|
In cryptography, the ''eXtended Sparse Linearization'' (XSL) attack is a method of cryptanalysis for block ciphers. The attack was first published in 2002 by researchers Nicolas Courtois and Josef Pieprzyk. It has caused some controversy as it was 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 could have wide implications. The method has a high work-factor, which unless lessened, means the technique does not reduce the effort to break AES in comparison to an exhaustive search. Therefore, it does not 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 analyzing the internals of a cipher and deriving a system of quadratic simultaneous equations. These systems of equations are typically very large, for example 8,000 equations with 1,600 variables for the 128-bit AES. Several methods for solving such systems are known. In the XSL attack, a specialized algorithm, termed ''eXtended Sparse Linearization'', 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 linear and differential cryptanalysis, often require unrealistically large numbers of known or chosen plaintexts. ==Solving multivariate quadratic equations== Solving multivariate quadratic equations (MQ) over a finite set of numbers 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 an overdetermined system of quadratic equations (more equations than unknowns). One technique for solving such systems is linearization, 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, linearization 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 ''re-linearization'', a technique where extra non-linear equations are added after linearization, and the resultant system is solved by a second application of linearization. Re-linearization 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 Linearization''), 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. Research into the efficiency of XL and its derivative algorithms remains ongoing (Yang and Chen, 2004). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「XSL attack」の詳細全文を読む スポンサード リンク
|