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XSL Attack
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chosen Plaintext
Chosen or The Chosen may refer to: Books *The Chosen (Potok novel), ''The Chosen'' (Potok novel), a 1967 novel by Chaim Potok * ''The Chosen'', a 1997 novel by L. J. Smith (author), L. J. Smith *The Chosen (Pinto novel), ''The Chosen'' (Pinto novel), a 1999 novel by Ricardo Pinto *The Chosen (Karabel book), ''The Chosen'' (Karabel book), a book by Jerome Karabel *Chosen (Dekker novel), ''Chosen'' (Dekker novel), a 2007 novel by Ted Dekker *Chosen (Cast novel), ''Chosen'' (Cast novel), a novel in the ''House of Night'' fantasy series *Chosen (Image Comics), ''Chosen'' (Image Comics), a comic book series by Mark Millar Film and television *''Holocaust 2000'', also released as ''The Chosen'', a 1977 horror film starring Kirk Douglas *The Chosen (1981 film), ''The Chosen'' (1981 film), a film based on Potok's novel *The Chosen (2015 film), ''The Chosen'' (2015 film), a film starring YouTube personality Kian Lawley *The Chosen (2016 film), ''The Chosen'' (2016 film), by Antonio Chavarr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plaintext
In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. Overview With the advent of computing, the term ''plaintext'' expanded beyond human-readable documents to mean any data, including binary files, in a form that can be viewed or used without requiring a key or other decryption device. Information—a message, document, file, etc.—if to be communicated or stored in an unencrypted form is referred to as plaintext. Plaintext is used as input to an encryption algorithm; the output is usually termed ciphertext, particularly when the algorithm is a cipher. Codetext is less often used, and almost always only when the algorithm involved is actually a code. Some systems use multiple layers of encryption, with the output of one encryption algorithm becoming "plaintext" input for the next. Secure handling Insecure handling of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Serpent (cipher)
Serpent is a symmetric key block cipher that was a finalist in the Advanced Encryption Standard process, Advanced Encryption Standard (AES) contest, in which it ranked second to Rijndael. Serpent was designed by Ross J. Anderson, Ross Anderson, Eli Biham, and Lars Knudsen. Like other Advanced Encryption Standard, AES submissions, Serpent has a block size (cryptography), block size of 128 bits and supports a key size of 128, 192, or 256 bits. The cipher is a 32-round substitution–permutation network operating on a block of four 32-bit Word (computer architecture), words. Each round applies one of eight 4-bit to 4-bit S-boxes 32 times in parallel. Serpent was designed so that all operations can be executed in parallel computing, parallel, using 32 bit slices. This maximizes parallelism but also allows use of the extensive cryptanalysis work performed on Data Encryption Standard, DES. Serpent took a conservative approach to security, opting for a large security margin: the design ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Degree Of A Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: # A monomial, also called a power product or primitive monomial, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. For example, x^2yz^3=xxyzzz is a monomial. The constant 1 is a primitive monomial, being equal to the empty product and to x^0 for any variable x. If only a single variable x is considered, this means that a monomial is either 1 or a power x^n of x, with n a positive integer. If several variables are considered, say, x, y, z, then each can be given an exponent, so that any monomial is of the form x^a y^b z^c with a,b,c non-negative integers (taking note that any exponent 0 makes the corresponding factor equal to 1). # A monomial in the first sense multiplied by a nonzero constant, called the coefficient of the monomial. A primitive monomial is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monomial
In mathematics, a monomial is, roughly speaking, a polynomial which has only one term. Two definitions of a monomial may be encountered: # A monomial, also called a power product or primitive monomial, is a product of powers of variables with nonnegative integer exponents, or, in other words, a product of variables, possibly with repetitions. For example, x^2yz^3=xxyzzz is a monomial. The constant 1 is a primitive monomial, being equal to the empty product and to x^0 for any variable x. If only a single variable x is considered, this means that a monomial is either 1 or a power x^n of x, with n a positive integer. If several variables are considered, say, x, y, z, then each can be given an exponent, so that any monomial is of the form x^a y^b z^c with a,b,c non-negative integers (taking note that any exponent 0 makes the corresponding factor equal to 1). # A monomial in the first sense multiplied by a nonzero constant, called the coefficient of the monomial. A primitive monomial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linearly Independent
