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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.

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.

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.

The attack is notable for requiring only a handful of known plaintexts to perform; previous methods of cryptanalysis, such as linearIn cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of two widely applicab and differential cryptanalysisDifferential cryptanalysis is a general form of cryptanalysis applicable primarily to block ciphers, but also to stream ciphers and cryptographic hash functions. In the broadest sense, it is the study of how differences in an input can affect the resultan, often require unrealistically large numbers of known or chosen plaintexts.

1 Solving multivariate quadratic equations

Solving multivariate quadratic equations (MQ) is an NP-hardIn 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''. problem (in the general case) with several applications in cryptography. The XSL attack requires an efficient algorithm for tackling MQ. In 1999For the album by Prince, see 1999 (album 1999 is a common year starting on Friday (see link for calendar), and was designated the International Year of Older Persons by the UN. Events Kosovo War Former child star Gary Coleman files for bankruptcy Y2K prep, Kipnis and ShamirAdi Shamir (born 1952) is an Israeli cryptographer. He was one of the inventors of the RSA algorithm (along with Ron Rivest and Len Adleman), and has made numerous contributions to the fields of cryptography and computer science. Education Born in Tel-Avi 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.

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.