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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 .
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.
In cryptography, the Niederreiter cryptosystem is a variation of the McEliece cryptosystem developed in 1986 by Harald Niederreiter. [1] It applies the same idea to the parity check matrix, H, of a linear code. Niederreiter is equivalent to McEliece from a security point of view.
The running time of this algorithm is O(log exponent). When working with large values of exponent, this offers a substantial speed benefit over the previous two algorithms, whose time is O(exponent). For example, if the exponent was 2 20 = 1048576, this algorithm would have 20 steps instead of 1048576 steps.
Hill's cipher machine, from figure 4 of the patent. In classical cryptography, the Hill cipher is a polygraphic substitution cipher based on linear algebra.Invented by Lester S. Hill in 1929, it was the first polygraphic cipher in which it was practical (though barely) to operate on more than three symbols at once.
One of the earliest applications of a non-commutative algebraic structure for cryptographic purposes was the use of braid groups to develop cryptographic protocols. Later several other non-commutative structures like Thompson groups , polycyclic groups , Grigorchuk groups , and matrix groups have been identified as potential candidates for ...
Modern Cryptography Theory and Practice ISBN 0-13-066943-1. An up-to-date book on cryptography. Touches on provable security, and written with students and practitioners in mind. Mel, H.X., and Baker, Doris (2001). Cryptography Decrypted, Addison Wesley ISBN 0-201-61647-5. This technical overview of basic cryptographic components (including ...
Goldwasser–Micali consists of three algorithms: a probabilistic key generation algorithm which produces a public and a private key, a probabilistic encryption algorithm, and a deterministic decryption algorithm. The scheme relies on deciding whether a given value x is a square mod N, given the factorization (p, q) of N. This can be ...