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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.
In overview, the XSL attack relies on first analyzing the internals of a cipher and deriving a set of quadratic simultaneous equations. These systems of equations are typically very large, for example 8,000 equations with 1,600 variables for the 128-bit AES. Several methods for solving such systems are known.
In cryptography, unicity distance is the length of an original ciphertext needed to break the cipher by reducing the number of possible spurious keys to zero in a brute force attack. That is, after trying every possible key , there should be just one decipherment that makes sense, i.e. expected amount of ciphertext needed to determine the key ...
So I had a set of six equations in three unknowns, S, N, and Q. While I puzzled over how to solve that set of equations, on December 9, 1932, completely unexpectedly and at the most opportune moment, a photocopy of two tables of daily keys for September and October 1932 was delivered to me. [26] Having the daily keys meant that S was now known ...
Conversely, the Hill equation proper reflects the cellular or tissue response to the ligand: the physiological output of the system, such as muscle contraction. The Hill equation was originally formulated by Archibald Hill in 1910 to describe the sigmoidal O 2 binding curve of haemoglobin .
In cryptography, differential equations of addition (DEA) are one of the most basic equations related to differential cryptanalysis that mix additions over two different groups (e.g. addition modulo 2 32 and addition over GF(2)) and where input and output differences are expressed as XORs.
Indeed, multiplying each equation of the second auxiliary system by , adding with the corresponding equation of the first auxiliary system and using the representation = +, we immediately see that equations number 2 through n of the original system are satisfied; it only remains to satisfy equation number 1.
Mathematician-cryptologist Marian Rejewski had already set up a system of equations describing the operation of the then new German Army Enigma rotor-wirings. The key -settings lists provided by Schmidt helped fill in enough of the unknowns in Rejewski's formulae , allowing him to speedily solve the equations and recover the wirings.