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MDS Matrix
An MDS matrix (maximum distance separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography. Technically, an m \times n matrix A over a finite field K is an MDS matrix if it is the transformation matrix of a linear transformation f(x) = Ax from K^n to K^m such that no two different (m + n)-tuples of the form (x, f(x)) coincide in n or more components. Equivalently, the set of all (m + n)-tuples (x, f(x)) is an MDS code, i.e., a linear code that reaches the Singleton bound. Let \tilde A = \begin \mathrm_n \\ \hline \mathrm \end be the matrix obtained by joining the identity matrix \mathrm_n to A. Then a necessary and sufficient condition for a matrix A to be MDS is that every possible n \times n submatrix obtained by removing m rows from \tilde A is non-singular. This is also equivalent to the following: all the sub-determinants of the matrix A are non-zero. Then a binary matrix A (namely over the field with two elem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (: matrices) is a rectangle, rectangular array or table of numbers, symbol (formal), symbols, or expression (mathematics), expressions, with elements or entries arranged in rows and columns, which is used to represent a mathematical object or property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two-by-three matrix", a " matrix", or a matrix of dimension . Matrices are commonly used in linear algebra, where they represent linear maps. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotation (mathematics), rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimensions. Matrices are used in most areas of mathematics and scientific fields, either directly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Advanced Encryption Standard
The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001. AES is a variant of the Rijndael block cipher developed by two Belgium, Belgian cryptographers, Joan Daemen and Vincent Rijmen, who submitted a proposal to NIST during the Advanced Encryption Standard process, AES selection process. Rijndael is a family of ciphers with different key size, key and Block size (cryptography), block sizes. For AES, NIST selected three members of the Rijndael family, each with a block size of 128 bits, but three different key lengths: 128, 192 and 256 bits. AES has been adopted by the Federal government of the United States, U.S. government. It supersedes the Data Encryption Standard (DES), which was published in 1977. The algorithm described by AES is a symmetric-key algorithm, meaning the same key is used for both encrypting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptographic Hash Function
A cryptographic hash function (CHF) is a hash algorithm (a map (mathematics), map of an arbitrary binary string to a binary string with a fixed size of n bits) that has special properties desirable for a cryptography, cryptographic application: * the probability of a particular n-bit output result (hash value) for a random input string ("message") is 2^ (as for any good hash), so the hash value can be used as a representative of the message; * finding an input string that matches a given hash value (a ''pre-image'') is infeasible, ''assuming all input strings are equally likely.'' The ''resistance'' to such search is quantified as security strength: a cryptographic hash with n bits of hash value is expected to have a ''preimage resistance'' strength of n bits, unless the space of possible input values is significantly smaller than 2^ (a practical example can be found in ); * a ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MUGI
In cryptography, MUGI is a pseudorandom number generator (PRNG) designed for use as a stream cipher. It was among the cryptographic techniques recommended for Japanese government use by CRYPTREC in 2003, however, has been dropped to "candidate" by CRYPTREC revision in 2013. MUGI takes a 128-bit secret key and a 128-bit initial vector (IV). After a key- and IV- setup process, MUGI outputs 64-bit output strings based on the internal state, while updating the internal state after each output block. MUGI has a 1216-bit internal state; there are three 64-bit registers (the "state") and 16 64-bit registers (the "buffer"). MUGI uses the non-linear S-box that was originally defined in Advanced Encryption Standard (AES). A part of the linear transformation also reuses the MDS matrix of AES. The basic design is influenced by that of Panama. Security As of September 2006, there are no known attacks against MUGI that are faster than serial brute-force of the key space or of the interna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stream Cipher
stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream ( keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream, to give a digit of the ciphertext stream. Since encryption of each digit is dependent on the current state of the cipher, it is also known as ''state cipher''. In practice, a digit is typically a bit and the combining operation is an exclusive-or (XOR). The pseudorandom keystream is typically generated serially from a random seed value using digital shift registers. The seed value serves as the cryptographic key for decrypting the ciphertext stream. Stream ciphers represent a different approach to symmetric encryption from block ciphers. Block ciphers operate on large blocks of digits with a fixed, unvarying transformation. This distinction is not always clear-cut: in some modes of operation, a block cipher primitive is used in such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Camellia (cipher)
