) contest. ... General Designer(s) Vincent Rijmen and Joan Daemen First published 1998 Derived from Square (cipher) Cipher(s) based on this design Crypton (cypher), Anubis (cipher), GRAND CRU Algorithm detail Block size(s) 128 bits note Key size(s) 128, 192 or 256 bits note Structure Substitution-permutation network Number of... Akelarre is a block cipher proposed in 1996, and combined features from IDEA and RC5. ... Anubis is a block cipher which operates on data blocks of 128 bits, accepting keys of length 32N bits (N=4. ... General Designer(s) Bruce Schneier First published 1993 Derived from - Cipher(s) based on this design - Algorithm detail Block size(s) 64 bits Key size(s) 32-448 bits in steps of 8 bits; default 128 bits Structure Feistel network Number of rounds 16 Best cryptanalysis Four rounds of Blowfish... In cryptography, Camellia is a block cipher that has been evaluated favorably by several organisations, including the European Unions NESSIE project (a selected algorithm), and the Japanese CRYPTREC project (a recommended algorithm). ... Three rounds of the CAST-128 block cipher In cryptography, CAST-128 (alternatively CAST5) is a block cipher used in a number of products, notably as the default cipher in some versions of GPG and PGP. It has also been approved for Canadian government use by the Communications Security Establishment. ... In cryptography, CAST-256 (or CAST6) is a block cipher published in June 1998 and submitted as a candidate for the Advanced Encryption Standard (AES). ... In cryptography, the Cellular Message Encryption Algorithm (CMEA) is a block cipher which was used for securing mobile phones in the United States. ... In cryptography, the CS-Cipher is a block cipher invented by Jacques Stern and Serge Vaudenay in 1998. ... Deal can refer to: an agreement reached after negotiation, for example a contract to sell as a dealer or dealership a bargain Deal$, a U.S. dollar store the town of Deal, Kent, England the borough of Deal, New Jersey, United States while playing card games, the act of distributing... General Designer(s) IBM First published 1975 (January 1977 as the standard) Derived from Lucifer (cipher) Cipher(s) based on this design Triple DES, G-DES, DES-X, LOKI89, ICE Algorithm detail Block size(s) 64 bits Key size(s) 56 bits Structure Feistel network Number of rounds 16 Best... In cryptography, DES-X (or DESX) is a variant on the DES (Data Encryption Standard) block cipher intended to increase the complexity of a brute force attack using a technique called key whitening. ... There have been several different revisions of FEAL, though all are Feistel ciphers, and make use of the same basic round function and operate on a 64-bit block. ... General Designer(s) Pascal Junod, Serge Vaudenay First published 2003 Derived from IDEA Cipher(s) based on this design None Algorithm detail Block size(s) 64, 128 bits Key size(s) 0-256 bits Structure Lai-Massey scheme Number of rounds 12 Best cryptanalysis Integral attack on 7 round FOX... Suborders Archaeobatrachia Mesobatrachia Neobatrachia - Full list of families Frog is the common name for amphibians in the order, Anura. ... In cryptography, the Generalized DES Scheme (G-DES or GDES) is a variant of the DES block cipher designed to speed-up the encryption. ... Diagram of GOST In cryptography, GOST (Russian Ð“ÐžÐ¡Ð¢) (GOsudarstvennyi STandard, Russian for Government Standard) is a symmetric key block cipher published in 1990 as the Soviet standard (GOST 28147-89). ... In cryptography, ICE (Information Concealment Engine) is a block cipher published by Kwan in 1997. ... General Designer(s) James Massey, Xuejia Lai First published 1991 Derived from PES Cipher(s) based on this design MESH, Akelarre, FOX (IDEA NXT) Algorithm detail Block size(s) 64 bits Key size(s) 128 bits Structure Substitution-permutation network Number of rounds 8. ... In cryptography, KASUMI, also termed A5/3, is a block cipher used in the confidentiality (f8) and integrity algorithms (f9) for 3GPP mobile communications. ... In cryptography, KHAZAD is a block cipher designed by Paulo S. L. M. Barreto together with Vincent Rijmen, one of the designers of the Advanced Encryption Standard (Rijndael). ... In cryptography, Khufu and Khafre are two block ciphers designed by Ralph Merkle in 1989 while working at Xeroxs Palo Alto Research Center. ... This picture, from an 18th century Icelandic manuscript, shows Loki with his invention - the fishing net. ... General Designer(s) Lawrie Brown, assisted by Jennifer Seberry and Josef Pieprzyk First published 1998 Derived from LOKI91 Cipher(s) based on this design - Algorithm detail Block size(s) 128 bits Key size(s) 128, 192 or 256 bits Structure Feistel network Number of rounds 16 Best cryptanalysis Linear cryptanalysis... In cryptography, Lucifer was the name given to several of the earliest civilian block ciphers, developed by Horst Feistel and his colleagues at IBM. Lucifer was a direct precursor to the Data Encryption Standard. ... In cryptography, MacGuffin is a block cipher created in 1994 by Bruce Schneier and Matt Blaze at a Fast Software Encryption workshop. ... In cryptography, Madryga is a block cipher created in 1984 by W. E. Madryga. ... In cryptography, MAGENTA is a symmetric key block cipher developed by Deutsche Telekom. ... Amongst the findings from the Opportunity rover is the presence of hematite on Mars in the form of small spheres on the Meridiani Planum. ... In cryptography, MISTY1 (or MISTY-1) is a block cipher designed in 1995 by Mitsuru Matsui for Mitsubishi Electric. ... In cryptography, MMB (Modular Multiplication-based Block cipher) is a block cipher designed by Joan Daemen as an improved replacement for the IDEA cipher. ... In cryptography, NewDES is a symmetric key block cipher. ... Noekeon is a block cipher with a block and key length of 128 bits. ... General Designer(s) Ron Rivest First published source code leaked 1996 (designed 1987) Derived from - Cipher(s) based on this design - Algorithm detail Block size(s) 64 bits Key size(s) 8â€“128 bits, in steps of eight bits; default 64 bits Structure Source-heavy Feistel network