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The affine cipher is a type of monoalphabetic substitution cipher, where each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and converted back to a letter. The formula used means that each letter encrypts to one other letter, and back again, meaning the cipher is essentially a ...
The Rijndael S-box was specifically designed to be resistant to linear and differential cryptanalysis. This was done by minimizing the correlation between linear transformations of input/output bits, and at the same time minimizing the difference propagation probability.
Suppose we have a non-linear function where the key is XOR'ed before evaluation and the values that allow the differential are {2,3} and {4,5}. If the attacker sends in the values of {6, 7} and observes the correct output difference it means the key is either 6 ⊕ K = 2, or 6 ⊕ K = 4, meaning the key K is either 2 or 4.
Mathematically, an S-box is a nonlinear [1] vectorial Boolean function. [2] In general, an S-box takes some number of input bits, m, and transforms them into some number of output bits, n, where n is not necessarily equal to m. [3] An m×n S-box can be implemented as a lookup table with 2 m words of n bits each.
In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryptanalysis.
Multivariate Quadratics involves a public and a private key. The private key consists of two affine transformations, S and T, and an easy to invert quadratic map ′:.We denote the matrix of the affine endomorphisms: by and the shift vector by and similarly for :.
Homomorphic encryption is a form of encryption that allows computations to be performed on encrypted data without first having to decrypt it. The resulting computations are left in an encrypted form which, when decrypted, result in an output that is identical to that of the operations performed on the unencrypted data.
Under the standard affine convention, an alphabet of m letters is mapped to the numbers 0, 1, ... , m − 1. (The Hebrew alphabet has m = 22, and the standard Latin alphabet has m = 26). The Atbash cipher may then be enciphered and deciphered using the encryption function for an affine cipher by setting a = b = ( m − 1):