In cryptography, Camellia is a symmetric key block cipher with a block size of 128 bits and key sizes of 128, 192 and 256 bits. It was jointly developed by Mitsubishi Electric and NTT of Japan. The cipher has been approved for use by the ISO/IEC, the European Union's NESSIE project and the Japanese CRYPTREC project. The cipher has security levels and processing abilities comparable to the Advanced Encryption Standard. The cipher was designed to be suitable for both software and hardware implementations, from low-cost smart cards to high-speed network systems. It is part of the Transport Layer Security (TLS) cryptographic protocol designed to provide communications security over a computer network such as the Internet. The cipher was named for the flower '' Camellia japonica'', which is known for being long-lived as well as because the cipher was developed in Japan. Design Camellia is a Feistel cipher with either 18 rounds (when using 128-bit keys) or 24 rounds (when usin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalyna (cipher)
Kalyna ( Ukrainian: Калина, Viburnum opulus) is a symmetric block cipher. It supports block sizes of 128, 256 or 512 bits; the key length is either equal to or double the block size. Kalyna was adopted as the national encryption standard of Ukraine in 2015 (standard DSTU 7624:2014) after holding Ukrainian national cryptographic competition. Kalyna is a substitution–permutation network and its design is based on the Rijndael The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001. AES is a variant ... (AES) encryption function having quite different key schedule, another set of four different S-boxes and increased MDS matrix size. Kalyna has 10 rounds for 128-bit keys, 14 rounds for 256-bit keys and 18 rounds for 512-bit keys. Independent researchers proposed some attacks on reduced-round variant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hierocrypt
In cryptography, Hierocrypt-L1 and Hierocrypt-3 are block ciphers created by Toshiba in 2000. They were submitted to the NESSIE project, but were not selected. Both algorithms were among the cryptographic techniques recommended for Japanese government use by CRYPTREC in 2003, however, both have been dropped to "candidate" by CRYPTREC revision in 2013. The Hierocrypt ciphers are very similar, differing mainly in block size: 64 bits for Hierocrypt-L1, 128 bits for Hierocrypt-3. Hierocrypt-L1's key size is 128 bits, while Hierocrypt-3 can use keys of 128, 192, or 256 bits. The number of rounds of encryption also varies: Hierocrypt-L1 uses 6.5 rounds, and Hierocrypt-3 uses 6.5, 7.5, or 8.5, depending on the key size. The Hierocrypt ciphers use a nested substitution–permutation network (SPN) structure. Each round consists of parallel applications of a transformation called the ''XS-box'', followed by a linear diffusion operation. The final half-round replaces the diffusion with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manta (cipher)
Manta or mantas may refer to: * Manta ray, large fish belonging to the genus ''Mobula'' Arts and entertainment App & Website * Manta (platform), a Korean digital comics provider Fictional entities * Manta (comics), a character in American Marvel Comics publications * Manta (''Uridium''), a spaceship in the British computer game ''Uridium'' * Manta Oyamada, a character in the Japanese manga series ''Shaman King'' * Manta and Moray, amphibious superheroes from the 1970s TV series ''Tarzan and the Super 7'' Film * ''Manta, Manta'', a 1991 German-language action comedy film People * Manta (surname) (includes a list of people with that name) * Mantas, Lithuanian given name (includes a list of people with that name) * Manta people, nomadic ethnic group in Bangladesh Places * Manta, Benin a town and ''arrondissement'' in Atakora department, Benin * Manta, Cundinamarca, a municipality and town Almeidas province, Colombia * Manta, Ecuador, a city in Manabí Province, Ecuador **Manta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
KHAZAD
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). KHAZAD is named after Khazad-dûm, the fictional dwarven realm in the writings of J. R. R. Tolkien (see also Khazad). KHAZAD was presented at the first NESSIE workshop in 2000, and, after some small changes, was selected as a finalist in the project. KHAZAD has an eight-round substitution–permutation network structure similar to that of SHARK, a forerunner to Rijndael. The design is classed as a "''legacy-level''" algorithm, with a 64-bit block size (in common with older ciphers such as DES and IDEA) and a 128-bit key. KHAZAD makes heavy use of involutions as subcomponents; this minimises the difference between the algorithms for encryption and decryption. The authors have stated that, ''"KHAZAD is not (and will never be) patent A patent is a type of intellectual property that gives its owner t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anubis (cipher)
Anubis is a block cipher designed by Vincent Rijmen and Paulo S. L. M. Barreto as an entrant in the NESSIE project, a former research program initiated by the European Commission in 2000 for the identification of new cryptographic algorithms. Although the cipher has not been included in the final NESSIE portfolio, its design is considered very strong, and no attacks have been found by 2004 after the project had been concluded. The cipher is not patented and has been released by the designers for free public use. Anubis operates on data blocks of 128 bits, accepting keys of length 32''N'' bits (''N'' = 4, ..., 10). It is designed as a substitution–permutation network, which bears large similarity to Rijndael. Like KHAZAD, designed by the same authors and also submitted to NESSIE, it uses involutions for the various operations. An involution is an operation whose inverse is the same as the forward operation. In other words, when an involution is run twice, it is the same as p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
