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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.
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 .
The following outline is provided as an overview of and topical guide to cryptography: Cryptography (or cryptology) – practice and study of hiding information. Modern cryptography intersects the disciplines of mathematics, computer science, and engineering. Applications of cryptography include ATM cards, computer passwords, and electronic ...
Hash the document, d, to be signed (with a public hash algorithm). Decrypt this hash value as if it were an instance of ciphertext. Append the decrypted message to the document as a signature. Verification then applies the public encryption function to the signature and checks whether or not this equals the hash value of the document.
The four-square algorithm allows for two separate keys, one for each of the two ciphertext matrices. As an example, here are the four-square matrices for the keywords "example" and "keyword." The plaintext matrices are in lowercase and the ciphertext matrices are in caps to make this example visually more simple:
For practical purposes, parity-check matrix of a binary Goppa code is usually converted to a more computer-friendly binary form by a trace construction, that converts the -by-matrix over () to a -by-binary matrix by writing polynomial coefficients of () elements on successive rows.
The Cayley–Purser algorithm was a public-key cryptography algorithm published in early 1999 by 16-year-old Irishwoman Sarah Flannery, based on an unpublished work by Michael Purser, founder of Baltimore Technologies, a Dublin data security company. Flannery named it for mathematician Arthur Cayley. It has since been found to be flawed as a ...
The Commercial National Security Algorithm Suite (CNSA) is a set of cryptographic algorithms promulgated by the National Security Agency as a replacement for NSA Suite B Cryptography algorithms. It serves as the cryptographic base to protect US National Security Systems information up to the top secret level, while the NSA plans for a ...