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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 ...
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.
In practice, frequency analysis relies as much on linguistic knowledge as it does on statistics, but as ciphers became more complex, mathematics became more important in cryptanalysis. This change was particularly evident before and during World War II , where efforts to crack Axis ciphers required new levels of mathematical sophistication.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Iraqi Block Cipher (IBC) KASUMI – 64-bit block; based on MISTY1, adopted for next generation W-CDMA cellular phone security; KHAZAD – 64-bit block designed by Barretto and Rijmen; Khufu and Khafre – 64-bit block ciphers; Kuznyechik – Russian 128-bit block cipher, defined in GOST R 34.12-2015 and RFC 7801.
Consider a block cipher with a unicity distance of three ciphertext blocks. Although there is clearly enough information for a computationally unbounded adversary to find the right key (simple exhaustive search), this may be computationally infeasible in practice. The unicity distance can be increased by reducing the plaintext redundancy.
Classical ciphers are typically vulnerable to known-plaintext attack. For example, a Caesar cipher can be solved using a single letter of corresponding plaintext and ciphertext to decrypt entirely. A general monoalphabetic substitution cipher needs several character pairs and some guessing if there are fewer than 26 distinct pairs.
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 :.