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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.
The MixColumns operation performed by the Rijndael cipher or Advanced Encryption Standard is, along with the ShiftRows step, its primary source of diffusion. Each column of bytes is treated as a four-term polynomial b ( x ) = b 3 x 3 + b 2 x 2 + b 1 x + b 0 {\displaystyle b(x)=b_{3}x^{3}+b_{2}x^{2}+b_{1}x+b_{0}} , each byte representing an ...
Polygraphic substitution is a cipher in which a uniform substitution is performed on blocks of letters. When the length of the block is specifically known, more precise terms are used: for instance, a cipher in which pairs of letters are substituted is bigraphic.
A sketch of a substitution–permutation network with 3 rounds, encrypting a plaintext block of 16 bits into a ciphertext block of 16 bits. The S-boxes are the S i, the P-boxes are the same P, and the round keys are the K i.
jblas is a linear algebra library, created by Mikio Braun, for the Java programming language built upon BLAS and LAPACK. Unlike most other Java linear algebra libraries, jblas is designed to be used with native code through the Java Native Interface and comes with precompiled binaries. When used on one of the targeted architectures, it will ...
A well-known example of a substitution cipher is the Caesar cipher. To encrypt a message with the Caesar cipher, each letter of message is replaced by the letter three positions later in the alphabet. Hence, A is replaced by D, B by E, C by F, etc. Finally, X, Y and Z are replaced by A, B and C respectively.
Matrix Toolkit Java (MTJ) is an open-source Java software library for performing numerical linear algebra. The library contains a full set of standard linear algebra operations for dense matrices based on BLAS and LAPACK code. Partial set of sparse operations is provided through the Templates project.
Lester S. Hill (1891–1961) was an American mathematician and educator who was interested in applications of mathematics to communications.He received a bachelor's degree (1911) and a master's degree (1913) from Columbia College and a Ph.D. from Yale University (1926).