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An MDS matrix (maximum distance separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography.Technically, an matrix over a finite field is an MDS matrix if it is the transformation matrix of a linear transformation = from to such that no two different (+)-tuples of the form (, ()) coincide in or more components.
Comparison of implementations of message authentication code (MAC) algorithms. A MAC is a short piece of information used to authenticate a message—in other words, to confirm that the message came from the stated sender (its authenticity) and has not been changed in transit (its integrity).
Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space : two matrices are congruent if and only if they represent the same bilinear form with respect to different bases .
Crypto++ (also known as CryptoPP, libcrypto++, and libcryptopp) is a free and open-source C++ class library of cryptographic algorithms and schemes written by Wei Dai.Crypto++ has been widely used in academia, student projects, open-source, and non-commercial projects, as well as businesses. [1]
For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8. Modular exponentiation can be performed with a negative exponent e by finding the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = b e mod m = d −e mod m, where e < 0 and b ⋅ d ≡ 1 (mod m).
It is a form of partitioning cryptanalysis that exploits unevenness in how the cipher operates over equivalence classes (congruence classes) modulo n. The method was first suggested in 1999 by John Kelsey , Bruce Schneier , and David Wagner and applied to RC5P (a variant of RC5 ) and M6 (a family of block ciphers used in the FireWire standard).
The algorithm attempts to set up a congruence of squares modulo n (the integer to be factorized), which often leads to a factorization of n.The algorithm works in two phases: the data collection phase, where it collects information that may lead to a congruence of squares; and the data processing phase, where it puts all the data it has collected into a matrix and solves it to obtain a ...
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 (Rijndael), 3-Way, Kalyna, Kuznyechik, PRESENT, SAFER, SHARK, and Square.