In the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. If such a linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space. Definition A sequence of vectors \mathbf_1, \mathbf_2, \dots, \mathbf_k from a vector space is said to be ''linearly dependent'', if there exist scalars a_1, a_2, \dots, a_k, not all zero, such that :a_1\mathbf_1 + a_2\mathbf_2 + \cdots + a_k\mathbf_k = \mathbf, where \mathbf denotes the zero vector. This implies that at least one of the scalars is nonzero, say a_1\ne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Elimination
In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of row-wise operations performed on the corresponding matrix of coefficients. This method can also be used to compute the rank of a matrix, the determinant of a square matrix, and the inverse of an invertible matrix. The method is named after Carl Friedrich Gauss (1777–1855). To perform row reduction on a matrix, one uses a sequence of elementary row operations to modify the matrix until the lower left-hand corner of the matrix is filled with zeros, as much as possible. There are three types of elementary row operations: * Swapping two rows, * Multiplying a row by a nonzero number, * Adding a multiple of one row to another row. Using these operations, a matrix can always be transformed into an upper triangular matrix (possibly bordered by rows or columns of zeros), and in fact one that is in row echelon form. Once all of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linearization (algebra)
In mathematics, linearization (British English: linearisation) is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear differential equations or discrete dynamical systems. This method is used in fields such as engineering, physics, economics, and ecology. Linearization of a function Linearizations of a function are lines—usually lines that can be used for purposes of calculation. Linearization is an effective method for approximating the output of a function y = f(x) at any x = a based on the value and slope of the function at x = b, given that f(x) is differentiable on , b/math> (or , a/math>) and that a is close to b. In short, linearization approximates the output of a function near x = a. For example, \sqrt = 2. Ho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overdetermined System
In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns. An overdetermined system is almost always inconsistent equations, inconsistent (it has no solution) when constructed with random coefficients. However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others. The terminology can be described in terms of the concept of constraint counting. Each Variable (mathematics), unknown can be seen as an available degree of freedom. Each equation introduced into the system can be viewed as a constraint (mathematics), constraint that restricts one degree of freedom. Therefore, the critical case occurs when the number of equations and the number of free variables are equal. For every variable giving a degree of freedom, there exists a corresponding constraint. The ''overdetermined'' case occurs when the syste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hidden Field Equations
Hidden Fields Equations (HFE), also known as HFE trapdoor function, is a public key cryptosystem which was introduced at Eurocrypt in 1996 and proposed by Jacques Patarin following the idea of the Matsumoto and Imai system. It is based on polynomials over finite fields \mathbb_q of different size to disguise the relationship between the private key and public key. HFE is in fact a family which consists of basic HFE and combinatorial versions of HFE. The HFE family of cryptosystems is based on the hardness of the problem of finding solutions to a system of multivariate quadratic equations (the so-called MQ problem) since it uses private affine transformations to hide the extension field and the private polynomials. Hidden Field Equations also have been used to construct digital signature schemes, e.g. Quartz and Sflash. Mathematical background One of the central notions to understand how Hidden Field Equations work is to see that for two extension fields \mathbb_ \mathbb_ o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public Key Algorithm
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. There are many kinds of public-key cryptosystems, with different security goals, including digital signature, Diffie–Hellman key exchange, public-key key encapsulation, and public-key encryption. Public key algorithms are fundamental security primitives in modern cryptosystems, including applications and protocols that offer assurance of the confidentiality and authenticity of electronic communications and data storage. They underpin numerous Internet standards, such as Transport Layer Security (TLS), SSH, S/MIME, and PGP ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