Number of rounds... General Designer(s) Ron Rivest First published 1994 Derived from - Cipher(s) based on this design RC6, Akelarre Algorithm detail Block size(s) 32, 64 or 128 bits (64 suggested) Key size(s) 0 to 2040 bits (128 suggested) Structure Feistel network Number of rounds 12 suggested originally Best cryptanalysis... In cryptography, RC6 is a symmetric key block cipher derived from RC5. ... In cryptography, REDOC II and REDOC III are block ciphers designed by Michael Wood for Cryptech Inc and are optimised for use in software. ... Red Pike is a classified United Kingdom government cipher, proposed for use by the National Health Service by GCHQ, but designed for a broad range of applications in the British government [1]. Little is publicly known about Red Pike, except that it is a block cipher with a 64-bit... Uplandia Regiment, or Upplands regemente, also S 1, is a Swedish Army signaling regiment that traces its origins back to the 19th Century. ... This article is about the encryption algorithm. ... SEED is a block cipher developed by the Korean Information Security Agency. ... Serpent is a symmetric key block cipher which was a finalist in the Advanced Encryption Standard contest, where it came second to Rijndael. ... SHACAL-1 and SHACAL-2 are block ciphers based on cryptographic hash function from the SHA family. ... Orders Hexanchiformes Squaliformes Pristiophoriformes Squatiniformes Heterodontiformes Orectolobiformes Carcharhiniformes Lamniformes Sharks are a group (superorder Selachimorpha) of fish, with a full cartilaginous skeleton, a streamlined body plan, with normally 5, but up to 7 (depending on species) gill slits along the side of, or beginning slightly behind, the head (in some... In cryptography, Skipjack is a block cipher â€” an algorithm for encryption â€” developed by the US National Security Agency (NSA). ... In cryptography, Square (sometimes written SQUARE) is a block cipher invented by Joan Daemen and Vincent Rijmen. ... Two rounds of the TEA block cipher In cryptography, the Tiny Encryption Algorithm (TEA) is a block cipher notable for its simplicity of description and implementation (typically a few lines of code). ... In cryptography, Triple DES (also 3DES) is a block cipher formed from the Data Encryption Standard (DES) cipher. ... In cryptography, Twofish is a symmetric key block cipher with a block size of 128 bits and key sizes up to 256 bits. ... General Designer(s) Roger Needham and David Wheeler First published 1997 Derived from Tiny Encryption Algorithm (TEA) Cipher(s) based on this design - Algorithm detail Block size(s) 64 bits Key size(s) 128 bits Structure Feistel network Number of rounds variable; recommended 64 Feistel rounds; 32 cycles Best cryptanalysis... In cryptography, a Feistel cipher is a block cipher with a particular structure, named after IBM cryptographer Horst Feistel; it is also commonly known as a Feistel network. ... The key-schedule of DES In cryptography, the algorithm for computing the subkeys for each round in a product cipher from the encryption (or decryption) key is called the key schedule. ... In cryptography, a product cipher is a popular type of block cipher that works by executing in sequence a number of simple transformations such as substitution, permutation, and modular arithmetic. ... In cryptography, a substitution box (or S-box) is a basic component of symmetric key algorithms. ... In cryptography, an SP-network, or substitution-permutation network (SPN), is a series of linked mathematical operations used in block cipher algorithms such as AES. These networks consist of S-boxes and P-boxes that transform blocks of input bits into output bits. ... The EFFs US$250,000 DES cracking machine contained over 18,000 custom chips and could brute force a DES key in a matter of days â€” the photograph shows a DES Cracker circuit board fitted with several Deep Crack chips In cryptanalysis, a brute force attack is a method... In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. ... Differential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. ... Cryptanalysis (from the Greek kryptÃ³s, hidden, and analÃ½ein, to loosen or to untie) is the study of methods for obtaining the meaning of encrypted information without access to the secret information which is normally required to do so. ... In cryptography, mod n cryptanalysis is an attack applicable to block and stream ciphers. ... In cryptography, a related-key attack is any form of cryptanalysis which presumes that the attacker has the capability to consider the operation of a cipher under several different keys. ... On January 2, 1997 the National Institute of Standards and Technology, or NIST, called for cryptographers to propose a new standard block cipher for United States Government use in non-classified but sensitive applications. ... CRYPTREC is the Cryptography Research and Evaluation Committee set up by the Japanese Government to evaluate and recommend cryptographic techniques for government and industrial use. ... NESSIE (New European Schemes for Signatures, Integrity and Encryption) was a European research project funded from 2000–2003 to identify secure cryptographic primitives. ... This article is about cryptography; for other meanings, see snowball effect. ... In modern cryptography, symmetric key ciphers are generally divided into stream ciphers and block ciphers. ... In cryptography, an initialization vector (IV) is a block of bits that is combined with the first block of data in any of several modes of a block cipher. ... In cryptography, the key size (alternatively key length) is a measure of the number of possible keys which can be used in a cipher. ... In cryptography, a block cipher operates on blocks of fixed length, often 64 or 128 bits. ... In cryptanalysis, the piling-up lemma is a principle used in linear cryptanalysis to construct linear approximations to the action of block ciphers. ... In cryptography, a weak key is a key which when used with a specific cipher, makes the cipher behave in some undesirable way. ...

Contents

Application to block ciphers

References

External links